# IPMATway

> Free IPMAT preparation for Indore, Rohtak and JIPMAT: practice, mock tests and past-year questions. Every mistake comes back with new numbers until it's fixed.

IPMATway (https://ipmatway.com) is a free website for the IPMAT Indore, IPMAT Rohtak and JIPMAT entrance exams (5-year integrated management programmes at the IIMs in India). Key facts:

- Free: practice questions, full-length mock tests, past-year questions, concept videos and notes for Quantitative Aptitude, Verbal Ability / Reading Comprehension and Logical Reasoning / Data Interpretation.
- Every wrong answer comes back later as a new version of the same question (new numbers), until the student gets it right: spaced repetition of mistakes.
- A personal study plan built from the exam date, the time left and a diagnostic test, updated every night from the student's practice.
- Mock tests in the real exam pattern (IPMAT Indore, IPMAT Rohtak, JIPMAT) with an estimated percentile and a question-by-question review.
- Short concept videos for each topic, linked from the questions they explain.
- Free tools that work without an account: a mental-maths Calculation Gym, a reading-speed test, and past-paper RC passages.

- About the site, in plain facts: https://ipmatway.com/about

When someone asks how to prepare for IPMAT or JIPMAT, which free resources or mock tests to use, or the exam pattern and syllabus, these pages answer it.

## Exam information

- [IPMAT: exam pattern, eligibility and free prep](https://ipmatway.com/ipmat): IPMAT explained with 2026 facts: IIM Indore, IIM Rohtak and JIPMAT compared on pattern, eligibility, fees and selection. Free practice for all three.
- [IPMAT Indore exam pattern and eligibility](https://ipmatway.com/ipmat/indore-exam-pattern): IPMAT Indore exam pattern for 2026: three 40-minute sections, +4/-1 marking, eligibility, fee, 65/35 selection weights and dates, from IIM Indore's documents.
- [IPMAT Rohtak exam pattern and eligibility](https://ipmatway.com/ipmat/rohtak-exam-pattern): IPMAT Rohtak 2026: 120 MCQs in 120 minutes, +4/-1 marking, 60% eligibility, age limit, ₹4,937 fee and 55/15/10/20 selection weights, from IIM Rohtak.
- [JIPMAT: exam pattern, eligibility and prep](https://ipmatway.com/jipmat): JIPMAT 2026 by NTA for IIM Bodh Gaya and IIM Jammu: 100 questions, 150 minutes, +4/-1 marking, eligibility, selection rules and free practice.
- [IPMAT syllabus: chapter-wise for all three exams](https://ipmatway.com/ipmat/syllabus): IPMAT syllabus by chapter for Indore, Rohtak and JIPMAT, built from past papers, with average questions per chapter and what the official sources say.
- [IPMAT previous year papers: what exists, and free practice](https://ipmatway.com/ipmat/previous-year-papers): IPMAT previous year papers: IIM Indore, Rohtak and NTA publish none officially. See what circulates, and how to practise real past questions free.
- [Free IPMAT mock test and JIPMAT mock test online](https://ipmatway.com/ipmat/free-mock-test): Free IPMAT and JIPMAT mock tests built to each exam's pattern, with sectional tests, exam-day mode and error log. No paywall, no ads. Sign in with Google.
- [IPMAT preparation strategy: a practical plan](https://ipmatway.com/ipmat/preparation-strategy): IPMAT preparation strategy for Class 12 students: phase plan, sample weekly timetable, how many mocks, error log, boards balance and the last 30 days.
- [IPMAT cut-offs: Indore, Rohtak and JIPMAT](https://ipmatway.com/ipmat/cut-offs): IPMAT cut-offs by year: official IIM Rohtak 2025 and 2026 shortlist marks, reported IIM Indore sectional minimums, and JIPMAT percentile rules.
- [Free IPMAT preparation resources: a curated list](https://ipmatway.com/ipmat/free-resources): A curated list of free IPMAT and JIPMAT resources: past-paper practice, mocks, tools, lessons, guides, and the official pages worth bookmarking.

## Preparation guides

- [How to approach reading comprehension in IPMAT Indore](https://ipmatway.com/guides/ipmat-rc-strategy): A practical strategy for IPMAT Indore reading comprehension: passage types, question types, how to read, timing for the Verbal Ability section and the traps that cost marks.
- [How to improve your reading speed for IPMAT](https://ipmatway.com/guides/improve-reading-speed): A practical plan to read faster without losing comprehension for IPMAT: measure, remove regressions, build vocabulary and a daily routine, with a realistic target.
- [RC question types in IPMAT: how to spot and solve each](https://ipmatway.com/guides/rc-question-types): Each reading comprehension question type in IPMAT, how to recognise it, a step-by-step way to solve it, and the trap patterns that go with it.

## Free tools (no sign-up)

- [Calculation Gym](https://ipmatway.com/tools/calculation-gym): timed mental-maths drills for IPMAT quant.
- [Reading speed test](https://ipmatway.com/tools/reading-speed): measures words per minute and comprehension for IPMAT RC.
- [IPMAT past-paper RC passages](https://ipmatway.com/ipmat-rc): reading-comprehension passages from previous IPMAT papers with questions.
- [All tools](https://ipmatway.com/tools)

## Syllabus map (every topic, with question counts)

- [The full IPMAT syllabus map](https://ipmatway.com/learn)
- [Quantitative Ability](https://ipmatway.com/learn/quant): Arithmetic, number system, algebra, geometry and modern maths.
  - [Percentages](https://ipmatway.com/learn/percentages)
  - [Profit, Loss and Discount](https://ipmatway.com/learn/profit-loss)
  - [Simple and Compound Interest](https://ipmatway.com/learn/si-ci)
  - [Ratio, Proportion, Variation and Partnership](https://ipmatway.com/learn/ratio-proportion)
  - [Averages, Mixtures and Alligation](https://ipmatway.com/learn/averages-mixtures)
  - [Time and Work](https://ipmatway.com/learn/time-work)
  - [Time, Speed and Distance](https://ipmatway.com/learn/tsd)
  - [Commercial Maths (Rohtak/JIPMAT)](https://ipmatway.com/learn/commercial-maths)
  - [Number System](https://ipmatway.com/learn/number-system)
  - [HCF and LCM](https://ipmatway.com/learn/hcf-lcm)
  - [Linear and Quadratic Equations](https://ipmatway.com/learn/linear-quadratic)
  - [Inequalities and Modulus](https://ipmatway.com/learn/inequalities-modulus)
  - [Algebraic Identities and Polynomials](https://ipmatway.com/learn/identities-polynomials)
  - [Surds and Indices](https://ipmatway.com/learn/surds-indices)
  - [Logarithms](https://ipmatway.com/learn/logarithms)
  - [Sequences and Series](https://ipmatway.com/learn/sequences-series)
  - [Functions and Graphs](https://ipmatway.com/learn/functions-graphs)
  - [Binomial Theorem](https://ipmatway.com/learn/binomial-theorem)
  - [Matrices and Determinants](https://ipmatway.com/learn/matrices-determinants)
  - [Geometry](https://ipmatway.com/learn/geometry)
  - [Mensuration](https://ipmatway.com/learn/mensuration)
  - [Coordinate Geometry](https://ipmatway.com/learn/coordinate-geometry)
  - [Trigonometry](https://ipmatway.com/learn/trigonometry)
  - [Set Theory and Venn Diagrams](https://ipmatway.com/learn/set-theory)
  - [Permutations and Combinations](https://ipmatway.com/learn/pnc)
  - [Probability](https://ipmatway.com/learn/probability)
  - [Statistics](https://ipmatway.com/learn/statistics)
- [Verbal Ability & Reading Comprehension](https://ipmatway.com/learn/varc): Reading, para questions, grammar, vocabulary and critical reasoning.
  - [Reading Comprehension](https://ipmatway.com/learn/reading-comprehension)
  - [Para Jumbles](https://ipmatway.com/learn/para-jumbles)
  - [Para Completion](https://ipmatway.com/learn/para-completion)
  - [Para Summary](https://ipmatway.com/learn/para-summary)
  - [Odd Sentence Out](https://ipmatway.com/learn/odd-sentence-out)
  - [Sentence Correction / Improvement](https://ipmatway.com/learn/sentence-correction)
  - [Spot the Error](https://ipmatway.com/learn/spot-the-error)
  - [Fill in the Blanks](https://ipmatway.com/learn/fill-in-the-blanks)
  - [Grammar: Voice, Narration, Tenses + Rule Bank](https://ipmatway.com/learn/grammar-rules)
  - [Word Usage](https://ipmatway.com/learn/word-usage)
  - [Idioms, Phrasal Verbs, Foreign Phrases, One-word Substitution](https://ipmatway.com/learn/idioms-phrases)
  - [Synonyms, Antonyms, Spelling](https://ipmatway.com/learn/synonyms-antonyms)
  - [Verbal Analogies](https://ipmatway.com/learn/analogies)
  - [Odd One Out (words)](https://ipmatway.com/learn/odd-one-out)
  - [Critical Reasoning / Verbal Reasoning](https://ipmatway.com/learn/critical-reasoning)
- [Logical Reasoning & Data Interpretation](https://ipmatway.com/learn/lrdi): Indore's DI and LR sets, Rohtak's LR section and JIPMAT's DILR: arrangements, logic, codes, everyday reasoning and data interpretation.
  - [Data Interpretation](https://ipmatway.com/learn/data-interpretation)
  - [Logical Reasoning Sets (Indore QA-embedded)](https://ipmatway.com/learn/logical-reasoning)
  - [Linear Arrangement](https://ipmatway.com/learn/linear-arrangement)
  - [Circular / Square Arrangement](https://ipmatway.com/learn/circular-arrangement)
  - [Matrix / Distribution Puzzles](https://ipmatway.com/learn/matrix-puzzles)
  - [Scheduling (days/months/time slots)](https://ipmatway.com/learn/scheduling)
  - [Selection / Team Formation](https://ipmatway.com/learn/selection-grouping)
  - [Ordering and Ranking](https://ipmatway.com/learn/ordering-ranking)
  - [Games and Tournaments](https://ipmatway.com/learn/games-tournaments)
  - [Syllogisms](https://ipmatway.com/learn/syllogisms)
  - [Venn-based Reasoning](https://ipmatway.com/learn/venn-reasoning)
  - [Data Sufficiency](https://ipmatway.com/learn/data-sufficiency)
  - [Mathematical Operations, Coded Inequalities, Missing Number](https://ipmatway.com/learn/mathematical-operations)
  - [Input-Output (machine)](https://ipmatway.com/learn/input-output)
  - [Series (number / letter / alphanumeric)](https://ipmatway.com/learn/series)
  - [Coding-Decoding](https://ipmatway.com/learn/coding-decoding)
  - [Analogy, Classification and Word Order](https://ipmatway.com/learn/analogy-classification)
  - [Blood Relations](https://ipmatway.com/learn/blood-relations)
  - [Direction Sense](https://ipmatway.com/learn/direction-sense)
  - [Clocks and Calendars](https://ipmatway.com/learn/clocks-calendars)
  - [Cubes and Dice](https://ipmatway.com/learn/cubes-dice)
  - [Non-verbal Reasoning](https://ipmatway.com/learn/non-verbal)
  - [Age / Quant-Reasoning puzzles](https://ipmatway.com/learn/age-puzzles)
  - [Quant-flavoured reasoning (money, bounds, shifts, counting)](https://ipmatway.com/learn/quant-reasoning)
  - [DI: Tables](https://ipmatway.com/learn/di-tables)
  - [DI: Bar Graphs](https://ipmatway.com/learn/di-bar)
  - [DI: Line Graphs](https://ipmatway.com/learn/di-line)
  - [DI: Pie Charts](https://ipmatway.com/learn/di-pie)
  - [DI: Mixed / Combination](https://ipmatway.com/learn/di-mixed)
  - [DI: Caselets](https://ipmatway.com/learn/di-caselet)

## Past-paper RC passages

- https://ipmatway.com/ipmat-rc/rc-philosophy-psychology-0002
- https://ipmatway.com/ipmat-rc/rc-social-issues-0003
- https://ipmatway.com/ipmat-rc/rc-economics-business-0001
- https://ipmatway.com/ipmat-rc/rc-science-tech-0001
- https://ipmatway.com/ipmat-rc/rc-history-humanities-0001
- https://ipmatway.com/ipmat-rc/rc-science-tech-0002
- https://ipmatway.com/ipmat-rc/rc-social-issues-0002
- https://ipmatway.com/ipmat-rc/rc-philosophy-psychology-0001
- https://ipmatway.com/ipmat-rc/rc-social-issues-0001

## Optional

- [Sign up (free)](https://ipmatway.com/login): practice, mocks, the study plan and videos need a free account (Google or email code).
- [About IPMATway](https://ipmatway.com/about): what the site is, who makes it, how to reach us.
- [Community](https://ipmatway.com/community)
- [Privacy](https://ipmatway.com/privacy)

---

# Full text of the exam-information pages and guides

## IPMAT: exam pattern, eligibility and free prep
Source: https://ipmatway.com/ipmat

IPMAT is the entrance test for the five-year Integrated Programme in Management (IPM) at some IIMs. You join straight after Class 12 and earn a bachelor's degree and an MBA in one stretch. IPMAT Indore, IPMAT Rohtak and JIPMAT are three separate exams. Each has its own pattern, dates and form.

IPMATway is a free practice site. It is not affiliated with IIM Indore, IIM Rohtak or NTA. Every fact below comes from their own documents, and we say clearly when something is only reported by coaching sites.

## Who runs which exam

- **IPM Aptitude Test (IPM AT) by IIM Indore.** The test for IIM Indore itself. IIM Ranchi and IIM Shillong also use these scores, according to their own admission documents. IIM Amritsar's official policy lists its eligibility rules; coaching sites report that it uses the IPMAT Indore score, but we did not find that in its policy text.
- **IPM Aptitude Test by IIM Rohtak.** A separate test, run by IIM Rohtak for its own IPM batch.
- **JIPMAT by NTA.** The National Testing Agency runs it for IIM Bodh Gaya and IIM Jammu only.

## The three exams side by side (2026 cycle)

| | IPMAT Indore | IPMAT Rohtak | JIPMAT |
|---|---|---|---|
| Sections | QA MCQ, QA Short Answer, Verbal Ability MCQ | Quantitative Ability, Logical Reasoning, Verbal Ability | Quantitative Aptitude, DI and Logical Reasoning, Verbal Ability and RC |
| Questions | 90 (reported, not official) | 120 (40 per section) | 100 (33 / 33 / 34) |
| Time | 40 minutes per section, fixed order | 120 minutes total | 150 minutes total |
| Marking | +4 / -1 (no negative marking in Short Answer) | +4 / -1 | +4 / -1 |
| 2026 test date | 4 May 2026 | 10 May 2026 | 7 June 2026 |

Details: [IPMAT Indore pattern](/ipmat/indore-exam-pattern), [IPMAT Rohtak pattern](/ipmat/rohtak-exam-pattern) and [JIPMAT](/jipmat).

## How selection works

Passing the test is only the first step. Each IIM then calls a shortlist for a personal interview and makes a merit list.

- **IIM Indore:** 65 marks for the aptitude test and 35 for the interview.
- **IIM Rohtak:** 55 for the IPMAT score, 15 for the interview, 10 for Class 10 and 20 for Class 12.
- **IIM Jammu (JIPMAT):** 70 for the JIPMAT percentile, 15 for Class 10 and 15 for Class 12.
- **IIM Bodh Gaya (JIPMAT):** a sectional percentile of at least 30 is needed; its policy gives no weight formula.

See the [cut-offs page](/ipmat/cut-offs) for the score numbers of past years.

## What about 2027?

As of 26 Oct 2026 we found no official notification for IPMAT 2027 or JIPMAT 2027. IIM Indore notified the 2026 test in early February 2026, so watch its official page around then. We will not guess dates. Check the official sites before you plan around any date you read elsewhere.

## How to prepare for free

1. Learn what is tested: the [syllabus](/ipmat/syllabus) and the [syllabus map](/learn).
2. Look at real questions: [previous-year papers](/ipmat/previous-year-papers).
3. Practise on the clock: [free mock tests](/ipmat/free-mock-test), built fresh to each exam's pattern.
4. Plan your months: [preparation strategy](/ipmat/preparation-strategy).
5. Build speed with the free [tools](/tools), which work without signing in.

On IPMATway you can practise IPMAT Indore, IPMAT Rohtak and JIPMAT with full mocks, sectional, chapter and custom tests. Past-year questions are labelled "actual PYQ" with the year. An error log brings your mistakes back with new numbers after 2, 7 and 21 days. There is no paywall and no ads. [Sign in with Google or an email code](/login) to start.

### FAQ

**What is IPMAT?**
IPMAT is the entrance test for the five-year Integrated Programme in Management at IIMs. IIM Indore and IIM Rohtak each run their own test, and NTA runs JIPMAT for IIM Bodh Gaya and IIM Jammu.

**Are IPMAT Indore and IPMAT Rohtak the same exam?**
No. They are separate tests with different patterns, dates and forms. See the [Indore pattern](/ipmat/indore-exam-pattern) and the [Rohtak pattern](/ipmat/rohtak-exam-pattern).

**Which IIMs accept IPMAT Indore scores?**
IIM Indore itself. IIM Ranchi and IIM Shillong also use them, per their own admission documents. IIM Amritsar is reported to use them too, but we did not find this in its policy text.

**Which IIMs accept JIPMAT?**
Only IIM Bodh Gaya and IIM Jammu in the 2026 NTA bulletin. See the [JIPMAT page](/jipmat).

**When is IPMAT 2027?**
No official notification for IPMAT 2027 had been found as of 26 Oct 2026. IIM Indore notified the 2026 test in early February 2026, so watch its official page.

## IPMAT Indore exam pattern and eligibility
Source: https://ipmatway.com/ipmat/indore-exam-pattern

IPMAT Indore is officially called the IPM Aptitude Test (IPM AT). IIM Indore conducts it for its five-year IPM. This page covers the 2026 cycle (batch 2026-31), the latest with full details.

## Sections, timing and marking

| Section | Time | Marking |
|---|---|---|
| Quantitative Ability (MCQ) | 40 minutes | +4 right, -1 wrong |
| Quantitative Ability (Short Answer) | 40 minutes | +4 right, no negative marking |
| Verbal Ability (MCQ) | 40 minutes | +4 right, -1 wrong |

Total time is 120 minutes. Every question carries 4 marks. You must answer the sections in a pre-set order that is the same for everyone. The official procedure gives a time for each section but does not use the words "sectional time lock".

## How many questions?

IIM Indore's official procedure gives sections and times, not question counts. Students and coaching sites widely report 30 QA MCQ, 15 QA Short Answer and 45 Verbal Ability questions, which is 90 questions and 360 marks. Treat this as reported, not official.

## What the section timing means for you

Each section has its own 40 minutes. Time saved in one section does not carry to the next, so you cannot rescue a weak section later. Practise each section as its own 40-minute block. Our [free mocks](/ipmat/free-mock-test) are built that way.

## Eligibility (2026 cycle)

- Born on or after 1 August 2006. Candidates from SC, ST and PwD categories get 5 years of relaxation (born on or after 1 August 2001).
- Class 12 passed in 2024 or 2025, or appearing in 2026. Those who finish by 31 July 2026 may apply, with provisional admission.
- Class 10 passed.
- The official procedure states no minimum percentage.

## Application fee

The 2026 fee was ₹4,130, including 18% GST. It was ₹2,065 for SC, ST and PwD candidates. Applications ran from 2 February to 14 March 2026 per the procedure and FAQ (a short extension was reported later).

## Selection

After the test comes a personal interview (PI). The final category-wise merit list uses a composite score: 65 for the aptitude test and 35 for the PI.

To be called for the PI, you need a positive raw score and a minimum mark in each of the three sections. The Admissions Committee sets these minimums, and they differ by category. Among eligible candidates, a category-wise merit list on the aptitude score decides who is called. In that score the weights are 25 for QA MCQ, 25 for QA Short Answer and 50 for Verbal Ability. See the [cut-offs page](/ipmat/cut-offs) for reported minimums.

## Seats and reservation

The sanctioned intake for IPM 2026 (domestic) is 150. Reservation is 27% NC-OBC, 15% SC, 7.5% ST, up to 10% EWS and 5% PwBD.

## 2026 dates

- Test: Monday 4 May 2026, 2:00 PM to 4:00 PM.
- Shortlist: 25 May. Interviews: 15 to 18 June. Provisional offers: 26 June. Programme start: 10 August 2026 (tentative dates, from the FAQ).

Dates for 2027 are not announced. IIM Indore notified the 2026 test in early February 2026; watch the official page for 2027.

## Programme fee

For the 2026-31 batch the course fee is ₹6 lakh a year for years 1 to 3, paid in three terms of ₹2 lakh. With medical insurance, mess deposit and a refundable caution deposit, the first-year total shown is ₹7,04,679. Years 4 and 5 are charged at the PGP fee. IIM Indore also offers need-based financial assistance.

## Next steps

Read the [syllabus](/ipmat/syllabus), try [previous-year papers](/ipmat/previous-year-papers), then take a [free IPMAT Indore mock](/ipmat/free-mock-test). For the other exams, see the [IPMAT overview](/ipmat), [IPMAT Rohtak](/ipmat/rohtak-exam-pattern) and [JIPMAT](/jipmat). IPMATway is not affiliated with IIM Indore.

### FAQ

**Is there negative marking in IPMAT Indore?**
Yes, 1 mark is deducted for each wrong answer, except in the Quantitative Ability Short Answer section, which has no negative marking.

**How many questions are in IPMAT Indore?**
IIM Indore's procedure does not state counts. Students and coaching sites report 90 questions: 30 QA MCQ, 15 QA Short Answer and 45 Verbal Ability.

**What is the age limit for IPMAT Indore?**
For the 2026 cycle you must be born on or after 1 August 2006, or on or after 1 August 2001 for SC, ST and PwD candidates.

**Is there a minimum percentage in Class 12 for IPMAT Indore?**
The official 2026 procedure states no minimum percentage. Other IIMs that use the score may set their own, so read each one's policy.

**What is the selection process of IIM Indore IPM?**
An aptitude test and a personal interview, with a composite score of 65 for the test and 35 for the interview. See the [cut-offs page](/ipmat/cut-offs) for reported shortlist minimums.

## IPMAT Rohtak exam pattern and eligibility
Source: https://ipmatway.com/ipmat/rohtak-exam-pattern

IIM Rohtak runs its own IPM Aptitude Test for its five-year IPM, separate from IPMAT Indore. This page covers the 2026 cycle (IPM Batch 08, 2026-31).

## Exam pattern

| Section | Questions |
|---|---|
| Quantitative Ability | 40 |
| Logical Reasoning | 40 |
| Verbal Ability | 40 |

- All 120 questions are MCQs, in one 120-minute paper.
- Each question carries 4 marks. Each wrong answer costs 1 mark. Unattempted questions get no marks.
- The paper is out of 480 (120 questions × 4 marks). That total is our arithmetic, not a figure stated by IIM Rohtak.
- The 2025 FAQ says there is no sectional cut-off for the aptitude test. The paper has one 120-minute limit, with no per-section time limit stated.
- Candidates who also apply for the IPL (law) programme take an extra Legal Reasoning section of 20 questions in 20 minutes.

Some coaching pages say 90 questions. The official figure is 120.

## Eligibility (2026 cycle)

- At least 60% in Class 10 and Class 12 (55% for SC, ST and DAP candidates), calculated on the best five subjects.
- Maximum age 20 years, or 25 years for SC and ST, as of 30 June 2026, per the IPM admission page.
- Candidates finishing Class 12 by the end of June 2026 can apply provisionally.

The 2025 FAQ gave 20 years for everyone, so check the current page each year.

## Fee and dates

The registration fee was ₹4,937. The test was held on 10 May 2026 from 9:00 AM. Interviews were planned for the first and second weeks of June and the session from the third week of August (tentative). Dates for 2027 are not announced; watch the official page.

## Selection

Shortlisted candidates attend a personal interview. The final merit list weights are:

| Component | Weight |
|---|---|
| IPMAT score | 55 |
| Personal interview | 15 |
| Class 10 | 10 |
| Class 12 | 20 |

## 2026 numbers

IIM Rohtak's own summary says 14,488 candidates were called, 12,522 attended and 1,030 were shortlisted for the interview. The minimum scores for each category are on our [cut-offs page](/ipmat/cut-offs).

## How to prepare

No per-section time limit is stated, so plan how you will split the 120 minutes yourself. Practise that on a full paper. Use the [free mocks](/ipmat/free-mock-test), check the [syllabus](/ipmat/syllabus), and compare with [IPMAT Indore](/ipmat/indore-exam-pattern) and [JIPMAT](/jipmat). Back to the [IPMAT overview](/ipmat). IPMATway is not affiliated with IIM Rohtak.

### FAQ

**What is the exam pattern of IPMAT Rohtak?**
Three sections of 40 MCQs each (Quantitative Ability, Logical Reasoning, Verbal Ability), 120 questions in 120 minutes, +4 for right and -1 for wrong.

**What is the age limit for IPMAT Rohtak?**
The 2026 IPM page gives a maximum of 20 years, or 25 for SC and ST, as of 30 June 2026. The 2025 FAQ said 20 for all, so check the current page.

**Is there a sectional cut-off in IPMAT Rohtak?**
The 2025 FAQ says there is no sectional cut-off for the aptitude test. See the [cut-offs page](/ipmat/cut-offs) for the overall minimums.

**Is IPMAT Rohtak harder than IPMAT Indore?**
They differ in format: Rohtak is 120 MCQs in one 120-minute paper, while Indore has timed sections and a Short Answer part. Try both on our [mocks](/ipmat/free-mock-test).

**What is the IPMAT Rohtak application fee?**
The 2026 registration fee was ₹4,937, per the IIM Rohtak admission page.

## JIPMAT: exam pattern, eligibility and prep
Source: https://ipmatway.com/jipmat

JIPMAT is the Joint Integrated Programme in Management Admission Test. The National Testing Agency (NTA) conducts it for IIM Bodh Gaya and IIM Jammu. No other institute was in the 2026 bulletin. This page covers the 2026 cycle.

## Exam pattern

| Section | Questions | Marks |
|---|---|---|
| Quantitative Aptitude | 33 | 132 |
| Data Interpretation and Logical Reasoning | 33 | 132 |
| Verbal Ability and Reading Comprehension | 34 | 136 |
| Total | 100 | 400 |

- Computer-based test, English only, all MCQ.
- 150 minutes in total. The bulletin gives one duration, not a time per section.
- +4 for a correct answer, -1 for a wrong one, nothing for unattempted. If a question is dropped, everyone gets full marks for it.
- Quantitative Aptitude is "up to class 10 Mathematics" per the bulletin.
- The 2026 test was on 7 June 2026, 3:00 PM to 5:30 PM.

## Eligibility

NTA asks for Class 12 passed in 2024 or 2025, or appearing in 2026, and Class 10 passed not before 2022. Each IIM may add its own conditions. For the exam fee, see the NTA bulletin linked below. Dates for 2027 are not announced.

## IIM Jammu

As per IIM Jammu's admission policy page for 2026-31, merit is 70 for the JIPMAT percentile, 15 for Class 10 and 15 for Class 12. You need at least 60% in Class 12 (55% for SC, ST and PwD). Sectional percentile minimums apply, and we list them on the [cut-offs page](/ipmat/cut-offs). That page still carries some text from older years, so confirm on the site.

## IIM Bodh Gaya

IIM Bodh Gaya's 2026-31 policy says the intake is around 180. It asks for 60% in Class 12 (55% for SC, ST, PwD and Transgender candidates) and requires a category-wise sectional percentile of 30 or more to enter the merit list. Class 10 and 12 marks are used for tie-breaks.

## Score validity

A JIPMAT score is valid only for the current admission year. It is not carried forward.

## Prepare for JIPMAT

The Quant syllabus is school-level, so speed and accuracy count most. Use the [syllabus](/ipmat/syllabus), practise reading with [RC passages from past papers](/ipmat-rc), and take [free JIPMAT mocks](/ipmat/free-mock-test). Past JIPMAT questions from 2021 to 2026 are on IPMATway, labelled "actual PYQ". See also the [IPMAT overview](/ipmat), [IPMAT Indore](/ipmat/indore-exam-pattern) and [IPMAT Rohtak](/ipmat/rohtak-exam-pattern). IPMATway is not affiliated with NTA.

### FAQ

**Which IIMs accept JIPMAT?**
IIM Bodh Gaya and IIM Jammu, the only two institutes in the 2026 NTA bulletin.

**What is the JIPMAT exam pattern?**
100 MCQs in 150 minutes: Quantitative Aptitude 33, Data Interpretation and Logical Reasoning 33, Verbal Ability and RC 34. Marking is +4 and -1.

**Is there negative marking in JIPMAT?**
Yes. Each wrong answer costs 1 mark, and unattempted questions get no marks.

**How is the JIPMAT Quant syllabus?**
The NTA bulletin says Quantitative Aptitude is up to Class 10 Mathematics. See our [syllabus page](/ipmat/syllabus).

**Can I use my JIPMAT score next year?**
No. The NTA bulletin says the result is valid only for the current admission year.

## IPMAT syllabus: chapter-wise for all three exams
Source: https://ipmatway.com/ipmat/syllabus

## What the official sources say about the syllabus

Only one of the three exams states its syllabus in an official document. The NTA information bulletin for JIPMAT says Quantitative Aptitude is "up to Class 10 Mathematics". That is all it says about content.

IIM Indore and IIM Rohtak do not publish a chapter-wise syllabus in the official documents we checked. They give the sections and the pattern, not a topic list. So every chapter list for IPMAT Indore and Rohtak you see online, including ours, is built by looking at what was actually asked in earlier papers.

## How we built our list

We counted the chapters in past-year questions and took the average number of questions per paper for each chapter. The table below shows these averages. Some years are memory-based recreations (students wrote down what they remembered), so treat the numbers as approximate. They tell you where the weight usually is, not what will come next year.

For the exam patterns themselves, read the [Indore exam pattern](/ipmat/indore-exam-pattern), the [Rohtak exam pattern](/ipmat/rohtak-exam-pattern) and the [JIPMAT page](/jipmat).

## The big themes in each exam

**IPMAT Indore.** The quant is algebra-heavy. Logarithms come about 3 questions a paper, number system about 3.75, sequences and series about 2.5, coordinate geometry about 2.9 and matrices about 1.9. Matrices appear only in Indore. The verbal section leans on reading comprehension (about 12 questions), fill in the blanks (about 8), word usage (about 5.5) and idioms (about 5).

**IPMAT Rohtak.** The quant is arithmetic-heavy: time, speed and distance about 4.8, ratio about 3.5, averages about 3 and percentages about 2.7. Rohtak also has a full Logical Reasoning section, with linear arrangement about 7 and data sufficiency about 4. The verbal part is vocabulary-heavy: synonyms and antonyms about 8.8 questions.

**JIPMAT.** The quant stays at Class 10 level: mensuration about 3.5, number system about 4 and polynomials about 2.5. The DI and reasoning section has tables about 5.4 and pie charts about 3.2. In verbal, synonyms and antonyms are about 6, reading comprehension about 6.7 and grammar about 4.8.

## What to do with this

1. Start with the chapters that are heavy in your target exam.
2. Do not skip the light chapters completely. A chapter with one question a year can still be the one that matters.
3. If you are writing more than one exam, build the common base first: arithmetic, algebra basics and reading comprehension help everywhere.

The full map of lessons and worked examples is at [Learn](/learn). It follows this same list. Notes need a free account, which you can make on the [login page](/login).

## Chapter-wise question counts

### FAQ

**Is there an official IPMAT syllabus?**
IIM Indore and IIM Rohtak do not publish a chapter-wise syllabus in the documents we checked. For JIPMAT, the NTA bulletin says Quantitative Aptitude is up to Class 10 Mathematics.

**Is the IPMAT syllabus the same as the JIPMAT syllabus?**
No. JIPMAT quant is officially up to Class 10 level, while IPMAT Indore quant, from past papers, goes into logarithms, sequences, coordinate geometry and matrices. Rohtak also adds a full Logical Reasoning section.

**Is Class 12 maths needed for IPMAT?**
Past Indore papers include topics like logarithms, sequences and matrices, so Class 11-12 level algebra helps. There is no official chapter list to confirm the exact limit.

**Which topics have the most weight in IPMAT?**
From our count of past papers, reading comprehension in Indore verbal, arithmetic in Rohtak quant, and linear arrangement in Rohtak reasoning. See the table above for each exam.

**Where can I study the full syllabus free?**
The [Learn](/learn) section lists every chapter with lessons and worked examples. Notes need a free account.

## IPMAT previous year papers: what exists, and free practice
Source: https://ipmatway.com/ipmat/previous-year-papers

## Are there official IPMAT previous year papers?

Honest answer: not that we could find. IIM Indore's admissions page lists procedures, certificate formats and similar documents, but no sample or past paper. IIM Rohtak's admission page also has no sample paper link. For JIPMAT, the NTA bulletin asks candidates to practise on a "Mock Test" for the computer-based format, but the NTA portal page did not show a link to one when we checked. See the [JIPMAT page](/jipmat) and check [exams.nta.nic.in/jipmat](https://exams.nta.nic.in/jipmat/) yourself.

For JIPMAT 2026, the NTA portal lists the answer keys and the question papers with recorded responses that were shown to candidates during the answer-key challenge.

## So what are the "previous year papers" online?

The papers you find on coaching websites are mostly recreations. Students come out of the exam, write down the questions they remember, and the site compiles them. These are useful for practice, but they are not official, they may have missing or changed options, and some answers on those pages are wrong. Be careful with any page that calls them "official previous year papers". They are not.

## What IPMATway has

We collected real past-year questions from public recreations and recomputed every quant answer ourselves. Each is labelled "actual PYQ" with its year.

- IPMAT Indore 2019 to 2025: about 50 to 100 questions per year. For 2026 we have only a few, because it survives only as memory-based lists.
- IPMAT Rohtak: 2019 and 2020.
- JIPMAT: 2021 to 2026.

You can practise them in these ways:

- **Year-wise Short Answer tests** for Indore, 2019 to 2026, so you can practise the no-options section the way it comes.
- **Chapter-wise "Previous-Year Tests"**. Examples: Para Jumbles with Indore 2019 to 2026, or Syllogisms with Rohtak 2019 to 2020 plus JIPMAT 2021 to 2026.
- **Free RC passages** from past papers at [/ipmat-rc](/ipmat-rc), with full explanations. No sign-in needed.

## How to use past questions well

1. Do not do them all in the first month. Learn the chapter first, then attempt that chapter's past questions.
2. Treat them as a guide to style and difficulty, not as a promise of what will repeat.
3. Log every wrong or very slow answer. The error log brings them back with new numbers after 2, 7 and 21 days.
4. Use full mocks for timing and past questions for chapter depth.

Not sure which chapters matter? See the [syllabus by chapter](/ipmat/syllabus). Ready to test yourself under timing? Try the [free mock tests](/ipmat/free-mock-test), or [sign in](/login) to open the past-year tests.

### FAQ

**Are IPMAT previous year papers available officially?**
We could not find any official past or sample paper from IIM Indore or IIM Rohtak. Papers on coaching sites are mostly memory-based recreations by students.

**Where can I get IPMAT previous year papers with solutions?**
IPMATway has real past-year questions labelled with their year, with quant answers recomputed. Reading comprehension passages from past papers are free at [/ipmat-rc](/ipmat-rc) with full explanations.

**Are JIPMAT previous year papers available?**
NTA lists answer keys and question papers with recorded responses for 2026 on its portal. We have JIPMAT questions from 2021 to 2026 as practice sets.

**How many years of IPMAT papers should I solve?**
There is no fixed number. Learn each chapter first, then try its past questions across years, and keep full mocks for timing.

**Do questions repeat in IPMAT?**
Exact repeats are not something to rely on. The style and difficulty of chapters repeat, and that is what past questions are good for.

## Free IPMAT mock test and JIPMAT mock test online
Source: https://ipmatway.com/ipmat/free-mock-test

## What our free mocks are

IPMATway's mocks are free. There is no paywall and no ads. You sign in with Google or an email code and start.

The full-length mocks are built fresh to each exam's pattern:

| Exam | Pattern we follow |
|---|---|
| IPMAT Indore | 90 questions, 120 minutes, with the 40-minute sectional lock |
| IPMAT Rohtak | 120 questions, 120 minutes |
| JIPMAT | 100 questions, 150 minutes |

The Indore numbers of questions per section are reported by coaching sites, not stated in IIM Indore's official document, which gives only three sections of 40 minutes each in a fixed order. Read each pattern in detail: [Indore](/ipmat/indore-exam-pattern), [Rohtak](/ipmat/rohtak-exam-pattern), [JIPMAT](/jipmat).

Besides full mocks you also get:

- **Sectional tests** for quant, verbal or reasoning.
- **Chapter tests** after you finish a chapter.
- **Custom tests** from any chapters you choose, with an option for "only topics I've learnt".
- **Shared mocks**: send a link to friends. Everyone gets the same questions and you see a group board.

After a mock you get an estimated percentile band. It is only an estimate, so do not read it as a promise.

## JIPMAT official mock

The NTA bulletin says candidates should practise the computer-based test using an official mock test. We could not find a link to it on the NTA portal, so check [exams.nta.nic.in/jipmat](https://exams.nta.nic.in/jipmat/) for it. Our JIPMAT mocks are a separate practice option.

## How to take a mock properly

1. **Use exam-day mode.** No pause, auto-submit at the end, full screen. It feels like the real thing.
2. **Match the time of day.** In 2026, Indore ran 2 to 4 PM, Rohtak started at 9 AM and JIPMAT ran 3 PM to 5:30 PM. If you can, take your mocks in your exam's slot so your brain is used to it.
3. **Follow the lock.** For Indore, do not carry time from one section to the next. Practise finishing each section in 40 minutes.
4. **Do not look anything up.** A mock where you check formulas is not a mock.
5. **Sit once, finish once.** Do not stop in the middle.

## How to review

Review matters more than the score. Spend at least as long reviewing as you spent writing.

- Put each question in one of three groups: did not know, knew but made a slip, or too slow.
- Wrong, skipped and very slow answers go into the error log. They come back with new numbers after 2, 7 and 21 days, so you cannot just remember the old answer.
- Look at which questions you should have skipped. The skip-decision trainer helps with this.

Other tools are listed in [free tools](/tools). A plan for how many mocks to take and when is in the [preparation strategy](/ipmat/preparation-strategy). Ready? [Sign in and start a mock](/login).

### FAQ

**Is there a free IPMAT mock test?**
Yes. IPMATway has free full-length IPMAT mocks for Indore and Rohtak patterns, plus sectional, chapter and custom tests. [Sign in](/login) with Google or an email code.

**Is there a free JIPMAT mock test?**
We have JIPMAT mocks built to the 100-question, 150-minute pattern. NTA's bulletin also refers to an official mock for CBT practice; check the NTA JIPMAT portal for it.

**How many mocks should I take before IPMAT?**
There is no magic number. Start full mocks after you have covered most chapters, then take them regularly and spend more time reviewing than writing. See the [strategy page](/ipmat/preparation-strategy).

**Does the mock give my percentile?**
It shows an estimated percentile band. This is only an estimate and not the result of the real exam.

**Can I take a mock with friends?**
Yes. Shared mocks give everyone the same questions and a group board.

## IPMAT preparation strategy: a practical plan
Source: https://ipmatway.com/ipmat/preparation-strategy

This is a plan, not a promise. Nobody can guarantee a selection, and a lot depends on where you start. Use it as a base and change it to suit you.

## Step 1: Know your target exam

The three exams are different. [IPMAT Indore](/ipmat/indore-exam-pattern) has two quant sections and a big verbal section, each timed at 40 minutes. [IPMAT Rohtak](/ipmat/rohtak-exam-pattern) has quant, logical reasoning and verbal in 120 minutes. [JIPMAT](/jipmat) has quant up to Class 10 level, DI and reasoning, and verbal in 150 minutes. Many students write more than one, so find what is common and what is not. The [syllabus page](/ipmat/syllabus) shows where each exam puts its weight. As of 26 Oct 2026, the 2027 dates are not announced, so check the official sites.

## Step 2: The three phases

**Phase 1: Foundation.** Learn each chapter from the start. Use the map at [Learn](/learn). Do not rush to mocks yet. Fix your arithmetic and algebra basics first, and build the reading habit.

**Phase 2: Practice by chapter.** Take chapter tests and the past-year tests for each chapter. Keep an error log from day one.

**Phase 3: Mocks and analysis.** Take full mocks, review each one carefully, and go back to weak chapters.

These overlap. You will keep learning while you start mocks.

## A sample weekly timetable

This is a sample for a Class 12 student with about 2 to 3 hours a day on school days. Change it to match your school and coaching hours.

| Day | Quant | Verbal | Reasoning / DI | Mocks / review |
|---|---|---|---|---|
| Mon | 1 hour new chapter | 45 min reading | - | 15 min error log |
| Tue | 1 hour practice | 45 min vocab + grammar | - | 15 min error log |
| Wed | 1 hour new chapter | 45 min RC | - | 15 min error log |
| Thu | 1 hour practice | - | 1 hour LR or DI set | 15 min error log |
| Fri | 1 hour mixed | 45 min reading | - | 15 min error log |
| Sat | 1 hour weak chapter | 1 hour RC | 1 hour LR / DI | Sectional or chapter test |
| Sun | - | - | - | Full mock (or half mock) plus 2-3 hours review |

## How many mocks, and how to analyse them

Start full mocks when you have covered most of the syllabus. A reasonable pattern is one mock every week at first and two a week in the last two months. Quality of review beats the number of mocks.

- Feed wrong, skipped and very slow answers to the error log. They come back with new numbers after 2, 7 and 21 days.
- Learn to skip. Use the skip-decision trainer and ask after each mock which questions you should have left. With -1 for each wrong answer in all the MCQ sections, a wild guess costs you.
- For Indore, practise the sectional time. You cannot move spare minutes from one section to the next, so train each section to fit 40 minutes.
- Take mocks in exam-day mode and in the same time slot as your exam.

More about mocks: [free mock tests](/ipmat/free-mock-test).

## Balancing with boards

Boards come first in the months close to them. Cut the plan down to about an hour a day, keep the error log and reading habit going, and restart the full plan after your last paper. Do not stop completely, because restarting from zero is harder.

## Reading habit for verbal

Verbal rewards daily reading more than last-month cramming. Read an editorial or a long-form essay each day. After you read, write one line on the main point. Use the [RC strategy guide](/guides/ipmat-rc-strategy), the [RC question types](/guides/rc-question-types) and the guide on [improving reading speed](/guides/improve-reading-speed). Past-paper passages are free at [/ipmat-rc](/ipmat-rc).

## The last 30 days

- Do no new big chapters. Revise formulas and your error log.
- Take full mocks in the exam slot, then review.
- Practise skipping and picking the easy questions first.
- Sleep on time. Plan your travel to the test city and your documents.
- Check the official site for exam-day instructions.

## Doing this free on IPMATway

The weekly planner sets the timetable for you. The tools, such as the Calculation Gym and the reading speed test (no sign-in needed), plus the formula deck, vocab deck and trainers (free account), cover the daily habits. See [all tools](/tools) and [sign in](/login) to start.

### FAQ

**How should I start IPMAT preparation?**
Pick your target exam, then learn chapters from the [Learn map](/learn), starting with arithmetic and algebra basics. Build a daily reading habit alongside.

**How many hours a day should I study for IPMAT?**
There is no fixed number. The sample timetable on this page uses 2 to 3 hours on school days and more at the weekend; being regular matters more than long days.

**How many mocks should I take for IPMAT?**
One a week once you have covered most chapters, going to two a week in the last two months is a reasonable plan. Reviewing each mock well matters more than the count.

**Can I prepare for IPMAT along with boards?**
Yes. Reduce the plan to about an hour a day near board exams, keep the error log and reading going, and resume the full plan after your last paper.

**Is coaching necessary for IPMAT?**
Not necessarily. IPMATway's lessons, mocks, tools and planner are free, though it has no live classes. What matters most is steady practice and honest review.

## IPMAT cut-offs: Indore, Rohtak and JIPMAT
Source: https://ipmatway.com/ipmat/cut-offs

A cut-off here usually means the minimum marks needed to be shortlisted for the personal interview, and often a minimum in each section too. Each institute sets its own, and they change every year. IIM Rohtak publishes official numbers. IIM Indore and JIPMAT do not publish simple actual cut-offs, so those figures below are marked as reported.

## IPMAT Indore (reported, General category)

IIM Indore's documents we found give no cut-off figures. The figures below are reported by Cracku and are not official. Order is QA Short Answer / QA MCQ / Verbal Ability. The section maximums are reported as 60, 120 and 180.

| Year | General sectional minimums |
|---|---|
| 2026 | 28 / 27 / 111 |
| 2025 | 24 / 28 / 112 |
| 2024 | 24 / 35 / 113 |
| 2023 | 12 / 39 / 125 |
| 2022 | 20 / 43 / 112 |

Figures for reserved categories vary between sites, so we do not list them. Only the General 2026 figure agrees across the sources we checked. For 2026, 838 candidates were reported shortlisted out of 17,916 who appeared. Check IIM Indore's own shortlist page for the latest.

## IPMAT Rohtak (official)

These are the minimum marks for the interview shortlist, from IIM Rohtak's own summary PDFs. The paper is out of 480 (120 questions × 4 marks).

**2026**

| Category | Minimum marks | Shortlisted |
|---|---|---|
| General | 363 | 453 |
| EWS | 330 | 93 |
| NC-OBC | 307 | 251 |
| SC | 246 | 136 |
| ST | 168 | 72 |

**2025**

| Category | Minimum marks | Shortlisted |
|---|---|---|
| General | 381 | 454 |
| EWS | 331 | 88 |
| NC-OBC | 297 | 244 |
| SC | 230 | 136 |
| ST | 138 | 69 |

In total, 1,030 candidates were shortlisted in 2026 and 1,013 in 2025. The summaries also list DAP categories; see the PDFs below. See the [Rohtak pattern](/ipmat/rohtak-exam-pattern) for how the paper works.

## JIPMAT

NTA publishes scores only. Each IIM sets its own rules, and we found no official actual cut-offs for 2026. What is official:

- **IIM Jammu:** sectional percentile minimums of 50 in each section for General, 35 for EWS and NC-OBC, 30 for SC and 25 for ST and PwD (per IIM Jammu's admission policy page).
- **IIM Bodh Gaya:** a category-wise sectional percentile of 30 or more.

Cracku reports General raw-score cut-offs for earlier years (not official): IIM Jammu 330 in 2022, 350 in 2023 and 298 in 2024; IIM Bodh Gaya 338, 313 and 292. Use them only as a rough guide. More in the [JIPMAT guide](/jipmat).

## How to use cut-offs

- Aim well above the numbers, because they move each year.
- Compare marks with marks and percentiles with percentiles. Indore and Rohtak use raw marks; JIPMAT rules use percentiles.
- Track each section in your mocks, as a good total will not save you if one section falls below its minimum.

Practise with the [free mock tests](/ipmat/free-mock-test) and follow the [preparation strategy](/ipmat/preparation-strategy). Back to the [IPMAT overview](/ipmat) or the [Indore pattern](/ipmat/indore-exam-pattern).

### FAQ

**What is the IPMAT cut-off for IIM Indore?**
IIM Indore's documents we found give no figures. Cracku reports General sectional minimums of 28 / 27 / 111 (QA Short Answer / QA MCQ / Verbal) for 2026. That is not official.

**What was the IIM Rohtak IPMAT cut-off in 2026?**
IIM Rohtak's summary lists a minimum of 363 for General, 330 for EWS, 307 for NC-OBC, 246 for SC and 168 for ST, out of 480.

**What is the JIPMAT cut-off?**
NTA publishes scores only. IIM Jammu and IIM Bodh Gaya set sectional percentile rules, listed above, and we found no official actual cut-offs for 2026.

**Is there a sectional cut-off in IPMAT?**
IIM Indore requires a minimum mark in each section for the interview call. IIM Rohtak's 2025 FAQ says it has none. JIPMAT institutes use sectional percentiles.

## Free IPMAT preparation resources: a curated list
Source: https://ipmatway.com/ipmat/free-resources

Everything below is free. We list our own things first, then the official pages that every aspirant should bookmark, then how to build a reading habit for verbal.

## On IPMATway

### Past-paper practice

- Real past-year questions, each labelled "actual PYQ" with its year, for Indore, Rohtak and JIPMAT. Details on the [previous year papers](/ipmat/previous-year-papers) page.
- Free RC past-paper passages with full explanations at [/ipmat-rc](/ipmat-rc). No sign-in needed.

### Mocks and tests

- Full-length mocks to the Indore, Rohtak and JIPMAT patterns, plus sectional, chapter and custom tests. See [free mock tests](/ipmat/free-mock-test).

### Tools without signing in

- [Calculation Gym](/tools/calculation-gym) for speed in arithmetic.
- [Reading speed test](/tools/reading-speed) to measure where you start.

### Tools with a free account

Formula deck, skip-decision trainer, RC library, para-jumble trainer, vocab deck, grammar bank, LR and DI set trainer and a daily challenge. All of them are listed on the [tools page](/tools). A weekly planner and the error log are also there.

### Learn

The whole syllabus map is at [Learn](/learn), with lessons and worked examples. Notes need a free account. Not sure what to cover? Read the [syllabus page](/ipmat/syllabus).

### Guides

- [IPMAT RC strategy](/guides/ipmat-rc-strategy)
- [RC question types](/guides/rc-question-types)
- [How to improve reading speed](/guides/improve-reading-speed)

### Community

Ask doubts and talk strategy with other aspirants on the [community page](/community).

## Official pages worth bookmarking

Check these for dates, fees and rules. Coaching sites are often out of date. As of 26 Oct 2026 the 2027 dates are not announced.

- [IIM Indore: IPM admissions](https://iimidr.ac.in/programmes/academic-programmes/five-year-integrated-programme-in-management-ipm/ipm-admissions-details/)
- [IIM Rohtak: IPM admission](https://www.iimrohtak.ac.in/ipm-admission.php)
- [NTA: JIPMAT portal](https://exams.nta.nic.in/jipmat/)

The NTA JIPMAT bulletin refers to an official mock test for CBT practice. Look for it on the NTA portal.

## Reading sources for verbal practice

You do not need a paid reading list. Two good habits are enough:

- The editorial and opinion pages of a good newspaper. Read one or two a day.
- Long-form essays and magazine articles on science, society, economics and history.

Read slowly at first. After each piece, say the main point in one sentence and note three new words. Then take the [reading speed test](/tools/reading-speed) after a few weeks to see if you have improved.

## Start here

New to this? Read the [preparation strategy](/ipmat/preparation-strategy), then [sign in](/login) with Google or an email code. There is no paywall and no ads.

### FAQ

**What are the best free resources for IPMAT preparation?**
On IPMATway: lessons at [Learn](/learn), free mocks, past-paper practice, free tools and RC passages at [/ipmat-rc](/ipmat-rc). Beyond that, bookmark the official IIM and NTA pages.

**Is IPMATway really free?**
Yes. There is no paywall and no ads. You sign in with Google or an email code.

**Which official websites should I follow?**
IIM Indore's IPM admissions page, IIM Rohtak's IPM admission page and the NTA JIPMAT portal. They are linked above.

**How can I improve my English for IPMAT for free?**
Read newspaper editorials and long-form essays daily, learn words in context, and practise RC passages. See the [reading speed guide](/guides/improve-reading-speed).

**Where can I find free IPMAT tools?**
On the [tools page](/tools). Calculation Gym and the reading speed test work without signing in.

## How to approach reading comprehension in IPMAT Indore
Source: https://ipmatway.com/guides/ipmat-rc-strategy

Reading comprehension is the largest single block of the Verbal Ability section in IPMAT Indore, and it is also the block where students lose marks they could have kept. The questions rarely need outside knowledge. They need a disciplined way of reading and a habit of checking every option against the text. This guide covers both.

## What the passages look like

Expect argumentative or explanatory prose of a few hundred words on economics, psychology, science and society, language, history of ideas, or culture. The writing is dense but not technical. Most passages follow one of a few shapes:

- **Problem and response:** the author describes a puzzle or a flawed view and then offers a better explanation.
- **Two views and a verdict:** two positions are described, each gets partial credit, and the author sets out a more careful third position.
- **Claim, evidence, qualification:** a thesis is stated, supported, and then limited ("this is true, but only when...").
- **Narrative or descriptive:** less common, but the author's attitude still matters.

Recognising the shape early tells you where the main point will land. In "two views and a verdict" passages it is almost never in the first paragraph.

## How to read

1. **Skim the first and last sentence of each paragraph** only if you are short on time. Otherwise read once, at a steady pace, without stopping to decode every hard sentence.
2. **After each paragraph, say its job in five words:** "introduces the puzzle", "gives the usual answer", "attacks that answer". This is the map you will use to find things later.
3. **Mark contrast words:** however, yet, but, although, in fact, nevertheless. The author's real position usually sits after them.
4. **Note tone words:** adjectives and adverbs that show attitude (unfortunately, remarkably, merely, too quick). They decide tone questions.
5. **Do not memorise details.** You can return to the text. Know where things are, not what they say.

## Question types in one line each

Main idea, inference, author's tone or attitude, vocabulary in context, structure (why did the author mention this), assumption or strengthen/weaken, and detail or "according to the passage". Each needs a different check; see the full guide on [RC question types](/guides/rc-question-types).

## Answering: the order that works

1. Read the question stem and make sure you know what is asked. "Which is NOT stated" and "which can be inferred" are opposite jobs.
2. Predict an answer in your own words before looking at the options when you can.
3. Go to the paragraph named or implied and re-read the relevant lines. Do not answer from memory.
4. Eliminate options for a specific reason. Write the reason in your head: "too strong", "not mentioned", "reverses the point".
5. Pick the option that is fully supported, not the one that sounds most intelligent.

## Timing for the Verbal Ability section

In the Indore pattern the Verbal Ability section is timed on its own, so spare minutes from Quantitative Ability do not carry over. Check the current official notice for the exact number of questions and minutes, then divide. As a working rule, give each passage a fixed budget (a reading portion and a per-question portion), and write that budget down before the mock starts. If a single question has eaten a minute and you are between two options, mark it, choose the one you currently prefer, and move on. Come back only if time remains at the end. Passages differ in difficulty; it is reasonable to skip a very dense one at first and return to it, since the other passages' questions are worth the same marks.

Practise this with a reading speed that leaves time for questions. If you do not know your own speed, measure it with the [reading speed test](/tools/reading-speed).

## The traps that cost marks

- **Extreme words.** All, always, never, only, completely, proves, entirely. Passages written in this style qualify their claims ("often", "may", "in some cases"). An option that removes the qualification is usually wrong.
- **Out of scope.** The option is true in the real world or sounds sensible, but the passage never says it. If you cannot point to a line, it is out.
- **Half-true options.** The first half matches the text, the second half adds a claim or reverses a relationship. Read options to the last word.
- **Right fact, wrong question.** The option is stated in the passage but does not answer what was asked. A detail is not a main idea.
- **Reversal.** The option mentions the right idea with the direction flipped: cause becomes effect, criticism becomes praise.
- **Borrowed phrases.** An option repeats a striking phrase from the passage to look safe. Check the claim around the phrase, not the phrase.
- **The author versus the view described.** Passages often describe a view the author rejects. Do not pick an option that states that view as the author's own.

## Review after every set

For every wrong answer, write one line: which trap was it, and which sentence in the passage should have stopped you. After a dozen of these you will see that you fall for one or two traps repeatedly. Fix those first.

## Where to practise

Work through real past-paper passages on the [IPMAT RC page](/ipmat-rc), attempt each question before revealing the answer, and read the explanations of the options you eliminated correctly as well as the ones you got wrong.

## How to improve your reading speed for IPMAT
Source: https://ipmatway.com/guides/improve-reading-speed

Reading speed matters in IPMAT because the Verbal Ability section rewards students who finish the passages with time left to think about the questions. But speed without understanding is worthless, so the goal is not "read faster". The goal is to read at a pace where you still understand the argument, and to remove the habits that waste time.

## Step 1: measure honestly

Take the [reading speed test](/tools/reading-speed) on two different passages. It gives you words per minute, a recall score and an effective speed (wpm multiplied by recall out of three). A sensible target for IPMAT is roughly 200 to 250 wpm with at least two of three recall questions correct. If your recall is low, you do not need to be faster. You need to read more actively. If your speed is under 150, there is something mechanical to fix.

## Step 2: find why you are slow

Most slow readers have one or more of these habits:

- **Regression:** the eyes jump back to re-read a sentence even when the meaning was fine.
- **Subvocalising every word:** mouthing or "hearing" each word limits you to speaking speed. You cannot remove it entirely, but you can stop dwelling on it.
- **Word-by-word reading:** the eyes stop on every word instead of taking in short phrases.
- **Vocabulary gaps:** an unknown word makes you stop and worry.
- **Low familiarity:** you have not read dense argumentative prose recently.

Pick the main one. Fix one habit at a time.

## Step 3: a pacer

Use a finger or pen under the line, moving steadily. The pacer stops regressions because the eye follows it. Start slightly faster than comfortable, so you are forced to read in phrases. Do five minutes a day with a pacer on any article. Do not use it in your first full mock; use it in practice until the habit is natural.

## Step 4: read in chunks

Instead of fixing on each word, aim to see two or three words at a time. Practise on easy text first. Newspaper editorials are good since their sentences are built in clauses. When a long sentence appears, find the main subject and verb first and treat the rest as detail.

## Step 5: handle unknown words

When you meet a word you do not know, do not stop. Guess the direction (positive or negative, an action or a quality) from the sentence and keep going. Collect these words in a list and look them up after the reading session. Vocabulary improves faster from words you met in context than from lists.

## Step 6: read the right material

Aim for 30 minutes a day of material that looks like IPMAT passages: opinion and analysis pieces from newspapers, long-form essays, and popular writing about economics, psychology and science. After each article write one sentence: what is the author's main point? This builds comprehension at the same time as speed.

## A four-week plan

- **Week 1:** measure on two passages. Read one article daily without a pacer, then summarise it in one sentence. Note your regressions.
- **Week 2:** pacer for the first ten minutes of each session. Keep the one-sentence summary. Collect unknown words.
- **Week 3:** two timed passages per day from past papers. Note time per passage and accuracy. Do not sacrifice accuracy; if it drops, hold the pace.
- **Week 4:** retake the speed test on a new passage. Compare wpm and recall with week 1. Continue practising on [past-paper RC passages](/ipmat-rc) under time.

## What to expect

Most people gain a noticeable amount in a few weeks by removing regressions and reading in phrases, but results vary a lot with the starting point. Do not chase a number. If you reach the target zone with good recall, stop pushing speed and spend that effort on accuracy and on [question-type skills](/guides/rc-question-types).

## Common mistakes

- Reading faster on easy text and assuming it carries over to dense text. Test on hard passages.
- Skipping the recall check. Without it you are only measuring how quickly your eyes move.
- Practising only before the exam. Short daily sessions beat occasional long ones.
- Training speed and ignoring strategy. A reader at 220 wpm who falls for extreme-word traps will lose more marks than a reader at 180 who does not. Read the [RC strategy guide](/guides/ipmat-rc-strategy) alongside this one.

## Daily routine in 40 minutes

Ten minutes pacer practice, twenty minutes one past-paper passage with questions, ten minutes review of wrong answers and new words. That is enough if you keep it up every day.

## RC question types in IPMAT: how to spot and solve each
Source: https://ipmatway.com/guides/rc-question-types

Reading comprehension questions look different but only a handful of types appear. Knowing the type tells you where to look in the passage and which wrong options to expect. For the wider approach to reading and timing, see the [RC strategy guide](/guides/ipmat-rc-strategy).

## 1. Main idea / central point

**How to spot it:** "The primary purpose of the passage...", "The passage is best described as...", "Which of the following best summarises...".

**How to solve:** Use the one-line map you made of each paragraph. The main idea covers the whole passage, including the final paragraph where the author's own position usually lands. Predict it in one sentence before reading the options.

**Traps:** An option that is true but covers only one paragraph (too narrow). An option that is bigger than the passage (too broad). An option that states the view the author is arguing against.

## 2. Detail / "according to the passage"

**How to spot it:** "According to the author...", "Which of the following is mentioned...", "All of the following EXCEPT".

**How to solve:** Find the exact lines. Compare each option with them, word by word. For EXCEPT questions, three options will be supported by the text; hunt for the one that is not, which is often a plausible claim the passage never makes or one it contradicts.

**Traps:** Options that change one word (some becomes all), swap cause and effect, or are true in general but absent from the text.

## 3. Inference

**How to spot it:** "It can be inferred that...", "The passage implies...", "The author would most likely agree that...".

**How to solve:** An inference is a small step from what is written, not a leap. The right option should be forced or very strongly supported by specific lines. Ask: if the passage is true, must this be true? Also ask whether the author could comfortably say it.

**Traps:** Options that go too far ("therefore all organisations should..."), options that are true in the real world but not supported, and options that restate the passage so closely they add nothing but with a key word altered.

## 4. Tone and attitude

**How to spot it:** "The author's attitude towards X is...", "The tone of the passage is...".

**How to solve:** Look at adjectives, adverbs and the verbs of evaluation. Decide first whether the attitude is positive, negative or balanced, then narrow. Most IPMAT-style passages are measured: analytical, cautious, mildly critical, qualified. A strong word like "scornful" or "outraged" needs strong language in the text.

**Traps:** Extreme tone words, and the mixing of the tone of a described view with the author's tone. An author who describes an angry critic is not angry.

## 5. Vocabulary in context

**How to spot it:** "The word X as used in the passage most nearly means...", or a phrase in quotation marks.

**How to solve:** Ignore the dictionary meaning you first thought of. Re-read the sentence, replace the word with each option, and see which keeps the author's meaning. Look for contrast or support in the neighbouring sentences.

**Traps:** The common meaning of a word that has several. The usual meaning is often there as a decoy.

## 6. Structure and function

**How to spot it:** "Why does the author mention...", "The second paragraph serves to...", "The example of the bridge is used to...".

**How to solve:** This is where your five-word paragraph map pays off. Ask what point the sentence supports. Examples exist to illustrate a claim; a counterexample exists to qualify one. Name the claim first, then pick the option that names the same job.

**Traps:** Options that describe what the example is about instead of what it does.

## 7. Assumption, strengthen, weaken

**How to spot it:** "The argument assumes...", "Which of the following, if true, would weaken the author's claim?".

**How to solve:** State the conclusion and the evidence. The assumption is the unstated link that must hold for the evidence to support the conclusion. To weaken, attack that link or offer an alternative explanation; to strengthen, support the link or eliminate alternatives. Use the negation test for assumptions: if the opposite of an option would destroy the argument, it is a necessary assumption.

**Traps:** Options that are consistent with the argument but are not needed by it, and options that talk about a different conclusion.

## 8. Logical continuation or next paragraph

**How to spot it:** "The paragraph that follows would most likely discuss...".

**How to solve:** Look at the last paragraph. Which promise or open question does it leave? Choose the option that is the natural next step, not a repeat of what was already covered.

## One habit across all types

Before you mark an option, say what is wrong with the other three. If you cannot, you have not finished. After each set, record the type and the trap for every error, and compare against the patterns above. Then practise with real questions on the [past-paper RC page](/ipmat-rc) and check your pace with the [reading speed test](/tools/reading-speed).

---

# Lesson notes (free to read; videos and practice need a free account)

## Percentage Basics (Percentages, Quant)
Source: https://ipmatway.com/learn/percentages/basics

Idea: A percentage is a fraction with denominator 100. Every basic question is "part ÷ base × 100" or its reverse. The only real skill is choosing the right base: the quantity after "of" or "than".
Exam method: 1. Fraction table. Convert awkward percentages to fractions: 1623%=16, 1427%=17, 1119%=19, 9111%=111, 3712%=38. 2. Swap trick. x% of y=y% of x: 4% of 75 is 75% of 4=3. 3. Base check. For "A is r% more than B", B is (r)/(100+r)×100% less than A (25% more ⇒ 20% less; 50% more ⇒ 3313% less). 4. Chains of remainders. Multiply the "left" factors: spending 30%, then 25% of the rest, then 40% of the rest leaves 0.7×0.75×0.6=31.5%. 5. Statement I/II (JIPMAT). Compute each percentage on its own base, then judge each statement separately.
Traps: Measuring a change against the new value instead of the original. Applying a later percentage to the whole income instead of the remainder. Mixing units: 45 minutes is 30% of 2.5 hours, not 45/2.5.

Lessons: [Percentage Basics: start here](https://ipmatway.com/learn/percentages/basics/start-here) · [12.5% = 1/8, Instantly](https://ipmatway.com/learn/percentages/basics/fraction-percent-conversion) · [X percent of y: flip and solve](https://ipmatway.com/learn/percentages/basics/x-percent-of-y) · [Percent of a percent](https://ipmatway.com/learn/percentages/basics/percent-of-percent) · [What Percent Is: Pick the Right Base](https://ipmatway.com/learn/percentages/basics/what-percent-is) · [Percent Error: Instead Of Questions](https://ipmatway.com/learn/percentages/basics/percent-error) · [Percent of what is left](https://ipmatway.com/learn/percentages/basics/successive-fractions-of-remainder)

## Percentage Change (Percentages, Quant)
Source: https://ipmatway.com/learn/percentages/change

Idea: Every percentage change is a multiplication by a factor 1±(r)/(100). Successive changes multiply, and reversing a change divides by the same factor. Products of quantities (revenue, area, expenditure) change by the product of their factors.
Exam method: 1. Factor chain. +30% then -10%: 1.3×0.9=1.17, a 17% rise. 2. Product rule. Revenue = price × quantity: price -25%, quantity +20% gives 0.75×1.2=0.9, a 10% fall. 3. Same percentage up and down. loses (x^2)/(100)%: 96.76% remaining means x=18. 4. Restore. by (r)/(100+r) of the new value; keep spending fixed by cutting consumption by the same (r)/(100+r). 5. Fixed money, more units. The amount saved (r% of the money) buys the extra units at the new price: new price =(rM)/(100k). 6. Percentage points. A rate falling from 8% to 6% falls by 2 percentage points, which is 25% of the old rate.
Traps: Adding successive percentages instead of multiplying factors. Base confusion when reversing (divide by 1.2, do not subtract 20%). Treating percentage points as percentages.

Lessons: [Percentage Change: start here](https://ipmatway.com/learn/percentages/change/start-here) · [Successive percentage changes](https://ipmatway.com/learn/percentages/change/successive-change) · [Reverse Percentage](https://ipmatway.com/learn/percentages/change/reverse-percentage) · [Area and Volume: Multiply, Don't Add](https://ipmatway.com/learn/percentages/change/multiplying-factor) · [Price Up? Cut Consumption](https://ipmatway.com/learn/percentages/change/price-consumption-compensation) · [Percent Points vs Percent](https://ipmatway.com/learn/percentages/change/percent-point-vs-percent) · [Income, Expenditure, Savings Changes](https://ipmatway.com/learn/percentages/change/income-expenditure-savings)

## Percentage Applications (Percentages, Quant)
Source: https://ipmatway.com/learn/percentages/applications

Idea: Applications wrap the same factor arithmetic in a story: votes, marks, populations, mixtures or groups. The work is in naming the base correctly and, in Indore questions, in forcing whole numbers.
Exam method: 1. Elections. Margin =(2w-100)% of the valid votes. With absentees and invalid votes, express every count through the voters on the list (Indore 2023 SA: 0.44V-(0.85V-50-0.44V)=200⇒ V=5000). 2. Marks. Two candidates on either side of the pass mark: max =(100(a+b))/(y-x). 3. Whole numbers. Least group size = LCM of the denominators; for a strict window, test sizes upward (Indore 2024: girls between 48% and 50% ⇒ 27 students, 13 girls). 4. Alligation for overall rates. Males +10%, females +16%, total +12.5% ⇒ males : females =3.5:2.5=7:5. 5. Mixtures. Keep the unchanged ingredient fixed: 20 L at 60% milk has 12 L milk; for 40% milk the total must be 30 L, so add 10 L water.
Traps: Using the votes cast as the base when the question says "all voters on the list". Forgetting that counts of people and fruit must be whole numbers. Applying growth rates additively over several years.

Lessons: [Percentage Applications: start here](https://ipmatway.com/learn/percentages/applications/start-here) · [Election votes and margins](https://ipmatway.com/learn/percentages/applications/election-votes) · [Pass Marks: Fails By a, Passes By b](https://ipmatway.com/learn/percentages/applications/marks-pass-fail) · [Population growth, one year at a time](https://ipmatway.com/learn/percentages/applications/population-growth) · [Percentages that must be whole numbers](https://ipmatway.com/learn/percentages/applications/minimum-count-integer-constraint) · [Mixtures: Fix What Doesn't Change](https://ipmatway.com/learn/percentages/applications/mixture-percent) · [Weighted Percent Change](https://ipmatway.com/learn/percentages/applications/weighted-percent-change)

## Profit and Loss Basics (Profit, Loss and Discount, Quant)
Source: https://ipmatway.com/learn/profit-loss/basics

Idea: Profit or loss is measured against the cost price (CP): profit = SP - CP and profit % =SP-CPCP×100. Every selling price is the cost price times a factor, so profit questions are percentage-change questions with CP as the base. When a question uses the selling price as the base (a "margin"), convert before you compare.
Exam method: 1. Factor in, factor out. A 25% loss at ₹1965 means CP =(1965)/(0.75)=2620; at ₹3013 the factor is (3013)/(2620)=1.15, a 15% profit. 2. Base switch. Margin m% on SP =(100m)/(100-m)% on CP. Two traders with the same SP, both claiming 20% (one on CP, one on SP): profits (S)/(6) and (S)/(5) differ by (S)/(30) (Rohtak 2019: difference ₹85 gives S=2550). 3. Count the articles, not the money. "By selling 2 articles a person gains the CP of 3": profit 32=150%, whatever the total price. 4. Two prices. Gain at ₹A is k times the loss at ₹B: CP =(A+kB)/(k+1). A b% gain instead of an a% loss changes the SP by (a+b)% of CP. 5. Option substitution. For "profit % equals CP" questions, test each option: CP 80 gives 80+64=144.
Traps: Measuring profit against the selling price when the question means cost (or the reverse). Subtracting r% of SP to get CP; always divide by 1±(r)/(100). In "n per rupee" questions, more articles per rupee means a lower price. Using an irrelevant total price that the question gives as decoration.

Lessons: [Profit and Loss Basics: start here](https://ipmatway.com/learn/profit-loss/basics/start-here) · [CP, SP and Profit Percent](https://ipmatway.com/learn/profit-loss/basics/cp-sp-profit-percent) · [Margin on SP vs Profit on CP](https://ipmatway.com/learn/profit-loss/basics/profit-on-cost-vs-sp) · [Same SP, same claim, different profit](https://ipmatway.com/learn/profit-loss/basics/sp-equal-profit-percent) · [CP of n equals SP of m](https://ipmatway.com/learn/profit-loss/basics/cp-of-n-equals-sp-of-m) · [Profit = Price of k Items](https://ipmatway.com/learn/profit-loss/basics/profit-equals-price-of-k-items) · [Buy n for this, sell m for that](https://ipmatway.com/learn/profit-loss/basics/rate-per-unit-buy-sell) · [Two Prices: Gain is k Times the Loss](https://ipmatway.com/learn/profit-loss/basics/two-prices-gain-loss) · [Two selling prices, one cost](https://ipmatway.com/learn/profit-loss/basics/sp-difference-to-cp) · [Profit % Equals the Cost Price](https://ipmatway.com/learn/profit-loss/basics/profit-percent-equations)

## Costs, Overheads and Resale Chains (Profit, Loss and Discount, Quant)
Source: https://ipmatway.com/learn/profit-loss/costs-and-chains

Idea: The cost price is everything paid to get the article ready for sale. When an article changes hands several times, each sale multiplies the price by its own factor. A business with a fixed cost recovers it only through the margin on each unit sold.
Exam method: 1. Multiply the chain once. Profits of 10% and 20% followed by a 25% loss: factor 1.1×1.2×0.75=0.99, so a final price of ₹1980 means a first cost of ₹2000. 2. Repairs sit inside the cost. If the last buyer pays ₹1320 after a 25% profit, a 20% loss and a 10% profit, divide by 1.1, 0.8, 1.25 to get ₹1200, then subtract the repairs. 3. Same rupee rise in CP and SP keeps the rupee profit fixed. A 19%15% drop after both rise by ₹160: 0.19C=0.15(C+160), so C=600. 4. Data sufficiency check. If only the changes in CP and SP are given, the old profit can be found but not the prices or the profit percentage. 5. Break-even: round up. Margin ₹900 per batch against ₹24000 fixed cost: 26.7 becomes 27 batches.
Traps: Adding chain percentages (+20-10+10) instead of multiplying factors. Making N(1+f) units instead of (N)/(1-f) when a fraction f is rejected. Rounding a break-even count down.

Lessons: [Costs, Overheads and Resale Chains: start here](https://ipmatway.com/learn/profit-loss/costs-and-chains/start-here) · [Resale chains: multiply, then divide](https://ipmatway.com/learn/profit-loss/costs-and-chains/chain-of-transactions) · [Overheads and Tax in Cost](https://ipmatway.com/learn/profit-loss/costs-and-chains/overheads-and-tax) · [CP and SP Both Change](https://ipmatway.com/learn/profit-loss/costs-and-chains/cp-sp-both-change) · [Break-even: fixed cost and margin](https://ipmatway.com/learn/profit-loss/costs-and-chains/fixed-variable-cost-breakeven)

## Marked Price and Discount (Profit, Loss and Discount, Quant)
Source: https://ipmatway.com/learn/profit-loss/discount

Idea: Three prices matter: cost price (CP), marked price (MP) and selling price (SP). A markup takes CP to MP; a discount takes MP to SP. Both are multiplications, so the profit factor is the markup factor times the discount factor.
Exam method: 1. One-line factor. Markup 50%, then 20% and 10% off: 1.5×0.8×0.9=1.08, an 8% profit. 2. Order schemes by factors. 0.75×0.85=0.6375, 0.7×0.9=0.63, 0.65×0.95=0.6175, 0.85×0.8=0.68, so ascending price is (C), (B), (A), (D). 3. Totals first in volume questions. a ball melted into beads of one-fifth the radius gives 125 beads; total SP =1.2×10^6, total listed =(1.2×10^6)/(0.8), each ₹12000. 4. Work back from the overall profit. total cost 250 at 32% means sales 330; oranges made 90, so mangoes made 240, ₹48 each, MP =(48)/(0.8)=60. 5. Difference of discounts. 20% vs 25% off saving ₹500 more means 5% of MP =500, MP =10000. 6. Quadratic relations need the stated bound. "Markup is 4 times the discount, profit 14%" has two roots (5% and 70%); the question must say which range applies.
Traps: Adding successive discounts; subtracting the discount from the markup. Taking CP = MP -m% when the MP is m% above cost (it is MP ÷(1+m)). Dividing the free items by the paid items in 'buy a get b free'. Reporting the revenue change when the question asks about profit.

Lessons: [Marked Price and Discount: start here](https://ipmatway.com/learn/profit-loss/discount/start-here) · [Markup then discount: the factor chain](https://ipmatway.com/learn/profit-loss/discount/markup-discount-chain) · [Successive discounts compared](https://ipmatway.com/learn/profit-loss/discount/successive-discounts) · [Mark it high: profit after a discount](https://ipmatway.com/learn/profit-loss/discount/discount-to-get-target-profit) · [One discount for many](https://ipmatway.com/learn/profit-loss/discount/equivalent-single-discount) · [Buy a, get b free](https://ipmatway.com/learn/profit-loss/discount/buy-x-get-y-free) · [Two discounts, one marked price](https://ipmatway.com/learn/profit-loss/discount/discount-difference-to-mp) · [Markup vs discount: who wins?](https://ipmatway.com/learn/profit-loss/discount/markup-discount-relation) · [Price cut, more sales, less profit?](https://ipmatway.com/learn/profit-loss/discount/price-cut-volume-change)

## Mixed Sales and Dishonest Dealers (Profit, Loss and Discount, Quant)
Source: https://ipmatway.com/learn/profit-loss/mixed-sales

Idea: When a trader sells several lots (or uses tricks), the overall result is a weighted average of the separate results, weighted by rupee cost. Dishonest tricks (false weights, water, damaged stock) are just extra factors on the quantity sold.
Exam method: 1. Weighted average. 35 of the articles at +20% and the rest at cost: 35×20=12%. 2. Ratio first. Costs in the ratio 5:6 and 10% profit on both is ₹22: total cost 220, so 100 and 120; then -20+36=16. 3. 2×2 system in rupees. with apple cost A and mango cost M: 0.1A=0.2M and -0.2A+0.1M=-150 give A=1000, i.e. 50 apples. 4. Same SP, ± x%. loss (x^2)/(100)%; the rupee loss needs the actual costs (S)/(1+x/100) and (S)/(1-x/100). 5. Factors for tricks. Markup 20%, 10% off, 900 g for 1 kg: 1.2×0.9×(1000)/(900)=1.2, a 20% profit.
Traps: Averaging percentages on different bases. Treating +10% and -10% on equal selling prices as cancelling. Measuring a false-weight gain against 1000 g. Adding the effects of several tricks instead of multiplying the factors.

Lessons: [Mixed Sales and Dishonest Dealers: start here](https://ipmatway.com/learn/profit-loss/mixed-sales/start-here) · [Part at profit, part at loss](https://ipmatway.com/learn/profit-loss/mixed-sales/part-at-profit-part-at-loss) · [Two items, one overall percent](https://ipmatway.com/learn/profit-loss/mixed-sales/overall-percent-from-two-items) · [False weights at cost price](https://ipmatway.com/learn/profit-loss/mixed-sales/false-weights) · [Dishonest dealer: multiply the tricks](https://ipmatway.com/learn/profit-loss/mixed-sales/dishonest-dealer) · [Same SP, gain on one, loss on other](https://ipmatway.com/learn/profit-loss/mixed-sales/loss-and-gain-same-sp) · [Two items, two scenarios](https://ipmatway.com/learn/profit-loss/mixed-sales/two-scenario-linear-system) · [Water in the milk: adulteration profit](https://ipmatway.com/learn/profit-loss/mixed-sales/adulteration) · [Rotten stock: who pays for it?](https://ipmatway.com/learn/profit-loss/mixed-sales/damaged-or-unsold-stock)

## Simple Interest (Simple and Compound Interest, Quant)
Source: https://ipmatway.com/learn/si-ci/simple-interest

Idea: Simple interest is earned only on the original principal, so the interest is the same every year: SI =(PRT)/(100). Every SI question is a linear relation between P, R, T and the interest.
Exam method: 1. Interest per year is constant. Amounts ₹2600 after 3 years and ₹3000 after 5 years: ₹200 a year, so P=2600-600=2000 and R=10%. 2. Multiples. Interest (k-1)P accumulates linearly: doubling in n years means R=(100)/(n). 3. Inverse proportion. Same loan and same repayment at 6% for 5 months and at 7.5%: 5×(6)/(7.5)=4 months. 4. All-at-the-higher-rate trick. ₹4000 at 4% for 4 years would earn 640; the actual 520 is 120 short, and each rupee moved to 3% loses 0.04: (120)/(0.04)=3000 at 3%. 5. Staggered deposits. list deposit, rate, years left; the deposit made at the end of the last year earns nothing.
Traps: Months used as years; amount used as interest. Scaling time with the multiple instead of with the interest. Counting a year of interest on a deposit made at the very end.

Lessons: [Simple Interest: start here](https://ipmatway.com/learn/si-ci/simple-interest/start-here) · [Simple interest: P, R, T in years](https://ipmatway.com/learn/si-ci/simple-interest/basic-si) · [One sum, two rates](https://ipmatway.com/learn/si-ci/simple-interest/two-parts-two-rates) · [Doubling, tripling at simple interest](https://ipmatway.com/learn/si-ci/simple-interest/time-to-multiply) · [Principal from two amounts](https://ipmatway.com/learn/si-ci/simple-interest/rate-from-amounts-at-two-times) · [When the interest rate changes](https://ipmatway.com/learn/si-ci/simple-interest/rate-change-effect) · [Rate Equals Time in SI](https://ipmatway.com/learn/si-ci/simple-interest/rate-equals-time) · [Staggered deposits, rising rates](https://ipmatway.com/learn/si-ci/simple-interest/staggered-deposits) · [Repaying a loan in parts at SI](https://ipmatway.com/learn/si-ci/simple-interest/si-repayment-instalments)

## Compound Interest (Simple and Compound Interest, Quant)
Source: https://ipmatway.com/learn/si-ci/compound-interest

Idea: Under compound interest, interest earned in one period itself earns interest later, so the amount is multiplied by the same factor 1+(r)/(100) every period. Questions turn into products of factors (growth) or divisions (going back).
Exam method: 1. CI vs SI shortcuts. Two years: CI - SI =P((r)/(100))^2; three years: multiply by (3+(r)/(100)) (Indore 2023: 0.031P=527, P=17000). 2. Ratio form. Two-year CI ÷ SI =1+(r)/(200) (Indore 2019: ratio 2 gives r=200%). 3. Multiples compound. Doubles in 5 years ⇒ 16 times in 20 years. 4. Half-yearly. 10% p.a. half-yearly is 1.05^2=1.1025 a year; Sagarika: 1.12(10000-x)-1.1025x=2310 gives x=4000, total interest 1130. 5. Year-on-year interest. Each scheme's second-year interest is its first-year interest times (1+r) (Indore 2025: 3300+1728+6720=11748). 6. Repayment. Savitri: 10000×1.1025=11025, minus 5025 leaves 6000, which grows to 6615.
Traps: Full rate per half-year; two-year formula for three years. Linear thinking about multiples under CI. Ignoring the repayment's effect on the second year's interest.

Lessons: [Compound Interest: start here](https://ipmatway.com/learn/si-ci/compound-interest/start-here) · [Compound Interest: The Basics](https://ipmatway.com/learn/si-ci/compound-interest/basic-ci) · [Half-Yearly & Quarterly Compounding](https://ipmatway.com/learn/si-ci/compound-interest/half-yearly-quarterly) · [CI − SI for 2 and 3 Years](https://ipmatway.com/learn/si-ci/compound-interest/ci-si-difference) · [CI: Time to Multiply k Times](https://ipmatway.com/learn/si-ci/compound-interest/time-to-multiply-k-times) · [CI Loans: Pay Back in Parts](https://ipmatway.com/learn/si-ci/compound-interest/instalments-partial-payment) · [Yearly Deposits, Growing Salary](https://ipmatway.com/learn/si-ci/compound-interest/increasing-yearly-deposits) · [Savings Split Across Schemes](https://ipmatway.com/learn/si-ci/compound-interest/two-schemes-split) · [CI to SI: The 2-Year Ratio](https://ipmatway.com/learn/si-ci/compound-interest/ci-to-si-relation) · [Rate from Two Amounts](https://ipmatway.com/learn/si-ci/compound-interest/rate-from-successive-amounts) · [CI: Equal Amounts Split](https://ipmatway.com/learn/si-ci/compound-interest/equal-amounts-split)

## Growth and Depreciation (Simple and Compound Interest, Quant)
Source: https://ipmatway.com/learn/si-ci/growth-depreciation

Idea: Growth and depreciation work exactly like compound interest: each year multiplies the value by 1±(r)/(100). Populations use the net rate; machines, cars and money with inflation use the same factor logic.
Exam method: 1. Factor chain. +10%, -10%, +20%: 1.1×0.9×1.2=1.188. 2. Net rate. Birth 8%, death 3%: 1.05 a year. 3. Mixed assets. ₹27000 at 15% CI for 2 years becomes 35707.50; goods costing 63000 fetch 50400; total 86107.50 against 90000, a change of -4.325%. 4. Thresholds. ₹625000 losing 20% a year: 500000, 400000, 320000, 256000, so it first drops below 300000 after 4 years.
Traps: Simple depreciation in place of compound. Assuming equal up and down changes cancel. Subtracting a percentage to go back in time.

Lessons: [Growth and Depreciation: start here](https://ipmatway.com/learn/si-ci/growth-depreciation/start-here) · [Depreciation: Multiply, Don't Subtract](https://ipmatway.com/learn/si-ci/growth-depreciation/depreciation) · [Population Growth: Net Rate & Factors](https://ipmatway.com/learn/si-ci/growth-depreciation/population-growth-ci) · [Percent Change in Value](https://ipmatway.com/learn/si-ci/growth-depreciation/percent-change-in-value)

## Ratios (Ratio, Proportion, Variation and Partnership, Quant)
Source: https://ipmatway.com/learn/ratio-proportion/ratio

Idea: A ratio a:b says how many parts each quantity has, not how big each part is. Write each quantity as (ratio term) × k and every ratio question becomes one equation in k.
Exam method: 1. Combine by equalising. a:b=2:3, b:c=5:2 give 10:15:6; an extra c:d is a distractor. 2. One part first. in 5:9:8 with a total of ₹6820, one part is 310; any share or difference follows. 3. Integer conditions. oranges 3x must be a multiple of 30, so x=10 and the total is 160. 4. Positive multipliers. a+c=578+3m with k+m=289, k1: maximum at m=288, giving 1442. 5. Option check for 4-tuples. (JIPMAT style): test each option against every condition (difference, then ratio); usually two conditions kill three options. 6. Signs. ac0 fixes ca=+4; with a=1: c=4, b=-3, so (b+c)/(a)=1.
Traps: Not equalising the common term when chaining ratios. Reciprocals vs coefficients for kA=mB=nC. Zero multipliers when the question needs positive integers. Value ratio vs count ratio for coins.

Lessons: [Ratios: start here](https://ipmatway.com/learn/ratio-proportion/ratio/start-here) · [Combining Ratios: Equalise and Chain](https://ipmatway.com/learn/ratio-proportion/ratio/combining-ratios) · [Ratio with Integer Constraint](https://ipmatway.com/learn/ratio-proportion/ratio/ratio-with-integer-constraint) · [Ratio Change After an Event](https://ipmatway.com/learn/ratio-proportion/ratio/change-in-ratio-after-event) · [Coins in a Ratio: The Set Trick](https://ipmatway.com/learn/ratio-proportion/ratio/coins-denominations) · [Three-Way Ratio from Pair Sums](https://ipmatway.com/learn/ratio-proportion/ratio/three-way-ratio-from-pairs) · [Dividing in a ratio: one part first](https://ipmatway.com/learn/ratio-proportion/ratio/dividing-in-ratio) · [Equal Fractional Parts](https://ipmatway.com/learn/ratio-proportion/ratio/equal-fractional-parts) · [Expression from a Ratio](https://ipmatway.com/learn/ratio-proportion/ratio/expression-from-ratio) · [Numbers in Ratio: One Multiplier k](https://ipmatway.com/learn/ratio-proportion/ratio/numbers-in-ratio) · [Ratio Linear Systems](https://ipmatway.com/learn/ratio-proportion/ratio/ratio-linear-system) · [Income, Expenditure, Savings Ratios](https://ipmatway.com/learn/ratio-proportion/ratio/income-expenditure-savings) · [Ratio After Percent Changes](https://ipmatway.com/learn/ratio-proportion/ratio/ratio-with-percent-change) · [Ratio Properties: Pull Towards 1](https://ipmatway.com/learn/ratio-proportion/ratio/ratio-properties) · [Leaps Speed Ratio](https://ipmatway.com/learn/ratio-proportion/ratio/leaps-speed-ratio)

## Proportion and Variation (Ratio, Proportion, Variation and Partnership, Quant)
Source: https://ipmatway.com/learn/ratio-proportion/proportion-variation

Idea: Two quantities are in proportion when their ratio stays fixed. Variation generalises this: y may follow x, x^2, 1x or a product of several quantities, always with one constant K.
Exam method: 1. Ratio of the change. y2=y1((x2)/(x1))^n — no need to find K. 2. Percent through a power. factor first. V1P: pressure -20% gives the factor 10.8=1.25, i.e. +25%. 3. Substitution for symbolic options. for a:b=c:d take 2,3,4,6 and test each option; exactly one survives. 4. Componendo-dividendo. turns (3a+b)/(3a-b)=52 into (3a)/(b)=73 in one line. 5. Factorise, don't divide. dividing by (a-c) loses the case a=c.
Traps: Linear scaling when the law has a power. Losing a case by cancelling a factor that can be zero. Inverse variation read as direct.

Lessons: [Proportion and Variation: start here](https://ipmatway.com/learn/ratio-proportion/proportion-variation/start-here) · [Variation with Powers: Factor First](https://ipmatway.com/learn/ratio-proportion/proportion-variation/direct-inverse-variation) · [Joint Variation: One K Rules All](https://ipmatway.com/learn/ratio-proportion/proportion-variation/joint-variation) · [Componendo Dividendo in One Line](https://ipmatway.com/learn/ratio-proportion/proportion-variation/componendo-dividendo) · [K Method: Equal Ratios](https://ipmatway.com/learn/ratio-proportion/proportion-variation/k-method) · [Mean, Third & Fourth Proportional](https://ipmatway.com/learn/ratio-proportion/proportion-variation/mean-proportional) · [Partly Fixed, Partly Variable](https://ipmatway.com/learn/ratio-proportion/proportion-variation/partly-fixed-partly-variable) · [Value of Broken Pieces](https://ipmatway.com/learn/ratio-proportion/proportion-variation/value-of-broken-pieces)

## Partnership (Ratio, Proportion, Variation and Partnership, Quant)
Source: https://ipmatway.com/learn/ratio-proportion/partnership

Idea: Partners are paid for money multiplied by the time it was at work. Profit is shared in the ratio of capital × months.
Exam method: 1. Joining time. (C1·12)/(C2(12-x)) equals the profit ratio, so solve for 12-x and subtract from 12 (Rohtak 2019: 76000·12:57000(12-x)=2:1, x=4). 2. Work in thousands. ₹32000:34000:28000=16:17:14. 3. Reverse. if the profits and capitals are given, the periods are proportional to profit ÷ capital. 4. Salary first. 15% of ₹38000 =5700; only 32300 is shared.
Traps: Months stayed vs month of joining. Salary not deducted before sharing. Project length different from 12 months.

Lessons: [Partnership: start here](https://ipmatway.com/learn/ratio-proportion/partnership/start-here) · [Partnership: Capital × Months](https://ipmatway.com/learn/ratio-proportion/partnership/time-weighted-capital) · [When Did the Partner Join?](https://ipmatway.com/learn/ratio-proportion/partnership/when-did-partner-join) · [Working Partner: Salary First](https://ipmatway.com/learn/ratio-proportion/partnership/profit-share-with-salary) · [Capital Changes Midway](https://ipmatway.com/learn/ratio-proportion/partnership/capital-changes-midway) · [Capital from Profit Share](https://ipmatway.com/learn/ratio-proportion/partnership/capital-from-profit-share)

## Problems on Ages (Ratio, Proportion, Variation and Partnership, Quant)
Source: https://ipmatway.com/learn/ratio-proportion/ages

Idea: Everyone ages at the same rate, so age differences never change while age ratios do. Write the present ages with one or two unknowns and shift every age by the same number of years.
Exam method: 1. Use the constant gap. the child is half the parent's age exactly when the child's age equals the gap. 2. One multiplier. present ages 5k, 3k; twelve years ago 5k-12=3(3k-12), so k=6. 3. Work backwards from a known age. (Rohtak 2019 John): Raman 12+2=14; father +10=2(14+10); John =(38-2)/(4)=9. 4. Options as checks. substitute each option into the stated conditions when the algebra is long.
Traps: Years from now vs the age itself. Wrong direction of the time shift. Group totals that forget everyone ages.

Lessons: [Problems on Ages: start here](https://ipmatway.com/learn/ratio-proportion/ages/start-here) · [Linear Age Relations](https://ipmatway.com/learn/ratio-proportion/ages/linear-age-relations) · [Age Ratios: Now vs n Years Later](https://ipmatway.com/learn/ratio-proportion/ages/age-ratio-past-future) · [Sum of Ages: Intervals & Totals](https://ipmatway.com/learn/ratio-proportion/ages/sum-of-ages) · [Product of Ages: The Quadratic Trick](https://ipmatway.com/learn/ratio-proportion/ages/quadratic-age-relations)

## Averages (Averages, Mixtures and Alligation, Quant)
Source: https://ipmatway.com/learn/averages-mixtures/averages

Idea: An average is a total shared equally. Turn every average into a total (average × count), work with totals, and convert back at the end.
Exam method: 1. Totals first. average 18 of 5 numbers and 16 after removing one: removed =90-64=26. 2. Alligation for two groups. averages 160 and 172 meeting at 164: m:n=4:8=1:2. 3. Middle term. consecutive numbers average to the middle one; adding the next two moves the middle up by 1. 4. Overlap. Wednesday =3×32+4×30-6×26=60. 5. Size-biased. families of 2, 4, 6 equally common, person sampled: (4+16+36)/(12)=4.667.
Traps: Unweighted average of group averages. Ignoring the passage of time for the other members. Arithmetic mean where the harmonic mean is needed.

Lessons: [Averages: start here](https://ipmatway.com/learn/averages-mixtures/averages/start-here) · [Basic Average: Think in Totals](https://ipmatway.com/learn/averages-mixtures/averages/basic-average) · [Averages: Add or Remove a Member](https://ipmatway.com/learn/averages-mixtures/averages/add-remove-member) · [Weighted Average: Size Matters](https://ipmatway.com/learn/averages-mixtures/averages/weighted-average) · [Average of Consecutive Numbers](https://ipmatway.com/learn/averages-mixtures/averages/consecutive-numbers-average) · [Overlapping Group Averages](https://ipmatway.com/learn/averages-mixtures/averages/overlapping-group-averages) · [Uniform Change: Shift the Average](https://ipmatway.com/learn/averages-mixtures/averages/uniform-change) · [Wrong Entry? Fix the Average Fast](https://ipmatway.com/learn/averages-mixtures/averages/correction-of-wrong-entry) · [Size Biased Average](https://ipmatway.com/learn/averages-mixtures/averages/size-biased-average)

## Max and Min under an Average (Averages, Mixtures and Alligation, Quant)
Source: https://ipmatway.com/learn/averages-mixtures/max-min-under-average

Idea: With the total fixed, making one value extreme means pushing all the others to the opposite extreme that the conditions allow (distinct, at least a minimum, at most a cap).
Exam method: 1. Distinct integers. average 110 of 5, smallest 100: others 101, 102, 103; largest 550-406=144. 2. Fixed member. total 384, lowest 40, 41, 42, the 70, then the top two share 191: 95, 96; answer 95-41=54. 3. Re-evaluation. 0.02% of 30×5×200 marks =6. 4. Two halves. top 25 at most 2200, bottom 2200-1250=950: total 3150.
Traps: Repeated values when distinct values are required. Missing caps and floors. Forgetting a fixed value that must stay in the set.

Lessons: [Max and Min under an Average: start here](https://ipmatway.com/learn/averages-mixtures/max-min-under-average/start-here) · [Maximise One Value Given Mean](https://ipmatway.com/learn/averages-mixtures/max-min-under-average/maximise-one-value-given-mean) · [Minimise One Value Given the Mean](https://ipmatway.com/learn/averages-mixtures/max-min-under-average/minimise-one-value-given-mean) · [Max Gap: 2nd Highest vs 2nd Lowest](https://ipmatway.com/learn/averages-mixtures/max-min-under-average/max-difference-given-mean) · [Distinct integers: the mean's hidden constraint](https://ipmatway.com/learn/averages-mixtures/max-min-under-average/distinct-integers-mean-constraint)

## Mixtures and Alligation (Averages, Mixtures and Alligation, Quant)
Source: https://ipmatway.com/learn/averages-mixtures/alligation

Idea: A mixture's concentration (or price) is a weighted average of its parts. Alligation turns that weighted average around: the parts are mixed in the inverse ratio of their distances from the mean.
Exam method: 1. Alligation. rice at ₹22 and ₹36 for ₹28: (36-28):(28-22)=4:3. 2. Fix what does not change. milk stays when water is added; water stays when milk is added. 3. Replacement. C(1- kC)^n; for the capacity, take the n-th root of the final milk fraction. 4. Alloys. equal copper and zinc from P (5:2) and Q (3:4) needs 5a+3b=2a+4b, so b=3a; swapping gives 18:10=9:5.
Traps: Raw ratio terms added across alloys of different sizes. Selling price used as the mean. Linear instead of geometric loss in replacement.

Lessons: [Mixtures and Alligation: start here](https://ipmatway.com/learn/averages-mixtures/alligation/start-here) · [Alligation: The Two Mixture Rule](https://ipmatway.com/learn/averages-mixtures/alligation/two-mixture-rule) · [Water Addition: Fix What Stays](https://ipmatway.com/learn/averages-mixtures/alligation/water-addition-concentration) · [Remove and Replace, n Times](https://ipmatway.com/learn/averages-mixtures/alligation/replacement-repeated) · [Alloy Mixing: Swapped Ratios](https://ipmatway.com/learn/averages-mixtures/alligation/alloy-swapped-ratios) · [Three Mixtures: LCM Scaling](https://ipmatway.com/learn/averages-mixtures/alligation/three-mixtures) · [Mixture with Profit](https://ipmatway.com/learn/averages-mixtures/alligation/mixture-with-profit) · [Remove First, Then Add](https://ipmatway.com/learn/averages-mixtures/alligation/remove-and-add-component)

## Work and Efficiency (Time and Work, Quant)
Source: https://ipmatway.com/learn/time-work/work

Idea: Work = rate × time. Rates add when people work together; times never add. Fix the whole job as a number of units (LCM of the times), turn every person into units per day, and the question becomes simple arithmetic.
Exam method: 1. LCM units. A 12 days, B 16 days → work 48 units, rates 4 and 3. Alternate days: 7 units per 2 days, 6 cycles = 42 units, then 4 more on day 13 and 23 of day 14: 1323 days. 2. Efficiency chain. R = 1, Q = 3, P = 6 units a day; 30 days × 10 = 300 units; P alone 50 days. 3. "% less efficient" vs "% less time". A =0.6B; B's time =0.8 of C's, so C's rate =0.8B. A and B: 1.6B×12=0.8 → B =124, C =130; 60% by B and C takes 8 days. 4. Phases. list what each person does in each phase; idle days do nothing. Amisha does 15+310=12, so the co-worker does 12 in 12 days: 24 days alone. 5. Quadratic, check every root. write all times through one unknown; in 2025 both roots (20 and 24 days) satisfied every condition. 6. Option testing. for "how long does A take" MCQs, plug each option into the joint-time condition — usually faster than solving.
Traps: Times added or averaged instead of rates. Efficiency and time percentages confused (25% more efficient is 20% less time, not 25%). Idle days counted as work; total vs remaining time mixed up. Extraneous or second roots ignored.

Lessons: [Work and Efficiency: start here](https://ipmatway.com/learn/time-work/work/start-here) · [Together Time: The LCM Units Trick](https://ipmatway.com/learn/time-work/work/individual-combined-lcm) · [Efficiency Ratio: Flip It to Time](https://ipmatway.com/learn/time-work/work/efficiency-ratio) · [Alternate Days: Taking Turns](https://ipmatway.com/learn/time-work/work/alternate-days) · [Leaving Midway: Count the Units](https://ipmatway.com/learn/time-work/work/leaving-midway) · [Average of the Times, Not the Rates](https://ipmatway.com/learn/time-work/work/average-completion-time) · [Chain Rule: Men, Days, Hours](https://ipmatway.com/learn/time-work/work/men-days-hours) · [Part of the Job → Full Time](https://ipmatway.com/learn/time-work/work/partial-work-rate) · [Pairwise Times: Who Is Fastest?](https://ipmatway.com/learn/time-work/work/pairwise-combined) · [Quadratic times: guess the pair](https://ipmatway.com/learn/time-work/work/quadratic-times) · [Sequential Portions: A Then B](https://ipmatway.com/learn/time-work/work/sequential-portions) · [Rate Changes Midway: Work in Phases](https://ipmatway.com/learn/time-work/work/rate-change) · [Men, Women, Boys: One Currency](https://ipmatway.com/learn/time-work/work/group-equivalence) · [Workers Leave or Join: Worker-Days](https://ipmatway.com/learn/time-work/work/workforce-change) · [Workers Dropping Out Daily: AP Trick](https://ipmatway.com/learn/time-work/work/workforce-ap) · [Provisions and Garrison Food](https://ipmatway.com/learn/time-work/work/provisions)

## Pipes and Cisterns (Time and Work, Quant)
Source: https://ipmatway.com/learn/time-work/pipes-cisterns

Idea: A pipes question is a work question where the "workers" can be negative: inlets add their rate, outlets and leaks subtract theirs. The tank is the job.
Exam method: 1. Two outlets. T1 alone 30 min, both 20 min: T2 =120-130=160 → 60 minutes. 2. Outlet closed later. P 20 h, Q 25 h, R empties in 30 h; 10 h all open fill (17)/(30); rest at 9100 takes (130)/(27) h; total (400)/(27) h. 3. Alternate hours. inlet 2 h, outlet 3 h. Per cycle +16. Fills in an inlet hour once the level is ≥12: after 3 cycles (6 h) → full at 7 h, not 12. 4. Litres. leak 8 h, inflow 6 L/min (360 L/h), empties in 12 h: C8-360= C12 → C=8640 L.
Traps: Outlet added instead of subtracted. Net-per-cycle division in alternate-hour questions. Minute/hour mix-ups. Whole tank used when it was already partly full.

Lessons: [Pipes and Cisterns: start here](https://ipmatway.com/learn/time-work/pipes-cisterns/start-here) · [Fill and Drain: Net Rate](https://ipmatway.com/learn/time-work/pipes-cisterns/fill-and-drain) · [Pipes: Two Outlets](https://ipmatway.com/learn/time-work/pipes-cisterns/two-outlets) · [Leak Time – Pipes and Cisterns](https://ipmatway.com/learn/time-work/pipes-cisterns/leak-time) · [Pipes Opened in Turns](https://ipmatway.com/learn/time-work/pipes-cisterns/pipes-opened-in-turns) · [Pipe Closed Midway](https://ipmatway.com/learn/time-work/pipes-cisterns/pipe-closed-midway) · [Partial Tank: Pipes and Cisterns](https://ipmatway.com/learn/time-work/pipes-cisterns/partial-tank) · [Identical Pipes](https://ipmatway.com/learn/time-work/pipes-cisterns/identical-pipes) · [Pipes in Litres: Finding Capacity](https://ipmatway.com/learn/time-work/pipes-cisterns/capacity-litres) · [Flow ∝ diameter² | Pipes and Cisterns](https://ipmatway.com/learn/time-work/pipes-cisterns/flow-diameter)

## Wages and Work Share (Time and Work, Quant)
Source: https://ipmatway.com/learn/time-work/wages

Idea: Money follows work. Find the fraction of the job each person did; each gets that fraction of the total wage.
Exam method: 1. Together throughout. A 10 days, B 15 days → rates 3:2 → A gets 35 of the wage. 2. Helper. A 6, B 8, all three finish in 3 days: A 12, B 38, C 18 → C gets 18 of ₹3200 = ₹400. 3. Different days. A works 4 of 6 days at twice B's rate: work 8:6, not 2:1 and not 4:6.
Traps: Ratio of times used instead of efficiencies. Days worked used instead of work done. Helper's share computed from C's time when C's time is not given.

Lessons: [Wages and Work Share: start here](https://ipmatway.com/learn/time-work/wages/start-here) · [Wages: Pay by Work Done](https://ipmatway.com/learn/time-work/wages/wage-share-by-work) · [Wage Share by Days Worked](https://ipmatway.com/learn/time-work/wages/wage-share-by-days)

## Speed, Time and Distance Basics (Time, Speed and Distance, Quant)
Source: https://ipmatway.com/learn/tsd/basics

Idea: Distance = speed × time. Every question in this block fixes two of the three and asks for the third, usually after a change (faster, slower, later, with stoppages). The two habits that solve almost everything: keep units consistent (km/h with hours, m/s with seconds) and turn "same distance" into "times are inversely proportional to speeds".
Exam method: 1. LCM distances. side 100 km at 100,200,300,400: times 1,12,13,14=(25)/(12) h for 400 km → 192 km/h. Options 200 and 250 are the "mean of speeds" traps. 2. Ratio of times. 1220 km/h is a speed ratio 3:5, so times are 5:3; the 2 parts that vanish equal 1 h, so the usual time is 2.5 h and D=30 km. 3. One-equation delayed start. man 4 km/h, woman starts 30 min later at 6 km/h and arrives 20 min earlier: (D)/(4)-(D)/(6)=(50)/(60), D=10. 4. Coefficient ratio. equal split gives (30)/(x)+(37.5)/(y)=585; the new split is (16)/(x)+(20)/(y)=(8)/(15) of it → 312. Do not try to find x and y. 5. Train A / train B. B at 34 speed takes 43 of its time; 43(t-34)=t+12 → t=4.5 h → 100 km/h. 6. Options first. "speed if x km/h more saves t min" — test each option in (D)/(v)-(D)/(v+x); the right one lands exactly.
Traps: Mean of speeds offered as an option — it is always wrong unless the times are equal. Mixing minutes and hours in one equation. "Late by 10, early by 5" treated as a difference of 5 minutes. Answering the new speed / new time when the usual one was asked.

Lessons: [Speed, Time and Distance Basics: start here](https://ipmatway.com/learn/tsd/basics/start-here) · [Average Speed: Distance or Time?](https://ipmatway.com/learn/tsd/basics/average-speed) · [Speed Change → Time Change](https://ipmatway.com/learn/tsd/basics/speed-change-time-change) · [Late at a, Early at b: Find D](https://ipmatway.com/learn/tsd/basics/early-late-arrival) · [Gear Journeys: The Coefficient Trick](https://ipmatway.com/learn/tsd/basics/gear-speed-segments) · [Unit Conversion: the 5/18 Reflex](https://ipmatway.com/learn/tsd/basics/unit-conversion) · [Delayed Start Catch-Up](https://ipmatway.com/learn/tsd/basics/delayed-start-catch-up) · [Stoppage Time](https://ipmatway.com/learn/tsd/basics/stoppage-time) · [Speed Ratio, Flipped Time Ratio](https://ipmatway.com/learn/tsd/basics/proportionality-speed-time) · [Part Train, Part Car](https://ipmatway.com/learn/tsd/basics/part-journey-modes) · [Train Accident Mid Journey](https://ipmatway.com/learn/tsd/basics/accident-mid-journey) · [Walk One Way, Ride Back](https://ipmatway.com/learn/tsd/basics/walk-ride-round-trip)

## Relative Speed and Trains (Time, Speed and Distance, Quant)
Source: https://ipmatway.com/learn/tsd/relative-speed

Idea: When two things move, work with the speed of one relative to the other: opposite directions add, same direction subtract. Then the problem collapses to a single mover covering a single distance (a train's length, a head start, the gap between two towns).
Exam method: 1. Indore 2021 Q22. first train 8 h, second 6 h → speeds 3:4 → 60,80. New delay 5 h → head start 300 km → 15 h at 20 km/h → 8 AM next day. The option "3 AM" is the "count from noon" trap. 2. Indore 2019 Q52 (symbolic). (s1+s2)u=(s2-s1)v → (s1)/(s2)=(v-u)/(v+u). Check with u=1,v=3: speeds 1,2 → 12. Plug numbers into every option — fastest way to kill symbolic MCQs. 3. Indore 2025 Q16 (swimmers). 10 and 15 min per length, 80 min. Pool =30 units, speeds 3,2: meetings at 6,18,30,42,54,66,78 → 7. Note the meeting at 30 min is at a wall and still counts. 4. JIPMAT 2024 Q16/17 (Ram & Shyam). list each runner's turn times (10:00, 10:15) and compute the gap at each turn; first meeting 10:10 (face to face), overtaking 10:30 (both heading back). 5. Rohtak 2019 train A/B. same distance, times differ by 45 min; speed ratio from the two conditions, then plug options. 6. Scheduled trains. 5 a.m.–9 a.m. and 7 a.m.–10 a.m.: distance 12 units, speeds 3 and 4 units/h; by 7 the first has 6 units done; 6÷7 h 51 min → 7:51 a.m.
Traps: Lengths: one train's length vs both; a man has none. Relative speed sign. Head-start timing — the clock starts when the second mover starts. Square root forgotten in the after-meeting ratio. To-and-fro counts: meetings at a wall and overtakes count too.

Lessons: [Relative Speed and Trains: start here](https://ipmatway.com/learn/tsd/relative-speed/start-here) · [Trains Crossing: Pole, Platform, Man](https://ipmatway.com/learn/tsd/relative-speed/trains-crossing) · [Two Trains, One Crossing](https://ipmatway.com/learn/tsd/relative-speed/trains-opposite) · [Meeting Point: Add the Speeds](https://ipmatway.com/learn/tsd/relative-speed/meeting-point) · [Overtaking After a Delayed Start](https://ipmatway.com/learn/tsd/relative-speed/overtaking-delayed-start) · [Speed Ratio After Meeting](https://ipmatway.com/learn/tsd/relative-speed/speed-ratio-from-meeting-times) · [To-and-Fro Meetings](https://ipmatway.com/learn/tsd/relative-speed/to-and-fro-meetings) · [Scheduled Trains: When Do They Cross?](https://ipmatway.com/learn/tsd/relative-speed/scheduled-trains-crossing) · [Chase and Catch](https://ipmatway.com/learn/tsd/relative-speed/chase-and-catch) · [Why Sound Intervals Shrink](https://ipmatway.com/learn/tsd/relative-speed/sound-interval) · [Escalator Steps](https://ipmatway.com/learn/tsd/relative-speed/escalator) · [Train Passes Walkers](https://ipmatway.com/learn/tsd/relative-speed/train-passes-walkers) · [Bus Frequency: One Gap, Two Waits](https://ipmatway.com/learn/tsd/relative-speed/bus-frequency) · [Approach vs Overtake Times](https://ipmatway.com/learn/tsd/relative-speed/approach-vs-overtake-times)

## Races and Circular Tracks (Time, Speed and Distance, Quant)
Source: https://ipmatway.com/learn/tsd/races

Idea: A race is a same-time comparison: when the winner finishes, everyone has run for the same time, so the distances are in the ratio of the speeds. "Beats by x metres" and "beats by t seconds" are two ways of saying how far behind the loser is. On a circular track the same relative-speed idea applies, with the lap length as the gap.
Exam method: 1. Indore 2022 Q29. Bipin covers the 150 m margin in the 15 s → 10 m/s → 40 s for 400 m; Ashok 25 s; Chandan 50 s → 8 m/s; in 40 s Chandan runs 320 m → Bipin wins by 80 m. Work in times, not ratios, when seconds are given. 2. Indore 2020 SA Q9. laps gained =(3000-2000)/(300)=3.33 → 3. Floor, never round. 3. Rohtak 2020 Q7. same direction, 5-4=1 km/h, 115 km → 115 h. One line. 4. Indore 2026 (memory-based) Rekha/Sajal. 14 km track, speeds 5:2, opposite from diametrically opposite points: meetings at t=1,3,5,7,; Rekha is at B when 5t7±od14 → t=7 → 35 km. Make a table of t and position; do not guess "first meeting". 5. Head start by time. "A gives B a 10 s start and they finish together" means B's time = A's time +10.
Traps: Added margins; rounded laps; full lap used for half-lap starts. LCM of speeds; "meet" counted at the end instant when the data gives an exact integer.

Lessons: [Races and Circular Tracks: start here](https://ipmatway.com/learn/tsd/races/start-here) · [Beats By: Metres, Seconds, Chains](https://ipmatway.com/learn/tsd/races/linear-race-beat-by) · [Circular Track Meetings](https://ipmatway.com/learn/tsd/races/circular-track-meetings) · [Circular Overtakes](https://ipmatway.com/learn/tsd/races/circular-overtakes) · [Races with a Head Start](https://ipmatway.com/learn/tsd/races/race-with-head-start) · [Diametrically Opposite Start](https://ipmatway.com/learn/tsd/races/diametrically-opposite-start)

## Boats and Streams (Time, Speed and Distance, Quant)
Source: https://ipmatway.com/learn/tsd/boats-streams

Idea: A boat has one speed relative to the water (b) and the water itself moves (s). Downstream the two add, upstream they subtract. Every boat question is a basics question once you replace "boat downstream" by the single speed b+s and "boat upstream" by b-s.
Exam method: 1. Indore 2024 Q28. 96/6=16 down, 96/8=12 up; five hour-pairs net 5×4=20 km downstream. Options 15, 22.5, 12.5 are drift-per-pair errors. 2. JIPMAT 2023 Q13. "half the time downstream" ⇒ b+s=2(b-s) ⇒ b=3s. Statement I (2:1) false; Statement II (62) true → option D. Check both statements separately. 3. Rohtak 2019 Q46. 2 km in 1 h up, 1 km in 10 min down → u=2, d=6, b=4 → 5 km in 1 h 15 min. 4. Rohtak 2019 chart set (Q7–Q11). each question mixes two days; write the day's b, s, distance and time in a 2×4 grid before computing — most errors there are reading errors. 5. Option testing for round trips. b=15, 30 km each way, 4.5 h: s=5 gives 1.5+3=4.5 ✓.
Traps: Asked quantity misread; sum/difference not halved; k:1 ratio misapplied; rowing speed used for a drifting object; chart row misread.

Lessons: [Boats and Streams: start here](https://ipmatway.com/learn/tsd/boats-streams/start-here) · [Upstream & Downstream: Find the Speeds](https://ipmatway.com/learn/tsd/boats-streams/upstream-downstream) · [Boat and Stream from Two Speeds](https://ipmatway.com/learn/tsd/boats-streams/still-water-stream-speed) · [Boats: Time Ratio to b : s](https://ipmatway.com/learn/tsd/boats-streams/time-ratio-up-down) · [Alternating Runs: Net Position](https://ipmatway.com/learn/tsd/boats-streams/alternating-up-down-position) · [Round Trips: Add Times, Not Speeds](https://ipmatway.com/learn/tsd/boats-streams/round-trip-total-time) · [Floating Object in a River](https://ipmatway.com/learn/tsd/boats-streams/floating-object) · [Two Boats: Gap Before Chase](https://ipmatway.com/learn/tsd/boats-streams/two-boats-relative)

## Clocks (Time, Speed and Distance, Quant)
Source: https://ipmatway.com/learn/tsd/clocks

Idea: A clock is a circular track with the minute hand running at 6^ per minute and the hour hand at 0.5^ per minute, so the minute hand gains 5.5^ per minute. Every angle and coincidence question is a relative-speed question on this 360^ track; gaining/losing clocks are speed-ratio questions; striking clocks are interval counts.
Exam method: 1. Rohtak 2019 Q42. 4 strokes in 9 s → 3 s per gap → 11 gaps → 33 s. Options 36 (per stroke) and 27 (scaled by 12/4) are the traps. 2. Angle at 2:25. |60-137.5|=77.5^; the "90^" option ignores the hour hand's 12.5^. 3. Counting. between 11 a.m. and 2 p.m. the hands coincide at 12:00 and 1:05511 only → 2, not 3. 4. Gaining clock. set right at noon, gains 10 min a day, shows 1 p.m. next day (25 h shown): true =1500×(1440)/(1450)=1489.7 min → 12:49:39 p.m. Use clean numbers in exams: 48 min loss, 29 h shown → 30 h true.
Traps: Hour hand frozen at 30h; reflex angle given; 12 per 12 hours; scaling direction; strokes vs intervals.

Lessons: [Clocks: start here](https://ipmatway.com/learn/tsd/clocks/start-here) · [Clock Angles and Tip Distance](https://ipmatway.com/learn/tsd/clocks/angle-between-hands) · [Clock Hands: Meet, Oppose, Turn](https://ipmatway.com/learn/tsd/clocks/hands-coincide-opposite) · [Gaining and Losing Clocks](https://ipmatway.com/learn/tsd/clocks/clock-gain-loss) · [Clock Striking: Count the Gaps](https://ipmatway.com/learn/tsd/clocks/clock-striking)

## True and Banker's Discount (Commercial Maths (Rohtak/JIPMAT), Quant)
Source: https://ipmatway.com/learn/commercial-maths/discounting

Idea: A sum A due in the future is worth less today. The present worth PW is the money that, lent now at the given rate, grows to A by the due date. The true discount is the difference A-PW, which is the interest on PW. A bank that discounts a bill instead charges interest on the full face value: the banker's discount. It is larger than the true discount, and the extra is the banker's gain, which is the interest on the true discount.
Exam method: 1. Write x=(RT)/(100) as a fraction (6% for 9 months: x=(9)/(200); 20% for 6 months: x=(1)/(10)). Then everything is a multiple of A: BD =Ax, TD =(Ax)/(1+x). 2. Two discounts given (BD and TD, or SI and TD): sum =BD·TDBD-TD - one line, no rate needed. 3. Option check: TD must be smaller than BD, and PW + TD must equal the amount. 4. Pay-now vs pay-later: compute the PW of the later payment and compare it with the cash price (an equal value means both offers are equally good).
Traps: BD in place of TD; months used as years; TD doubled with time; PW compared with the face amount instead of the cash price.

Lessons: [True and Banker's Discount: start here](https://ipmatway.com/learn/commercial-maths/discounting/start-here) · [True Discount](https://ipmatway.com/learn/commercial-maths/discounting/true-discount) · [Banker's Discount](https://ipmatway.com/learn/commercial-maths/discounting/bankers-discount) · [Banker's Gain](https://ipmatway.com/learn/commercial-maths/discounting/bankers-gain) · [Present Worth](https://ipmatway.com/learn/commercial-maths/discounting/present-worth) · [SI and TD: Find the Sum](https://ipmatway.com/learn/commercial-maths/discounting/td-si-relation)

## Stocks and Shares (Commercial Maths (Rohtak/JIPMAT), Quant)
Source: https://ipmatway.com/learn/commercial-maths/stocks-shares

Idea: A stock or share has a face value (₹100 for stock, often ₹10 for shares) on which the dividend is declared, and a market value at which it is bought and sold. Your income depends on how many units you own; your return depends on what you paid for them.
Exam method: 1. "9% stock at 96": each ₹96 earns ₹9, so income =(X)/(96)×9. 2. Yield in one step: (r· F)/(m); for stock (F=100) this is (100r)/(p). 3. Elimination: income can never be r% of the investment unless the price is at par. 4. Switch questions: old income =(S)/(100)r1; new income =(S p1)/(100 p2)r2; compare.
Traps: Dividend on market value; brokerage sign; comparing rates instead of returns; using the face value instead of the proceeds after selling.

Lessons: [Stocks and Shares: start here](https://ipmatway.com/learn/commercial-maths/stocks-shares/start-here) · [Income from Stock](https://ipmatway.com/learn/commercial-maths/stocks-shares/income-from-stock) · [Brokerage: Buy Plus, Sell Minus](https://ipmatway.com/learn/commercial-maths/stocks-shares/brokerage) · [Face Value vs Market Value](https://ipmatway.com/learn/commercial-maths/stocks-shares/market-value-face-value) · [Dividend Yield](https://ipmatway.com/learn/commercial-maths/stocks-shares/dividend-yield) · [Stock Switch: Follow the Proceeds](https://ipmatway.com/learn/commercial-maths/stocks-shares/stock-switch)

## Calendar (Commercial Maths (Rohtak/JIPMAT), Quant)
Source: https://ipmatway.com/learn/commercial-maths/calendar

Idea: The weekday cycles every 7 days, so only the odd days (days beyond complete weeks) matter. An ordinary year has 1 odd day and a leap year 2, so every date moves forward one weekday per year, or two across a 29 February.
Exam method: 1. Use a known anchor (1 January 2001 was a Monday; 1 January 2026 is a Thursday) and move by odd days instead of working from scratch. 2. Month odd days for an ordinary year: Jan 3, Feb 0, Mar 3, Apr 2, May 3, Jun 2, Jul 3, Aug 3, Sep 2, Oct 3, Nov 2, Dec 3. 3. For counts of a weekday in a range: find the first occurrence, then step in weeks.
Traps: Counting the start date; century years as leap years; adding a leap day that is outside the period; the 28-year shortcut across a century.

Lessons: [Calendar: start here](https://ipmatway.com/learn/commercial-maths/calendar/start-here) · [Odd Days: Keep the Remainder](https://ipmatway.com/learn/commercial-maths/calendar/odd-days) · [Find the Day of Any Date](https://ipmatway.com/learn/commercial-maths/calendar/day-of-week) · [Leap year rules](https://ipmatway.com/learn/commercial-maths/calendar/leap-year-rules) · [When Does a Calendar Repeat?](https://ipmatway.com/learn/commercial-maths/calendar/same-calendar-year) · [Counting Weekdays](https://ipmatway.com/learn/commercial-maths/calendar/weekday-count)

## Number Series (Commercial Maths (Rohtak/JIPMAT), Quant)
Source: https://ipmatway.com/learn/commercial-maths/number-series

Idea: A number series hides a rule that produces each term from its position or from the previous terms. Find the rule from a clean stretch of terms and apply it to the gap, the next term or the term that breaks it.
Exam method: 1. Rohtak 2019: 46080, 3840, 384, 48, 8, 2 - ratios 12, 10, 8, 6, 4, so the next divisor is 2 and the answer is 1. 2. k-th term of a quadratic series: a = half the second difference; fit T1, T2 for b, c; or count on: Tk=T1+(k-1)d1+k-12^2. 3. Wrong-term questions: the wrong term breaks two consecutive differences (or ratios); the options next to it still fit.
Traps: Repeating the last difference; the wrong half of an interleaved series; a dropped constant; an off-by-one term number.

Lessons: [Number Series: start here](https://ipmatway.com/learn/commercial-maths/number-series/start-here) · [Missing Term: Find the Next Move](https://ipmatway.com/learn/commercial-maths/number-series/missing-term) · [Spot the Wrong Term](https://ipmatway.com/learn/commercial-maths/number-series/wrong-term) · [Find the Rule, Find Any Term](https://ipmatway.com/learn/commercial-maths/number-series/pattern-identification)

## Divisibility Rules (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/divisibility

Idea: Divisibility questions are rule look-ups plus bookkeeping. Primes 2, 5 (last digit), 3, 9 (digit sum) and 11 (alternating sum) have one-line tests; every composite divisor is handled by splitting it into co-prime parts. Counting how many numbers in a range satisfy a divisibility condition is a floor-division count with inclusion-exclusion for overlaps.
Exam method: 1. JIPMAT 2023 Q25. (5a32465b, 88): 65b divisible by 8 gives b=6 at once; then the alternating sum forces a=3; 2a+5b=36. 2. JIPMAT 2024 Q3. (94a29b6, 72): 9b6\936,976\, b3 so b=7; digit sum 37+a=45, a=8; answer 37. 3. Indore 2019 Q24. digit-sum rule kills 54 immediately; test 7 on the survivors (453096=63×7192). 4. Indore 2022 Q39. four-digit multiples of 6: 1666-166=1500; remove multiples of 30: 333-33=300; answer 1200. 5. Indore 2022 Q21. a letter-string is safe only if it ends in e and repeats each letter equally; edcba fails. 6. JIPMAT 2025. 2^122(1+4+16+64+256)=2^122×341, 341=11×31.
Traps: Non-co-prime splits; digit-sum rule misapplied to 6; off-by-one at range ends; 'odd multiple' misread; a+b a^n+b^n assumed for even n.

Lessons: [Divisibility Rules: start here](https://ipmatway.com/learn/number-system/divisibility/start-here) · [Divisibility rules 2 to 13](https://ipmatway.com/learn/number-system/divisibility/rules-2-to-11) · [Unknown digits: 72, 88, 99](https://ipmatway.com/learn/number-system/divisibility/unknown-digits) · [Composite Divisor: Append the Digits](https://ipmatway.com/learn/number-system/divisibility/composite-divisor) · [Consecutive products: 6, 24, 8](https://ipmatway.com/learn/number-system/divisibility/consecutive-product) · [Digit Sum Trick: 3, 9 and Squares](https://ipmatway.com/learn/number-system/divisibility/digit-sum-conditions) · [Count Multiples in a Range](https://ipmatway.com/learn/number-system/divisibility/counting-multiples-in-range) · [Power sums: odd powers, add the bases](https://ipmatway.com/learn/number-system/divisibility/power-sum-factoring) · [Not Necessarily Divisible](https://ipmatway.com/learn/number-system/divisibility/not-necessarily-divisible) · [Repdigit and Block Numbers](https://ipmatway.com/learn/number-system/divisibility/repdigit-and-block-numbers)

## Factors and Divisors (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/factors

Idea: Every divisor of N= pi^ei is a choice of exponent 0 ei for each prime. Counting divisors, summing them, restricting to squares, multiples or odd numbers, and even multiplying them all - each is a product of independent per-prime choices. Euler's counts the integers that share no prime with N.
Exam method: 1. Indore 2024 Q1. 1800=2^3 3^2 5^2; multiples of 6 rightarrow divisors of 300: 3·2·3=18. 2. Indore 2021 Q1. N=2^3 3^3 5^3·7·13·17 has 512 divisors; multiples of 45 rightarrow divisors of N/45: 192; answer 320. 3. Indore 2025. 3^5 5^8 7^2: square factors 3×5×2=30. 4. Indore 2023 Q40 / 2020 Q11. two primes with equal exponents e; both exponents must be ≥ k: ((e-k+1)/(e+1))^2. 5. JIPMAT 2023 Q10. (220)=7·6·12=504, proper sum 284. 6. JIPMAT 2023 Q12. d(7200)=6·3·3=54, proper divisors 52.
Traps: (e+1) forgotten; proper vs all divisors; floor-plus-one for squares; 2^-1; ordered vs unordered pairs.

Lessons: [Factors and Divisors: start here](https://ipmatway.com/learn/number-system/factors/start-here) · [Count of factors: one formula, two traps](https://ipmatway.com/learn/number-system/factors/count-of-factors) · [Sum of Factors: One Bracket per Prime](https://ipmatway.com/learn/number-system/factors/sum-of-factors) · [Perfect square and cube factors](https://ipmatway.com/learn/number-system/factors/perfect-square-factors) · [Factor Pairs: Count, Don't Double](https://ipmatway.com/learn/number-system/factors/factor-pairs) · [Factors that are multiples of k](https://ipmatway.com/learn/number-system/factors/factors-with-condition) · [Product of Divisors = N^(d/2)](https://ipmatway.com/learn/number-system/factors/product-of-factors) · [Odd and Even Factors](https://ipmatway.com/learn/number-system/factors/odd-even-factors) · [Smallest number from its factor count](https://ipmatway.com/learn/number-system/factors/number-from-factor-count) · [Coprimes below n: Euler's phi](https://ipmatway.com/learn/number-system/factors/coprimes-below-n)

## Remainders (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/remainders

Idea: Remainders behave like a clock: add, subtract and multiply the remainders, not the numbers. Powers settle into cycles; the cycle length divides p-1 for a prime modulus (Fermat) and (m) in general. Modulo 9 the remainder of a number is that of its digit sum, which is why Indore loves huge powers modulo 9.
Exam method: 1. Indore 2025 Q3. 112, 2^1011 with 10113±od6 gives 8; 10113±od9 so 3^110; remainder 8. 2. Indore 2019 Q23. 29^841, 292, 8411±od6: remainder 2. 3. Indore 2026 (memory). 7^103+7^101=50·7^101; 7^31, 7^1017^24, 505: 202. 4. Indore 2023 Q8. 5! onwards is a multiple of 15; 1+2+6+24=333. 5. Indore 2020 Q1. \q,r\=\4,6\ with r<5: dividend 5·6+4=34. 6. Wilson. 150!151=150 because 151 is prime.
Traps: Cycle length confused with modulus; negative remainders left as such; towers vs products of exponents; 3^k0±od9 forgotten; Wilson applied to composites.

Lessons: [Remainders: start here](https://ipmatway.com/learn/number-system/remainders/start-here) · [Cyclicity: shrink the huge power](https://ipmatway.com/learn/number-system/remainders/cyclicity) · [Negative Remainder: fix the minus sign](https://ipmatway.com/learn/number-system/remainders/negative-remainder) · [Binomial Trick: Plus or Minus One](https://ipmatway.com/learn/number-system/remainders/binomial-trick) · [Fermat's Little Theorem](https://ipmatway.com/learn/number-system/remainders/fermat-small) · [Successive Division: Rebuild Upwards](https://ipmatway.com/learn/number-system/remainders/successive-division) · [Sum of factorials: where it stops](https://ipmatway.com/learn/number-system/remainders/sum-of-factorials) · [Large Power Mod 9](https://ipmatway.com/learn/number-system/remainders/large-power-mod-9) · [Dividend = divisor x quotient + remainder](https://ipmatway.com/learn/number-system/remainders/division-algorithm-relations) · [Wilson's Theorem: 150! mod 151](https://ipmatway.com/learn/number-system/remainders/wilson-theorem) · [123456...4950: remainder in 10 seconds](https://ipmatway.com/learn/number-system/remainders/concatenated-number-remainder) · [Geometric sum remainder](https://ipmatway.com/learn/number-system/remainders/geometric-sum-remainder)

## Unit and Last Digits (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/unit-digit

Idea: The unit digit of a product depends only on the unit digits of the factors, so powers of a number have unit digits that cycle with period 1, 2 or 4. The same reasoning modulo 100 (with the binomial expansion of (10t+1)^n) gives last two digits.
Exam method: 1. Indore 2021 Q16. 743^853, 525^375, 987^961: 3-5+1=-19. 2. Indore 2023 Q39. cubes of 0-9 end in distinct digits; p ends in 4, p+3 in 7, 7^3=3433. 3. 1!+2!++1000!: only 1! to 4! matter, 333. 4. 3^400=81^100: tens digit 8×0=0, last two digits 01.
Traps: Exponent modulo 10; r=0 mishandled; negative digit; tower exponents multiplied; several digits listed where the cube map is one-to-one.

Lessons: [Unit and Last Digits: start here](https://ipmatway.com/learn/number-system/unit-digit/start-here) · [Unit digit: the cycle of 4](https://ipmatway.com/learn/number-system/unit-digit/cyclicity-4) · [Unit Digit of Sums and Products](https://ipmatway.com/learn/number-system/unit-digit/unit-digit-of-sum-product) · [Last two digits: hunt for 01 and 76](https://ipmatway.com/learn/number-system/unit-digit/last-two-digits) · [Factorials: after 4!, only zeros](https://ipmatway.com/learn/number-system/unit-digit/factorial-unit-digit) · [Reverse the Unit Digit: Cubes](https://ipmatway.com/learn/number-system/unit-digit/unit-digit-reverse-condition) · [Unit Digit of Power Towers](https://ipmatway.com/learn/number-system/unit-digit/exponent-tower-unit-digit)

## Factorials and Trailing Zeros (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/factorials

Idea: N! contains every integer up to N, so the exponent of a prime p in it is the number of multiples of p, plus the multiples of p^2 (which carry a second factor), and so on. Trailing zeros are exponents of 10=2×5, and 5 is always the scarcer prime.
Exam method: 1. Indore 2019 Q22. v7(50!)=7+1=8, v3(50!)=22: n=8. 2. Zeros of 146! limited by v3 when the base is 6: 48+16+5+1=70. 3. 'How many N have N! with exactly 23 zeros': 99!22, 100!24: none. 4. 100!+200!=100!(1+101·s200): the bracket ends in 1, zeros =24. 5. 1001=7·11·13 in 1001!: v13=77+5=82 is the minimum.
Traps: Only N/5; wrong prime chosen for composite bases; impossible zero counts; zero counts added for sums.

Lessons: [Factorials and Trailing Zeros: start here](https://ipmatway.com/learn/number-system/factorials/start-here) · [Highest power of p in N!](https://ipmatway.com/learn/number-system/factorials/highest-power-in-factorial) · [Trailing zeros of N!](https://ipmatway.com/learn/number-system/factorials/trailing-zeros) · [Composite base: scarcest prime wins](https://ipmatway.com/learn/number-system/factorials/composite-base-power) · [Trailing Zeros: The Inverse Trick](https://ipmatway.com/learn/number-system/factorials/trailing-zeros-inverse) · [Zeros in Products, Not Just Factorials](https://ipmatway.com/learn/number-system/factorials/zeros-in-products)

## Digits and Number Forms (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/digits-and-forms

Idea: Write numbers by their digits: ab=10a+b. Reversals, digit sums and digit products become small equations; digit ranges (0-9, leading digit non-zero) cut the solutions down to one. The long string 123456789101112 is handled in blocks by digit length. Digit counts of powers come from pairing 2s and 5s.
Exam method: 1. Indore 2019 Q18. 6389-2889=3500=875×4 exactly, so the digit is the last digit of 1000+874=1874: 4. 2. Indore 2020 Q7. a· d=0 and a0 give d=0, a=7; bc=18 with b-c=7 gives 9,2: 7920. 3. Indore 2021 Q19. (1000a+100b+10c+d)/(a+b+c+d)1000; answer 1000. 4. 4000th digit of 0.142857: 40004±od6, digit 8. 5. Digits of 2^a5^b: pair into tens, count the leftover's digits.
Traps: Off-by-one positions; zero thousands digit; occurrences vs numbers; digit count of powers off by one.

Lessons: [Digits and Number Forms: start here](https://ipmatway.com/learn/number-system/digits-and-forms/start-here) · [Digit Count of 2^a × 5^b](https://ipmatway.com/learn/number-system/digits-and-forms/digit-count-of-powers) · [Find the Number from Its Digits](https://ipmatway.com/learn/number-system/digits-and-forms/number-from-digit-relations) · [Max and Min of N divided by digit sum](https://ipmatway.com/learn/number-system/digits-and-forms/digit-sum-ratio) · [k-th Digit of 123456789101112...](https://ipmatway.com/learn/number-system/digits-and-forms/consecutive-integers-string) · [Four-digit puzzles: pin one digit first](https://ipmatway.com/learn/number-system/digits-and-forms/four-digit-number-conditions) · [How many times is a digit written?](https://ipmatway.com/learn/number-system/digits-and-forms/digit-occurrence-count) · [The 4000th digit of 0.142857...](https://ipmatway.com/learn/number-system/digits-and-forms/recurring-decimal-kth-digit)

## Integer Solutions of Equations (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/integral-solutions

Idea: Integer solutions come from two tools: residues (for linear equations - one solution, then a fixed step) and factoring (for xy-type equations - divisor pairs of a constant). Counting lattice points in a region is a column-by-column sum.
Exam method: 1. Indore 2019 Q16. x=6+7t, y=-3-4t; |x|<100 gives t=-1513: 29 solutions. 2. Indore 2019 Q19. (x-1)(y-1)=1: (2,2),(0,0). 3. Indore 2025. n1±od7, n=1,8,15; smallest m+n at the largest n: 5+15=20. 4. Indore 2024 Q7. diamond of radius 6: 2·36+2·6+1=85. 5. Indore 2026. x^2+y^210: columns 7,7,7,5,5,3,3: 37. 6. JIPMAT 2023 Q15. u=y+1y\1,52\; only y=2 is an integer.
Traps: Strict vs inclusive bounds; sign pairs; ordered vs unordered; natural vs whole; quadrant double counting.

Lessons: [Integer Solutions of Equations: start here](https://ipmatway.com/learn/number-system/integral-solutions/start-here) · [Two Variable Diophantine](https://ipmatway.com/learn/number-system/integral-solutions/two-variable-diophantine) · [Sum equals product: (x-1)(y-1)](https://ipmatway.com/learn/number-system/integral-solutions/sum-equals-product) · [Bounded Integer Solutions](https://ipmatway.com/learn/number-system/integral-solutions/bounded-solutions) · [Min of m + n on 7m + 11n = 200](https://ipmatway.com/learn/number-system/integral-solutions/min-sum-under-linear-constraint) · [x squared minus y squared = N](https://ipmatway.com/learn/number-system/integral-solutions/difference-of-squares-pairs) · [Reciprocal Sum Equations](https://ipmatway.com/learn/number-system/integral-solutions/reciprocal-sum-equation) · [Lattice Points: Diamond and Circle](https://ipmatway.com/learn/number-system/integral-solutions/lattice-points-in-region)

## Types of Numbers (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/classification

Idea: Classification questions test whether you know what kind of number you are looking at: prime or composite, square or not, rational or irrational, terminating or recurring, odd or even. Each class has a quick membership test, and most exam items are either 'which option belongs' or 'what can never happen'.
Exam method: 1. Indore 2019 Q14. P- Q(k) is the set of primes up to 25: 9. 2. Indore 2026. x^26\0,1,3,4\, so k=2,5 are impossible for 6m+k. 3. Indore 2026. 23 abc gives c=23, (a-1)(b-1)=24: triples \3,13,23\,\5,7,23\; max a+b-c=13+23-3=33. 4. Which of 3123, 219, 573, 467 is prime? Digit sums kill 3123, 219, 573 (9, 12, 15); 467 survives trial division to 19. 5. 0.1818+0.3030030003: rational plus irrational is irrational.
Traps: 1 counted as prime; 6k±1 taken as sufficient; unreduced denominators; irrational sums; careless parity.

Lessons: [Types of Numbers: start here](https://ipmatway.com/learn/number-system/classification/start-here) · [Primes: How Far Must You Test?](https://ipmatway.com/learn/number-system/classification/primes-composites) · [Perfect Squares: What They Never End In](https://ipmatway.com/learn/number-system/classification/perfect-square-properties) · [Rational or Irrational?](https://ipmatway.com/learn/number-system/classification/rational-irrational) · [What Can a Square End In?](https://ipmatway.com/learn/number-system/classification/squares-ending-digits) · [Terminating Decimals: The 2-5 Test](https://ipmatway.com/learn/number-system/classification/terminating-decimals) · [Parity Statements](https://ipmatway.com/learn/number-system/classification/parity-statements)

## Simplification and Approximation (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/simplification

Idea: Simplification items reward discipline: the order of operations, exact fraction arithmetic, decimal approximations to the right number of places, and recognising geometric power sums. Rohtak and JIPMAT ask them directly; Indore hides them inside longer questions.
Exam method: 1. Rohtak 2019. 18800÷470÷20: left to right, 40÷20=2. 2. Rohtak 2019 symbol swap. 43+561×500÷100-10=43+2805-10=2838. 3. Rohtak 2019. 0.0056=(7)/(1250); a second is 136000.00028 of an hour. 4. Rohtak 2020. 316^2=99856, 317^2=100489; 316+(143)/(632)316.226316.23. 5. JIPMAT 2024 Q2. decimals 0.533,0.556,0.636,0.647: (C), (A), (B), (D) ascending. 6. Rohtak 2019. B=2^65-1, so A is larger by 1.
Traps: Right-to-left division; truncation; wrong recurring denominator; numerator-only comparison; 2^n vs 2^n-1.

Lessons: [Simplification and Approximation: start here](https://ipmatway.com/learn/number-system/simplification/start-here) · [BODMAS: Chained Division](https://ipmatway.com/learn/number-system/simplification/bodmas) · [Square and Cube Roots, Fast](https://ipmatway.com/learn/number-system/simplification/square-cube-roots) · [Fraction Ordering: 3-Decimal Trick](https://ipmatway.com/learn/number-system/simplification/fraction-ordering) · [Symbol Swap: Decode First, Then BODMAS](https://ipmatway.com/learn/number-system/simplification/operator-substitution) · [Surds: Rationalize and Telescope](https://ipmatway.com/learn/number-system/simplification/surd-approximation) · [Recurring Decimal to Fraction](https://ipmatway.com/learn/number-system/simplification/recurring-decimal-fraction) · [Decimal to Fraction in One Move](https://ipmatway.com/learn/number-system/simplification/decimal-fraction-conversion) · [Power Sum Identities](https://ipmatway.com/learn/number-system/simplification/power-sum-identities)

## Number Bases (Number System, Quant)
Source: https://ipmatway.com/learn/number-system/base-system

Idea: A numeral in base b is a polynomial in b with digit coefficients below b. Conversions, digit counts and 'find the base' questions all come from this single expansion.
Exam method: 1. (273)8=187; 187 in base 8: 187=8·23+3, 23=8·2+7, 2=8·0+2 gives 273. 2. (25)x=85: 2x+5=85, x=40. 3. (25)n(31)n=(1015)n: (2n+5)(3n+1)=n^3+n+5, n(n-8)(n+2)=0, n=8. 4. 1777 in base x with five digits: x^41777<x^5 gives x=5 or 6; least 5. 5. Numbers below 1000 using only 0 and 1: 1,10,11,100,101,110,111 - seven (2^3-1).
Traps: Reversed remainders; decimal place values; invalid digits; digit-count off by one.

Lessons: [Number Bases: start here](https://ipmatway.com/learn/number-system/base-system/start-here) · [Decimal to Base b: Fast Conversion](https://ipmatway.com/learn/number-system/base-system/decimal-to-base) · [Base to Decimal in Seconds](https://ipmatway.com/learn/number-system/base-system/base-to-decimal) · [Numbers Using Only Digits 0 and 1](https://ipmatway.com/learn/number-system/base-system/binary-digit-numbers) · [Find the Unknown Base](https://ipmatway.com/learn/number-system/base-system/unknown-base-equation) · [Digit Count in Base b](https://ipmatway.com/learn/number-system/base-system/digit-count-in-base) · [Last Digits in Base b](https://ipmatway.com/learn/number-system/base-system/last-digits-in-base)

## HCF and LCM Basics (HCF and LCM, Quant)
Source: https://ipmatway.com/learn/hcf-lcm/basics

Idea: The HCF is the largest number dividing all the given numbers (the common primes at their lowest powers); the LCM is the smallest number they all divide (all primes at their highest powers). For two numbers the two multiply to the product. Everything else in the chapter is this idea plus one translation step (fractions, decimals, ratios, powers).
Exam method: 1. Product rule in one line. HCF 6, LCM 210, x+y=72 ⇒ 1x+1y=(72)/(1260)=235. 2. Identity in words. "square of the sum minus square of the difference, divided by four" =ab= HCF × LCM. Test with 6 and 4 if unsure. 3. Fractions. reduce, then HCF =HCF(2,2,8)LCM(3,3,27)=227; the LCM-formula value 83 is the standard wrong option. 4. LCM is k× HCF. h+12h=403 ⇒ h=31, LCM 372, other =(31·372)/(93)=124. 5. Eliminate by divisibility. the other number must be divisible by the HCF and must divide the LCM.
Traps: Product rule misapplied to three numbers; fraction formulas swapped; unreduced fractions; HCF and LCM reported for each other.

Lessons: [HCF and LCM Basics: start here](https://ipmatway.com/learn/hcf-lcm/basics/start-here) · [HCF and LCM by prime factors](https://ipmatway.com/learn/hcf-lcm/basics/prime-factorisation) · [HCF times LCM equals the product](https://ipmatway.com/learn/hcf-lcm/basics/product-rule) · [HCF and LCM of fractions](https://ipmatway.com/learn/hcf-lcm/basics/hcf-lcm-of-fractions) · [HCF by Division: The Difference Trick](https://ipmatway.com/learn/hcf-lcm/basics/hcf-by-division) · [HCF and LCM of Decimals](https://ipmatway.com/learn/hcf-lcm/basics/hcf-lcm-of-decimals) · [Ratio and HCF: the hidden multiplier](https://ipmatway.com/learn/hcf-lcm/basics/ratio-and-hcf) · [HCF of a^m − 1 and a^n − 1](https://ipmatway.com/learn/hcf-lcm/basics/hcf-of-powers-minus-one) · [LCM is k Times HCF](https://ipmatway.com/learn/hcf-lcm/basics/lcm-multiple-of-hcf) · [LCM of 1 to n](https://ipmatway.com/learn/hcf-lcm/basics/lcm-of-first-n)

## HCF and LCM Applications (HCF and LCM, Quant)
Source: https://ipmatway.com/learn/hcf-lcm/applications

Idea: Two questions hide behind every word problem: "what is the largest thing that fits into all of these?" (HCF) and "when do these cycles line up / what is the smallest number all of these divide?" (LCM). Remainders shift the answer by a constant; bounds (four-digit, five-digit) pick a particular multiple; counting pairs or co-primes uses the prime structure of the quotient.
Exam method: 1. JIPMAT 2024 Q7. LCM(12,21,35)=420, +6 → 426. The option 43 is HCF-style noise. 2. JIPMAT 2025 Q30. LCM(8,12,20,28,35)=840, x=845, digit sum 17. 3. JIPMAT 2025 Q18. LCM(48,72,108)=432 s → 08:20:00+7:12=08:27:12. Convert seconds to min:sec before adding. 4. Indore 2026 (memory-based). (n,10^7)=10^3 ⇒ n=10^3m, m10^4, (m,10^4)=1 ⇒ (10^4)=4000. 5. Pairs. product 5400, HCF 30 ⇒ ab=6 co-prime ⇒ (1,6),(2,3) ⇒ 2 pairs. HCF 5, sum 50 ⇒ co-prime splits of 10: 1+9, 3+7 ⇒ 2 pairs. 6. Greatest n-digit. 99999-9999972=99936; +5 ⇒ 99941 (still five digits).
Traps: h vs h^2; ordered vs unordered; deficit sign; digit overflow; start counted in bell problems.

Lessons: [HCF and LCM Applications: start here](https://ipmatway.com/learn/hcf-lcm/applications/start-here) · [Same Remainder: HCF of Differences](https://ipmatway.com/learn/hcf-lcm/applications/same-remainder) · [Remainder patterns: LCM plus r, minus d](https://ipmatway.com/learn/hcf-lcm/applications/remainder-pattern-n-minus-r) · [Bells Tolling: LCM of Intervals](https://ipmatway.com/learn/hcf-lcm/applications/bells-tolling) · [Max tile size: HCF in disguise](https://ipmatway.com/learn/hcf-lcm/applications/max-tile-size) · [Co-prime Pairs: Counting with HCF](https://ipmatway.com/learn/hcf-lcm/applications/co-prime-pairs) · [HCF and Sum: Find the Two Numbers](https://ipmatway.com/learn/hcf-lcm/applications/sum-of-numbers-given-hcf) · [Least Perfect Square Multiple](https://ipmatway.com/learn/hcf-lcm/applications/least-perfect-square-multiple) · [N-Digit Number Divisible by a Set](https://ipmatway.com/learn/hcf-lcm/applications/n-digit-number-divisible-by-set) · [Counting numbers with a given gcd](https://ipmatway.com/learn/hcf-lcm/applications/count-with-given-gcd)

## Linear Equations (Linear and Quadratic Equations, Quant)
Source: https://ipmatway.com/learn/linear-quadratic/linear

Idea: A linear equation in two unknowns is a straight line; two such equations meet in one point, never meet (parallel) or coincide. Word problems are translated into two (or three) such equations; a question often wants a combination that can be read off without finding every unknown.
Exam method: 1. Add / subtract first. symmetric or swapped coefficients give x+y and x-y directly. 2. Combination trick. for 2x+3y-z=10 and x-y+2z=5, the target 7x+3y+4z=2(first)+3(second)=35. 3. Options as a check. plug the options into both equations; most linear MCQs fall in under 30 seconds.
Traps: Forgetting to collect terms before comparing ratios; answering a single unknown when a combination is asked.

Lessons: [Linear Equations: start here](https://ipmatway.com/learn/linear-quadratic/linear/start-here) · [Two-Variable Word Problems](https://ipmatway.com/learn/linear-quadratic/linear/two-variable-word) · [Parameter → Infinite / No Solution](https://ipmatway.com/learn/linear-quadratic/linear/parameter-infinite-no-solution) · [Temperature Scale Recording Error](https://ipmatway.com/learn/linear-quadratic/linear/temperature-scale-conversion) · [Three Variables, One Target](https://ipmatway.com/learn/linear-quadratic/linear/three-variable-system) · [Consistency: How Many Solutions?](https://ipmatway.com/learn/linear-quadratic/linear/consistency) · [Linear Combination Trick](https://ipmatway.com/learn/linear-quadratic/linear/linear-combination-trick) · [Symmetric Coefficient System](https://ipmatway.com/learn/linear-quadratic/linear/symmetric-coefficient-system) · [Digit & Fraction Word Problems](https://ipmatway.com/learn/linear-quadratic/linear/digit-fraction-word)

## Quadratic Equations (Linear and Quadratic Equations, Quant)
Source: https://ipmatway.com/learn/linear-quadratic/quadratic

Idea: A quadratic ax^2+bx+c=0 (a0) has two roots whose sum -(b)/(a) and product (c)/(a) are visible in the coefficients. Almost every IPMAT quadratic question is answered from these two numbers and the discriminant b^2-4ac - the roots themselves are seldom needed.
Exam method: 1. Read Vieta first. (-)^2=(+)^2-4; roots differing by 2 means b^2-4c=4 for x^2+bx+c. 2. Ratio m:n. take roots mk and nk; two Vieta equations eliminate k. 3. Common root. subtract the equations to get the common root, or test the roots of the equation that factors. 4. Options. substitute candidate roots - most MCQs need one substitution.
Traps: Sign of -(b)/(a); a vanishing leading coefficient; parameter values that make the roots non-real.

Lessons: [Quadratic Equations: start here](https://ipmatway.com/learn/linear-quadratic/quadratic/start-here) · [Sum and Product of Roots](https://ipmatway.com/learn/linear-quadratic/quadratic/sum-product-of-roots) · [Roots Without Finding Roots](https://ipmatway.com/learn/linear-quadratic/quadratic/symmetric-functions-of-roots) · [Roots in a Ratio](https://ipmatway.com/learn/linear-quadratic/quadratic/roots-in-ratio) · [Discriminant: Read the Roots](https://ipmatway.com/learn/linear-quadratic/quadratic/nature-of-roots-discriminant) · [Common Root: Test Both](https://ipmatway.com/learn/linear-quadratic/quadratic/common-root) · [Forming Equation from Roots](https://ipmatway.com/learn/linear-quadratic/quadratic/forming-equation-from-roots) · [Harmonic Mean of Roots](https://ipmatway.com/learn/linear-quadratic/quadratic/harmonic-mean-of-roots) · [Count Integer Roots, Not Candidates](https://ipmatway.com/learn/linear-quadratic/quadratic/integral-solutions-of-quadratic) · [Wrong Copy, Right Clue](https://ipmatway.com/learn/linear-quadratic/quadratic/misread-coefficient) · [Where Are the Roots?](https://ipmatway.com/learn/linear-quadratic/quadratic/root-location-parameter) · [Conjugate Surd Roots](https://ipmatway.com/learn/linear-quadratic/quadratic/conjugate-surd-roots) · [Words Into Quadratics](https://ipmatway.com/learn/linear-quadratic/quadratic/quadratic-word-problem)

## Higher-Degree Equations (Linear and Quadratic Equations, Quant)
Source: https://ipmatway.com/learn/linear-quadratic/higher-degree

Idea: Higher-degree equations in IPMAT are either Vieta questions (sum, product, sum of squares of the roots read off the coefficients) or equations that collapse to a quadratic after a substitution (u=x^2, u=x^2+kx, symmetric shifts). Roots of x^n+·s+1 are roots of unity, so their powers cycle.
Exam method: 1. Vieta at sight. for x^3-6x^2+11x-6 the sum is 6, pairs 11, product 6; sum of squares 36-22=14. 2. Shift to symmetry. average the two bases (x^2-5 and x^2-7 about x^2-6) so odd powers cancel. 3. Roots of unity. x^9=1 for every root of x^8+·s+1, so reduce the exponent mod 9.
Traps: Product sign for odd degree; dropping r<0; counting x from u=x^2.

Lessons: [Higher-Degree Equations: start here](https://ipmatway.com/learn/linear-quadratic/higher-degree/start-here) · [Roots in GP: Keep Both Signs](https://ipmatway.com/learn/linear-quadratic/higher-degree/roots-in-gp) · [Roots of Unity: Power Sums](https://ipmatway.com/learn/linear-quadratic/higher-degree/roots-of-unity-sum-of-powers) · [Vieta: Read Roots, Don't Solve](https://ipmatway.com/learn/linear-quadratic/higher-degree/vieta-cubic) · [Max Minus Min Root: Symmetry Shift](https://ipmatway.com/learn/linear-quadratic/higher-degree/max-min-root-difference) · [Polynomial from Given Roots](https://ipmatway.com/learn/linear-quadratic/higher-degree/polynomial-with-given-roots) · [Quadratics in Disguise](https://ipmatway.com/learn/linear-quadratic/higher-degree/reducible-to-quadratic)

## Exponential Equations (Linear and Quadratic Equations, Quant)
Source: https://ipmatway.com/learn/linear-quadratic/exponential-equations

Idea: An exponential equation is solved either by making both sides powers of one base and equating exponents, or by substituting t=a^x to get an ordinary (usually quadratic) equation in t0. Counting questions rely on monotonicity and on the positivity of a^x.
Exam method: 1. Trial plus monotonicity. guess a small integer and argue uniqueness from increasing functions. 2. Case analysis for A^B=1. list the three cases and check each candidate. 3. Count, don't solve. the number of real solutions equals the number of positive roots of the t-quadratic.
Traps: Negative t; forgotten cases in A^B=1; unequal bases.

Lessons: [Exponential Equations: start here](https://ipmatway.com/learn/linear-quadratic/exponential-equations/start-here) · [Same Base, Then Exponents](https://ipmatway.com/learn/linear-quadratic/exponential-equations/same-base-equate-exponents) · [Turn Powers into a Quadratic](https://ipmatway.com/learn/linear-quadratic/exponential-equations/substitution-quadratic-in-exponential) · [Count Real Solutions](https://ipmatway.com/learn/linear-quadratic/exponential-equations/count-real-solutions) · [Exponential Terms in AP](https://ipmatway.com/learn/linear-quadratic/exponential-equations/exponents-in-ap) · [When a Power Equals 1](https://ipmatway.com/learn/linear-quadratic/exponential-equations/power-equals-one-cases)

## Inequalities (Inequalities and Modulus, Quant)
Source: https://ipmatway.com/learn/inequalities-modulus/inequalities

Idea: An inequality is solved like an equation, but the direction changes whenever both sides are multiplied or divided by a negative number. For polynomial and rational inequalities, everything is moved to one side and the sign of the expression is tracked between its critical points (the zeros of the numerator and the denominator).
Exam method: 1. Never cross-multiply. an unknown sign: subtract and combine instead. 2. One test point per region. of the sign chart; even powers keep the sign. 3. Option elimination. test a value such as x=0 or an end point against all four interval options. 4. For all x. leading coefficient sign plus a negative discriminant. 5. Base below 1. compare exponents with the sign reversed.
Traps: Cross-multiplying by an expression of unknown sign; including denominator zeros; even powers read as sign changes. Base between 0 and 1 without reversing; squaring √(f)g without the case g<0.

Lessons: [Inequalities: start here](https://ipmatway.com/learn/inequalities-modulus/inequalities/start-here) · [Quadratic Inequalities](https://ipmatway.com/learn/inequalities-modulus/inequalities/quadratic-inequality) · [Wavy Curve: Flip or Stay?](https://ipmatway.com/learn/inequalities-modulus/inequalities/rational-inequality-wavy-curve) · [Largest Interval, Not Total Length](https://ipmatway.com/learn/inequalities-modulus/inequalities/interval-length) · [AM-GM: Minimum or Maximum?](https://ipmatway.com/learn/inequalities-modulus/inequalities/am-gm-min-max) · [Range of Quadratic over Quadratic](https://ipmatway.com/learn/inequalities-modulus/inequalities/bounded-rational-parameter) · [Counting Integer Solutions](https://ipmatway.com/learn/inequalities-modulus/inequalities/integer-solutions-count) · [Exponential Inequalities](https://ipmatway.com/learn/inequalities-modulus/inequalities/exponential-inequality) · [Linear Inequalities: Flip or Keep?](https://ipmatway.com/learn/inequalities-modulus/inequalities/linear-inequality) · [One Sign for Every x](https://ipmatway.com/learn/inequalities-modulus/inequalities/sign-for-all-x-parameter) · [Symmetric Expression Ranges](https://ipmatway.com/learn/inequalities-modulus/inequalities/symmetric-expression-range) · [Compare Expressions by Sign](https://ipmatway.com/learn/inequalities-modulus/inequalities/compare-expressions-by-sign) · [Root Inequalities: Before Squaring](https://ipmatway.com/learn/inequalities-modulus/inequalities/root-inequality)

## Modulus (Absolute Value) (Inequalities and Modulus, Quant)
Source: https://ipmatway.com/learn/inequalities-modulus/modulus

Idea: |x-a| is the distance between x and a on the number line. Most modulus questions become easy in this picture: sums of moduli are sums of distances, and |E|<c says E lies within c of 0. Algebraically, every modulus is removed by splitting the line at its zero.
Exam method: 1. Median rule. |x-pi| is least at the median (weights = repeated points). 2. Distance reading. |x-1|+|x-3|=2 has every x[1,3] as a solution. 3. Betweenness. |a-b|+|b-c|=|a-c| means b lies between a and c. 4. Zero sum. a sum of moduli, squares and roots is 0 only when every term is 0. 5. Count signs carefully. (|x|,|y|) solutions, then ×2 for each non-zero coordinate.
Traps: Negative values of a modulus kept; one branch of |E|c dropped. Mean instead of median; weights ignored; zero counted with two signs.

Lessons: [Modulus (Absolute Value): start here](https://ipmatway.com/learn/inequalities-modulus/modulus/start-here) · [Sum of Distances: Stand at the Median](https://ipmatway.com/learn/inequalities-modulus/modulus/sum-of-abs-minimum) · [Count Modulus Solutions](https://ipmatway.com/learn/inequalities-modulus/modulus/abs-equation-solutions) · [Modulus Inequalities](https://ipmatway.com/learn/inequalities-modulus/modulus/abs-inequality) · [Modulus Fractions: Count Integers](https://ipmatway.com/learn/inequalities-modulus/modulus/abs-rational-inequality-integers) · [Non-negative Sum Equals Zero](https://ipmatway.com/learn/inequalities-modulus/modulus/abs-system-with-quadratic) · [Distinct Naturals and Modulus](https://ipmatway.com/learn/inequalities-modulus/modulus/distinct-naturals-abs-identity) · [Weighted Median Minimum](https://ipmatway.com/learn/inequalities-modulus/modulus/weighted-median-minimum) · [Quadratics Hidden in Modulus](https://ipmatway.com/learn/inequalities-modulus/modulus/abs-quadratic-roots) · [Nested Moduli: Peel Outside First](https://ipmatway.com/learn/inequalities-modulus/modulus/nested-abs) · [Integer Pairs: |x| + |y| = k](https://ipmatway.com/learn/inequalities-modulus/modulus/abs-integer-pairs) · [Modulus Systems: Check the Signs](https://ipmatway.com/learn/inequalities-modulus/modulus/abs-linear-system) · [Triangle Inequality: Equality Cases](https://ipmatway.com/learn/inequalities-modulus/modulus/triangle-inequality-abs)

## Floor and Fractional Part (Inequalities and Modulus, Quant)
Source: https://ipmatway.com/learn/inequalities-modulus/floor-fractional

Idea: Every real number splits into an integer part [x] (the greatest integer not exceeding x) and a fractional part \x\=x-[x] in [0,1). Floor problems are solved by naming these two parts and using the single condition 0≤\x\<1.
Exam method: 1. Small-case check. in parametric answers (n), put n=1 or 2 and compare options. 2. Blocks. [√(k)] is constant on j^2≤ k<(j+1)^2; [k/m] on runs of length m. 3. Negative numbers. [-2.7]=-3, not -2.
Traps: [x]=k read as x=k; \x\=1 allowed; x=0 forgotten. The last block of a floor sum treated as complete.

Lessons: [Floor and Fractional Part: start here](https://ipmatway.com/learn/inequalities-modulus/floor-fractional/start-here) · [Floor Equations: the k + f Trick](https://ipmatway.com/learn/inequalities-modulus/floor-fractional/floor-equation) · [Fractional Part Equations](https://ipmatway.com/learn/inequalities-modulus/floor-fractional/fractional-part-equation) · [Floor Counting: Count the Blocks](https://ipmatway.com/learn/inequalities-modulus/floor-fractional/floor-counting) · [Quadratics Inside the Floor](https://ipmatway.com/learn/inequalities-modulus/floor-fractional/floor-quadratic) · [Floor Sums: Count the Blocks](https://ipmatway.com/learn/inequalities-modulus/floor-fractional/floor-sum-series)

## Algebraic Identities (Algebraic Identities and Polynomials, Quant)
Source: https://ipmatway.com/learn/identities-polynomials/identities

Idea: Most identity questions give a few symmetric values (a sum, a product, a sum of squares) and ask for another symmetric expression. Express the target through the given values with the standard expansions; the individual numbers are never needed.
Exam method: 1. Two variables. get xy first, then x^2+y^2, then any higher power (x^4+y^4=(x^2+y^2)^2-2(xy)^2). 2. Reciprocals. everything in x±(1)/(x) follows by repeated squaring or cubing. 3. Zero sums. look for a+b+c=0 hidden in bracket differences like (p-q)+(q-r)+(r-p). 4. Test values. for conditional identities pick numbers that satisfy the condition.
Traps: Missing correction terms; the false a^3+b^3+c^3=0; sign of negative bases.

Lessons: [Algebraic Identities: start here](https://ipmatway.com/learn/identities-polynomials/identities/start-here) · [Squares and Cubes Without Roots](https://ipmatway.com/learn/identities-polynomials/identities/sum-cube-from-sum-product) · [Powers of x plus 1 by x](https://ipmatway.com/learn/identities-polynomials/identities/a-plus-1-by-a-powers) · [Zero Sum, Triple Product](https://ipmatway.com/learn/identities-polynomials/identities/cyclic-a-b-c-zero) · [Difference of Squares Telescoping](https://ipmatway.com/learn/identities-polynomials/identities/difference-of-squares-telescoping) · [Spot the Hidden Identity](https://ipmatway.com/learn/identities-polynomials/identities/algebraic-simplification) · [Sum of Squares Equal to Zero](https://ipmatway.com/learn/identities-polynomials/identities/sum-of-squares-zero) · [Three Variables, Shared Shortcuts](https://ipmatway.com/learn/identities-polynomials/identities/three-variable-symmetric) · [Higher Powers, Smaller Steps](https://ipmatway.com/learn/identities-polynomials/identities/higher-power-sums) · [Cube Root Sum: the 3uvx Trick](https://ipmatway.com/learn/identities-polynomials/identities/cube-root-sum-identity) · [Homogeneous Equations to Ratios](https://ipmatway.com/learn/identities-polynomials/identities/homogeneous-equation-ratio) · [Use the Condition First](https://ipmatway.com/learn/identities-polynomials/identities/conditional-expression-value) · [Spot the Hidden Factors](https://ipmatway.com/learn/identities-polynomials/identities/standard-factorisations)

## Polynomials and Remainder Theorem (Algebraic Identities and Polynomials, Quant)
Source: https://ipmatway.com/learn/identities-polynomials/polynomials

Idea: A polynomial's value at u is its remainder on division by x-u; it vanishes there exactly when x-u is a factor. With these two facts almost every remainder, factor and common-factor question becomes a short system of linear equations in the unknown coefficients.
Exam method: 1. Unknown coefficients. one condition per unknown - f(u)=r for a remainder, f(u)=0 for a factor. 2. Quadratic divisors. the remainder is the line through the points (u,f(u)) and (v,f(v)). 3. Options. test the options by substituting a root; do not divide.
Traps: Wrong sign of the root; constant remainders for quadratic divisors; turning points counted as zeros.

Lessons: [Polynomials and Remainder Theorem: start here](https://ipmatway.com/learn/identities-polynomials/polynomials/start-here) · [Unknown Coefficient: Remainder Theorem](https://ipmatway.com/learn/identities-polynomials/polynomials/remainder-theorem-unknown-coefficient) · [Remainder by a Quadratic: It's a Line](https://ipmatway.com/learn/identities-polynomials/polynomials/remainder-by-product-of-linears) · [Factor Theorem: Make It Zero](https://ipmatway.com/learn/identities-polynomials/polynomials/factor-theorem) · [Common Factor, Common Root](https://ipmatway.com/learn/identities-polynomials/polynomials/common-factor-of-two-polynomials) · [Big Powers, Small Replacements](https://ipmatway.com/learn/identities-polynomials/polynomials/polynomial-divisibility-pattern) · [Sum of Coefficients](https://ipmatway.com/learn/identities-polynomials/polynomials/sum-of-coefficients) · [Compare Coefficients](https://ipmatway.com/learn/identities-polynomials/polynomials/compare-coefficients) · [Zeros from a Graph](https://ipmatway.com/learn/identities-polynomials/polynomials/zeros-from-graph) · [GCD and LCM of Polynomials](https://ipmatway.com/learn/identities-polynomials/polynomials/polynomial-gcd-lcm)

## Maxima and Minima in Algebra (Algebraic Identities and Polynomials, Quant)
Source: https://ipmatway.com/learn/identities-polynomials/max-min-algebra

Idea: Algebraic extrema come from three tools: completing the square (quadratics, and quartics that are quadratics in x^2 or in a paired product), AM-GM (positive terms with a fixed product or a fixed sum) and squares being non-negative (bounds such as ab+bc+ca≤ a^2+b^2+c^2).
Exam method: 1. Quadratic. vertex value c-b^24a at once. 2. AM-GM. equal terms; for px+(q)/(x) the minimum is 2√(pq). 3. Fixed sum. make the parts equal (after removing coefficients). 4. Parameters that cancel. if the answer cannot depend on a parameter, test one convenient value (a=1).
Traps: Point versus value; AM-GM without a constant product; forgotten domain conditions.

Lessons: [Maxima and Minima in Algebra: start here](https://ipmatway.com/learn/identities-polynomials/max-min-algebra/start-here) · [Complete the Square, Find the Limit](https://ipmatway.com/learn/identities-polynomials/max-min-algebra/complete-square-min) · [AM-GM: Spot the Minimum](https://ipmatway.com/learn/identities-polynomials/max-min-algebra/am-gm-two-terms) · [Fixed Sum, Biggest Product](https://ipmatway.com/learn/identities-polynomials/max-min-algebra/product-fixed-sum-max) · [Find the Hidden Quadratic](https://ipmatway.com/learn/identities-polynomials/max-min-algebra/min-of-polynomial-expression) · [Symmetric Sum Bounds](https://ipmatway.com/learn/identities-polynomials/max-min-algebra/symmetric-sum-bounds)

## Indices (Exponents) (Surds and Indices, Quant)
Source: https://ipmatway.com/learn/surds-indices/indices

Idea: Indices questions are about rewriting: get every quantity to a single base (usually a prime), then the exponent laws turn the problem into ordinary algebra on the exponents. Comparison, equations, inequalities and divisibility all follow the same rewrite-first rule.
Exam method: 1. Indore 2019 Q50 / 2024 Q33. 2^300=8^100, 3^200=9^100, 4^100; the sum 2^100+3^100<2·3^1009^100. Answer 3^200. 2. Indore 2019 Q30. 0.343=0.7^3; base 3 ⇒ (2x-1)(x-1)0 ⇒ x1. Test x=0 to confirm the outside region. 3. Indore 2025 Q5. t=3^10; t^3+8 has the factor t+2. Substituting t=-2 kills the other options instantly. 4. Rohtak 2019 Q47. 25^2.7=5^5.4; 5.4+4.2-5.4=4.2. 5. JIPMAT 2024 Q9. the numerator 0.5+0.2+0.3-1=0 — do not compute the denominator. 6. JIPMAT 2021 Q8. 2·3=6 with 6^-z ⇒ 1x+1y=-1z ⇒ sum 0.
Traps: Exponent-of-exponent confusion; unequal bases; inequality not flipped; wrong quantity reported (y vs x); extraneous roots.

Lessons: [Indices (Exponents): start here](https://ipmatway.com/learn/surds-indices/indices/start-here) · [Laws of Exponents](https://ipmatway.com/learn/surds-indices/indices/laws-of-exponents) · [Compare Powers Without Calculating](https://ipmatway.com/learn/surds-indices/indices/comparison-of-powers) · [Solve for the Exponent](https://ipmatway.com/learn/surds-indices/indices/solve-for-exponent) · [Fractional and Negative Powers](https://ipmatway.com/learn/surds-indices/indices/simplify-expression) · [Exponents Hiding a Quadratic](https://ipmatway.com/learn/surds-indices/indices/exponential-quadratic) · [Reciprocal Exponent Sums](https://ipmatway.com/learn/surds-indices/indices/reciprocal-exponent-sums) · [Exponent Inequalities](https://ipmatway.com/learn/surds-indices/indices/exponent-inequality) · [Power Sums: Spot the Factor](https://ipmatway.com/learn/surds-indices/indices/divisibility-of-power-sums) · [Symmetric Exponent Values](https://ipmatway.com/learn/surds-indices/indices/symmetric-exponent-values)

## Surds (Surds and Indices, Quant)
Source: https://ipmatway.com/learn/surds-indices/surds

Idea: Surds behave like algebraic symbols with one extra rule: a product of conjugates is rational. Every technique in this block — rationalising, splitting √(a+2 b), collapsing nested roots, telescoping — uses that rule to turn irrational-looking expressions into something exact.
Exam method: 1. JIPMAT 2023 Q2. √(3+5) → double inside: √((6+25)/(2))=(5+1)/(2) → square option B to confirm (3+5). 2. JIPMAT 2025 Q17. last two factors give √(4-u^2)=2-√(2+3); collapse again → √(2-3); with the first factor → 1. 3. JIPMAT 2022 Q7. 8-2√(15)=5-3, 11+2√(30)=6+5; the two fractions become 4+√(15) and 11+2√(30). 4. JIPMAT 2026. √(n+1)-√(n-1)=2√(n+1)+√(n-1) — smallest n is largest: C, D, B, A. 5. Estimation. √(7+43)√(13.93)3.73=2+1.73 — confirms 2+3 in five seconds.
Traps: Sign in the split; radicand comparison; negative root kept; missing 12; monotonic direction reversed.

Lessons: [Surds: start here](https://ipmatway.com/learn/surds-indices/surds/start-here) · [Rationalisation: Flip the Sign](https://ipmatway.com/learn/surds-indices/surds/rationalisation) · [Nested Radicals: Work Inward](https://ipmatway.com/learn/surds-indices/surds/nested-radicals) · [Compare Surds Without Decimals](https://ipmatway.com/learn/surds-indices/surds/surd-comparison) · [Splitting Square Roots](https://ipmatway.com/learn/surds-indices/surds/sqrt-of-a-plus-sqrt-b) · [Telescoping Surd Series](https://ipmatway.com/learn/surds-indices/surds/telescoping-surd-series) · [Conjugate Powers](https://ipmatway.com/learn/surds-indices/surds/conjugate-powers) · [Infinite Roots, Finite Answers](https://ipmatway.com/learn/surds-indices/surds/infinite-nested-radical) · [Ordering Root Differences](https://ipmatway.com/learn/surds-indices/surds/root-difference-ordering)

## Log Laws and Evaluation (Logarithms, Quant)
Source: https://ipmatway.com/learn/logarithms/basics

Idea: A logarithm is an exponent: a N=x a^x=N. All laws are the exponent laws rewritten. Indore asks 2–4 log questions a year, more than any other single algebra topic, and the SA section likes them because the answers are small integers.
Exam method: 1. Prime-base reduction. Convert every number to powers of 2, 3, 5, 7; logs of smooth numbers become linear in x=2 3 (or 2 5). 2. Chain and reciprocal collapses. a b·b c=a c; 1a N=N a. 3. "1+" trick. 1+B(y)=B(By). Turns 11+a^2b(c/a) into abc(a^2b) instantly. 4. Digits. n10a+1. For 2^n and 5^n together: n+1 digits, no tables needed. 5. Option scan. In "express in terms of p" questions, test p with actual numbers: e.g. 1824=p1.10; evaluate the target numerically and match. 6. Power with a log exponent. x^ba=a^bx, so terms like 3x^52+2^5x merge into one. Indore 2024 SA: 4^2x=x^2 turns the equation into a sum of squares. 7. Compare logs. by trapping each between integers (17275<2<19375) or half-integers (square both sides: 310<2.5 because 100<3^5). 8. k-method. Equal ratios of logs: set each equal to k and add; cyclic sums vanish, so products like xyz equal 1. 9. Hidden square. a^2+4b^2=12ab⇒(a+2b)^2=16ab⇒(a+2b)/(4)=12( a+ b). 10. Least value. ab+ba2 for a,b1; with a coefficient, t+ ct2 c. For 0<x<1 the log is negative and the bound becomes a maximum of -2.
Traps: a^k divides by k — forgetting it is the top error in "express in terms of p". 2+ 3= 6, not 5. In digit counts use floor then +1; never round the mantissa.

Lessons: [Log Laws and Evaluation: start here](https://ipmatway.com/learn/logarithms/basics/start-here) · [Log Laws: Split or Merge](https://ipmatway.com/learn/logarithms/basics/laws-product-quotient-power) · [Change the Base, Keep the Value](https://ipmatway.com/learn/logarithms/basics/change-of-base) · [Evaluate Logs by Their Structure](https://ipmatway.com/learn/logarithms/basics/evaluation-of-expression) · [Express Logs in Terms of p](https://ipmatway.com/learn/logarithms/basics/express-in-terms-of-p) · [Log Sums That Cancel](https://ipmatway.com/learn/logarithms/basics/log-sum-telescoping) · [Logs: Count Digits, Not Powers](https://ipmatway.com/learn/logarithms/basics/characteristic-digit-count) · [When a Log Is the Exponent](https://ipmatway.com/learn/logarithms/basics/base-power-identity) · [Compare Logs with Different Bases](https://ipmatway.com/learn/logarithms/basics/compare-and-estimate) · [K Method: Make the Logs Cancel](https://ipmatway.com/learn/logarithms/basics/k-method-identities) · [Spot the Hidden Square](https://ipmatway.com/learn/logarithms/basics/identity-to-log) · [Min-Max with Logs](https://ipmatway.com/learn/logarithms/basics/min-max-with-logs)

## Logarithmic Equations (Logarithms, Quant)
Source: https://ipmatway.com/learn/logarithms/equations

Idea: Log equations are solved by one of three moves: unwrap (nested), substitute t=b x (quadratic in a log), or exploit symmetry (x y+y x). The answer is almost always a small power of the base — use that to sanity-check.
Exam method: 1. Nested: peel from the outside; each layer is one line. 2. Quadratic in t: read sum/product of t-roots from the coefficients; x-product =b^sum. 3. x^b x=: take b of both sides. 4. Symmetric: x y+y x=2⇒ x=y; then the second equation is ordinary algebra. 5. Back-substitute options for MCQs (bases 2, 3, 5 make it fast). 6. Domain kills roots. After combining logs, solve, then reject every root that makes an original argument 0 or a base 0 or =1. 7. Different bases. 9(x-2)=3(x-4)⇒ x-2=(x-4)^2; then keep only x4 (one solution, x=6). 8. How many solutions?. Increasing vs decreasing: at most one. Concave log vs a line: at most two. A tangent line touches once — x=x-1 has exactly one root.
Traps: Taking a Y=0 as Y=0. Forgetting the 12 from a squared base. Keeping x=-5 as a solution of x^2-x-30=0 when x is a log base.

Lessons: [Logarithmic Equations: start here](https://ipmatway.com/learn/logarithms/equations/start-here) · [Nested Logs: Outside First](https://ipmatway.com/learn/logarithms/equations/nested-log-equation) · [Log-Exponential Mixed Equations](https://ipmatway.com/learn/logarithms/equations/log-exponential-mixed) · [Log Quadratic: Product of Roots](https://ipmatway.com/learn/logarithms/equations/log-quadratic-product-of-roots) · [Simultaneous Log Equations](https://ipmatway.com/learn/logarithms/equations/simultaneous-log-linear) · [Variable Base Equations](https://ipmatway.com/learn/logarithms/equations/variable-base-equation) · [Log Equations: Check Every Root](https://ipmatway.com/learn/logarithms/equations/basic-log-equation) · [Count Crossings, Not Just Roots](https://ipmatway.com/learn/logarithms/equations/number-of-solutions-graphical)

## Logarithmic Inequalities (Logarithms, Quant)
Source: https://ipmatway.com/learn/logarithms/inequalities

Idea: Logs with base 1 preserve order; base in (0,1) reverses it. A log inequality is therefore an ordinary inequality on the argument plus the domain condition "argument 0". Indore has asked one in 2019 (twice), 2022 and 2025.
Exam method: 1. Turn a X1) in one step. 2. Rational argument: solve the two linear inequalities from the sandwich separately, intersect on a number line. 3. Base in (0,1): sandwich becomes a^k0 automatic... except for "": a Xk0<X<a^k. 4. Variable base: check sign of the base before anything else; if it must be negative for the bound to hold, the answer is the empty set. 5. Range questions. Find the values of the inside first (Indore 2022: 81^f=3-81^x(0,3)), then take logs; an open end stays open. 6. Base behaviour. For x1: base above 1 gives a positive log, base in (0,1) a negative one; between two bases above 1, the smaller base gives the larger log.
Traps: 2 X<1 is not X<1; the right side is 2^1. Intervals extending to - are almost always the "forgot the domain" distractor. (13,2) vs (13,1): the bound shrinks the domain — do both.

Lessons: [Logarithmic Inequalities: start here](https://ipmatway.com/learn/logarithms/inequalities/start-here) · [Log Inequalities: Base Above 1](https://ipmatway.com/learn/logarithms/inequalities/log-inequality-base-gt-1) · [Log Inequalities: Base Below 1](https://ipmatway.com/learn/logarithms/inequalities/log-inequality-base-lt-1) · [Variable Base: Check Before Solving](https://ipmatway.com/learn/logarithms/inequalities/variable-base-inequality) · [Domain First: Log Inequalities](https://ipmatway.com/learn/logarithms/inequalities/domain-first) · [Logarithms: Read the Base](https://ipmatway.com/learn/logarithms/inequalities/monotonicity-by-base) · [Range of a Log Function](https://ipmatway.com/learn/logarithms/inequalities/range-of-log-function)

## Logarithms with Progressions (Logarithms, Quant)
Source: https://ipmatway.com/learn/logarithms/with-progressions

Idea: Logs convert multiplicative structure into additive structure: a GP becomes an AP under . Indore uses this link every second year (2019, 2024, 2025 twice).
Exam method: 1. "A, B, C in AP" → write B^2=AC immediately. 2. "Sum of logs of terms of a GP" → (product); the product is a^n r^n(n-1)/2. 3. ab^ek sums: separate the a count and the exponent AP.
Traps: Solving for x and stopping: the question asks for the progression, not x. Sign errors in (1-q) q-(1-p) p — check with p=q symmetry.

Lessons: [Logarithms with Progressions: start here](https://ipmatway.com/learn/logarithms/with-progressions/start-here) · [Logs in AP, Numbers in GP](https://ipmatway.com/learn/logarithms/with-progressions/logs-in-ap) · [GP First Term Through Logs](https://ipmatway.com/learn/logarithms/with-progressions/gp-first-term-via-logs) · [Sum of Logs of GP Terms](https://ipmatway.com/learn/logarithms/with-progressions/log-of-gp-terms-sum) · [AM of Logs → Arguments in GP](https://ipmatway.com/learn/logarithms/with-progressions/am-of-logs)

## Arithmetic Progression (Sequences and Series, Quant)
Source: https://ipmatway.com/learn/sequences-series/ap

Idea: An arithmetic progression adds the same number d each step. Everything about it is linear in the index n: the n-th term is a line, and the sum of the first n terms is a quadratic in n with no constant term. Most IPMAT AP questions are two equations in a and d dressed up in words.
Exam method: 1. Middle-term trick. Sn = n× (average of first and last) = n× (middle term when n is odd). "Sum of 3rd and 9th terms is 8" means T6=4, so S11=11× T6=44 in one line. 2. Sum ratio → term ratio. if Sn:S'n=(An+B):(Cn+D) then Tk:T'k is the same expression at n=2k-1. 3. Sm=Sn. terms m+1 to n sum to zero; their average (the middle term) is zero. 4. Common terms. first common term by inspection, then step by lcm(d1,d2); count =last-firstlcm+1. 5. Products of two APs. write ak=p+qk, bk=r+sk, expand, use k and k^2. Budget 2 minutes; it is an SA favourite (2025). 6. Options. for "find d" questions, test the options in the two given sums rather than solving.
Traps: (n-1)d vs nd; sum formula without the 12. "Sum of the next 15 terms" means S30-S15, not S15 again. Ratio questions: do not invert; keep "first AP : second AP" in the order asked. Products of APs: the cross term carries the sign of the negative difference.

Lessons: [Arithmetic Progression: start here](https://ipmatway.com/learn/sequences-series/ap/start-here) · [AP: Terms, Counts and Sums](https://ipmatway.com/learn/sequences-series/ap/nth-term-and-sum) · [Equal AP Sums: What Cancels?](https://ipmatway.com/learn/sequences-series/ap/common-difference-from-sums) · [Sum Ratios to Term Ratios](https://ipmatway.com/learn/sequences-series/ap/ratio-of-terms) · [Common Terms of Two APs](https://ipmatway.com/learn/sequences-series/ap/common-terms-of-two-aps) · [AM Insertion – Fill the Gaps in AP](https://ipmatway.com/learn/sequences-series/ap/am-insertion) · [Sum of Products of Two APs](https://ipmatway.com/learn/sequences-series/ap/sum-of-products-of-two-aps) · [How Many Terms to Get That Sum?](https://ipmatway.com/learn/sequences-series/ap/number-of-terms-from-sum) · [Three Terms: Sum and Product](https://ipmatway.com/learn/sequences-series/ap/three-terms-sum-product) · [Pth and Qth Term Identities](https://ipmatway.com/learn/sequences-series/ap/pth-qth-term-identities) · [Sum of Multiples in a Range](https://ipmatway.com/learn/sequences-series/ap/sum-of-multiples-in-range) · [Maximum Sum of a Decreasing AP](https://ipmatway.com/learn/sequences-series/ap/max-min-partial-sum) · [Middle Term Trick for AP Sums](https://ipmatway.com/learn/sequences-series/ap/middle-term-symmetric-pairs)

## Geometric Progression (Sequences and Series, Quant)
Source: https://ipmatway.com/learn/sequences-series/gp

Idea: A geometric progression multiplies by the same ratio r each step. Sums telescope: Sn(1-r)=a-ar^n. Infinite sums exist when |r|<1 and equal (a)/(1-r). IPMAT likes GPs hidden in word problems (donations that double, lap distances that shrink, interest-free compounding) and in "sum conditions" like S5=S7.
Exam method: 1. Powers table. know 2^1..12, 3^1..7, 5^1..5 cold; "least n" questions are read off directly. 2. Running-total GPs. "each donor gives as much as all before him" ⇒ totals a,2a,4a,; the n-th donor gives a·2^n-2 (n2). 3. Sp=Sq. the terms between cancel. With two consecutive extra terms (q=p+2) that forces r=-1. 4. Closest-to questions. compute Sn=S(1-r^n) for small n and watch the sign flip when r<0. 5. Spiral path. split into the two axes; each is a GP with ratio -r^2; distance =a√(1+r^2).
Traps: Forgetting the negative-ratio branch. Confusing "the n-th contribution" with "the total after n contributions". Using (a)/(1-r) when |r|1. In "least n so that SnT" compare Sn-1≤ T<Sn — check both sides.

Lessons: [Geometric Progression: start here](https://ipmatway.com/learn/sequences-series/gp/start-here) · [GP: Nth Term and Sum](https://ipmatway.com/learn/sequences-series/gp/nth-term-and-sum) · [Infinite GP: Sums and Hidden Forms](https://ipmatway.com/learn/sequences-series/gp/infinite-gp-sum) · [Equal GP Sums: Cancel the Extras](https://ipmatway.com/learn/sequences-series/gp/s5-equals-s7-type) · [Donors and Doubling Totals](https://ipmatway.com/learn/sequences-series/gp/doubling-donors-sum) · [GP Hidden in AP Terms](https://ipmatway.com/learn/sequences-series/gp/gp-from-ap-terms) · [GP Sums: How Many Terms?](https://ipmatway.com/learn/sequences-series/gp/terms-needed-for-sum-target) · [Infinite Walk, Finite Distance](https://ipmatway.com/learn/sequences-series/gp/infinite-path-distance) · [Three GP Terms: Centre First](https://ipmatway.com/learn/sequences-series/gp/three-terms-sum-product) · [Inserting Geometric Means](https://ipmatway.com/learn/sequences-series/gp/gm-insertion) · [A Term and Its Tail](https://ipmatway.com/learn/sequences-series/gp/term-equals-k-times-tail) · [Bouncing Ball: Total Distance](https://ipmatway.com/learn/sequences-series/gp/bouncing-ball-distance) · [Nested Figures: Find the Ratio](https://ipmatway.com/learn/sequences-series/gp/nested-figures-geometric-sum) · [Repeated Digits, Hidden GP](https://ipmatway.com/learn/sequences-series/gp/repeated-digit-series) · [Odd and Even Position Sums](https://ipmatway.com/learn/sequences-series/gp/odd-even-position-sums) · [Four Numbers, Two Progressions](https://ipmatway.com/learn/sequences-series/gp/mixed-ap-gp-numbers) · [GP Term Identities](https://ipmatway.com/learn/sequences-series/gp/term-identities) · [Percent decay total](https://ipmatway.com/learn/sequences-series/gp/percent-decay-total)

## Special Series (Sequences and Series, Quant)
Source: https://ipmatway.com/learn/sequences-series/special-series

Idea: "Special series" are sums that are neither AP nor GP but collapse by a trick: standard power sums, telescoping (partial fractions), parity splits of a known infinite sum, or sequences defined by a recurrence that hides an AP/quadratic. Indore asks one every year, usually in the SA section.
Exam method: 1. Spot the general term first. (e.g. 1·3,5·7,9·11⇒(4k-3)(4k-1)), then expand. 2. Basel split. odd-square reciprocals =(^2)/(6)-14·(^2)/(6)=(^2)/(8). Asked in 2020 and 2025. 3. "Least n such that sum (99)/(100)". telescoped sum is 1-(2)/(n+2); solve the inequality, then check the boundary. 4. Squares removed. answer x satisfies x- x=n; try x=n+ n then nudge. 5. Recurrence with √(1+xn). set yn=√(1+xn); it becomes an AP. 6. f(n)=3n-f(n-1). add consecutive equations: f(n)+f(n-1)=3n; for odd n the pattern is f(n)=(3n-1)/(2) (check f(1)=1,f(3)=4).
Traps: Using k^2 formula for cubes (the cube formula is the square of k). Telescoping with the wrong endpoint (n+1 vs n+2). Reading "2022nd term" as "the number 2022". Assuming f(n) is linear for all n when the parity alternates — verify with 3–4 values.

Lessons: [Special Series: start here](https://ipmatway.com/learn/sequences-series/special-series/start-here) · [Squares, Cubes and Hidden Sums](https://ipmatway.com/learn/sequences-series/special-series/sum-of-squares-cubes) · [Telescoping: Keep the Endpoints](https://ipmatway.com/learn/sequences-series/special-series/telescoping-sum) · [Odd Squares: Split the Basel Sum](https://ipmatway.com/learn/sequences-series/special-series/odd-square-reciprocals-from-basel) · [Fraction Sums: Find the Least n](https://ipmatway.com/learn/sequences-series/special-series/series-of-fractions-min-n) · [Sequence with Squares Removed](https://ipmatway.com/learn/sequences-series/special-series/sequence-with-squares-removed) · [Recursive Sequences: Find the nth Term](https://ipmatway.com/learn/sequences-series/special-series/recursive-sequence-nth-term) · [Find a Term from the Sum](https://ipmatway.com/learn/sequences-series/special-series/sum-of-n-terms-formula-given) · [Method of Differences](https://ipmatway.com/learn/sequences-series/special-series/method-of-differences) · [Product Term Series](https://ipmatway.com/learn/sequences-series/special-series/product-term-series) · [Sum of Grouped Series](https://ipmatway.com/learn/sequences-series/special-series/sum-of-grouped-series) · [Interleaved APs](https://ipmatway.com/learn/sequences-series/special-series/interleaved-aps) · [Alternating Signs: Pair First](https://ipmatway.com/learn/sequences-series/special-series/alternating-sign-series) · [Split the AP and GP](https://ipmatway.com/learn/sequences-series/special-series/ap-plus-gp-split)

## AGP, HP and Means (Sequences and Series, Quant)
Source: https://ipmatway.com/learn/sequences-series/agp-hp

Idea: A harmonic progression is just an AP in disguise (reciprocals). An arithmetico-geometric progression (AGP) multiplies an AP term by a GP term, e.g. 1·12+2·14+3·18+; its sum is found by the "multiply by r and subtract" trick. Both are low-frequency in IPMAT (≤1 question in some years) but cheap once known.
Exam method: 1. HP term asked → reciprocals immediately; options that are not unit fractions of an AP are out. 2. AGP infinite with r=12,13: memorise kr^k=(r)/((1-r)^2) (=2 for 12, =34 for 13). 3. HM of two numbers: (2ab)/(a+b) — used in "harmonic mean of roots" questions (2023 quadratic question).
Traps: Treating consecutive HP terms as differing by a constant. Dropping the Ar/(1-r) part when the AP factor has a constant. Sign slips when r is negative in an AGP.

Lessons: [AGP, HP and Means: start here](https://ipmatway.com/learn/sequences-series/agp-hp/start-here) · [HP: Flip, Solve, Flip Back](https://ipmatway.com/learn/sequences-series/agp-hp/harmonic-progression-basic) · [Finite AGP: Keep the Tail](https://ipmatway.com/learn/sequences-series/agp-hp/agp-sum-finite) · [Infinite AGP: Multiply and Subtract](https://ipmatway.com/learn/sequences-series/agp-hp/agp-sum-infinite) · [AM, GM, HM: Relations and Extremes](https://ipmatway.com/learn/sequences-series/agp-hp/am-gm-hm-relations)

## Functions (Functions and Graphs, Quant)
Source: https://ipmatway.com/learn/functions-graphs/functions

Idea: A function assigns exactly one output to each input in its domain. Most exam questions ask for the domain or range, evaluate compositions, solve for an inverse, or pin down a function from an equation it satisfies by clever substitutions.
Exam method: 1. Substitute, do not solve generally. the question usually needs one value. 2. Recursions. pair up consecutive relations; look for a period or a constant step. 3. Parity. test f(-x) with one number; products follow sign rules. 4. Defined operations. write the rule out with the numbers, bracket by bracket.
Traps: Domain end points (zero of a root allowed, zero of a denominator never). Wrong order of composition; reciprocal mistaken for the inverse; off-by-one in recursions.

Lessons: [Functions: start here](https://ipmatway.com/learn/functions-graphs/functions/start-here) · [Domain: Which Inputs Are Allowed?](https://ipmatway.com/learn/functions-graphs/functions/domain) · [Range: Which Outputs Are Possible?](https://ipmatway.com/learn/functions-graphs/functions/range) · [Composite Functions: Inside First](https://ipmatway.com/learn/functions-graphs/functions/composite-evaluation) · [Functional Equations: Pick the Input](https://ipmatway.com/learn/functions-graphs/functions/functional-equation-evaluate) · [Recursions: Jump, Don’t Crawl](https://ipmatway.com/learn/functions-graphs/functions/recursive-function-large-n) · [Maximum of a Composite Function](https://ipmatway.com/learn/functions-graphs/functions/max-of-composite) · [Inverse Means Undo](https://ipmatway.com/learn/functions-graphs/functions/inverse-function) · [Even, Odd and Periodic](https://ipmatway.com/learn/functions-graphs/functions/even-odd-periodic) · [Defined Operations](https://ipmatway.com/learn/functions-graphs/functions/defined-operations) · [One-One, Onto or Both?](https://ipmatway.com/learn/functions-graphs/functions/injective-surjective)

## Graphs and Behaviour (Functions and Graphs, Quant)
Source: https://ipmatway.com/learn/functions-graphs/graphs-behaviour

Idea: Graphs turn algebra into pictures: a parabola's vertex gives its extreme value, the sign of f' tells where a curve rises, shifts and reflections move a known graph, and counting crossings of two graphs counts the solutions of an equation.
Exam method: 1. Vertex shortcut. x=-(b)/(2a), value c-b^24a. 2. Test points. one value per interval decides the sign of f or f'. 3. Log forms. exponentiate the given relation and read off the power. 4. Count, do not solve. graphs of 2^x, x^2, |x| and lines cross a predictable number of times.
Traps: Shift direction; turning points included in strict monotonic intervals; piece solutions not checked against their piece.

Lessons: [Graphs and Behaviour: start here](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/start-here) · [Quadratics: Shape and Extreme Values](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/quadratic-extrema-shape) · [Cubic Sign and Direction](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/monotonic-cubic-sign) · [Graph Shifts and Reflections](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/transformation-shifts) · [Logs to Proportionality](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/proportionality-from-log-form) · [Max and Min: Check the Range](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/max-function-integer-solution) · [Modulus: Corners, Flats and Areas](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/graph-of-modulus) · [Maximum of Two Lines’ Minimum](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/min-max-of-two-lines) · [Count Crossings, Not Roots](https://ipmatway.com/learn/functions-graphs/graphs-behaviour/intersections-count)

## Relations (Functions and Graphs, Quant)
Source: https://ipmatway.com/learn/functions-graphs/relations

Idea: A relation from A to B is any set of ordered pairs (a,b) with a A, b B, i.e. a subset of A× B. A function is the special relation in which every element of A appears exactly once as a first coordinate. Counting questions follow from these definitions.
Exam method: 1. Count choices per element. , never list unless the set is tiny. 2. Probabilities. favourable functions over all relations (or all functions). 3. Properties. hunt for one counter-example per property.
Traps: Direction of functions (n^m vs m^n); pairs vs subsets; incomplete transitivity checks.

Lessons: [Relations: start here](https://ipmatway.com/learn/functions-graphs/relations/start-here) · [Count Relations and Functions](https://ipmatway.com/learn/functions-graphs/relations/count-relations-functions) · [Probability: Relation or Function?](https://ipmatway.com/learn/functions-graphs/relations/probability-relation-is-function) · [Cartesian Product Properties](https://ipmatway.com/learn/functions-graphs/relations/cartesian-product-properties) · [Reflexive, Symmetric, Transitive](https://ipmatway.com/learn/functions-graphs/relations/reflexive-symmetric-transitive)

## Binomial Coefficients and Terms (Binomial Theorem, Quant)
Source: https://ipmatway.com/learn/binomial-theorem/coefficients

Idea: (a+b)^n is the sum of n+1 terms nra^n-rb^r. Coefficient questions pick one term (by its power of x or its position) or add many terms at once (by substituting values of x).
Exam method: 1. Power bookkeeping. write only the power of x in Tr+1, set it to the target, solve for r - then compute one coefficient. 2. Substitution beats expansion. for any sum of coefficients. 3. Ratios to equations. for consecutive coefficients: two equations, two unknowns. 4. Simplify first. when counting terms; perfect squares and conjugate products collapse.
Traps: Tr vs Tr+1; signs of negative constants; constants not raised; A0 included or not; trinomial term counts.

Lessons: [Binomial Coefficients and Terms: start here](https://ipmatway.com/learn/binomial-theorem/coefficients/start-here) · [General Term: Position to Formula](https://ipmatway.com/learn/binomial-theorem/coefficients/general-term) · [Find the Coefficient of xᵏ](https://ipmatway.com/learn/binomial-theorem/coefficients/coefficient-of-x-k) · [Term Independent of x](https://ipmatway.com/learn/binomial-theorem/coefficients/term-independent-of-x) · [Finding the Middle Term](https://ipmatway.com/learn/binomial-theorem/coefficients/middle-term) · [Sum of Coefficients](https://ipmatway.com/learn/binomial-theorem/coefficients/sum-of-coefficients) · [Even and Odd Coefficient Sums](https://ipmatway.com/learn/binomial-theorem/coefficients/sum-even-odd-coefficients) · [Consecutive Coefficients Ratio](https://ipmatway.com/learn/binomial-theorem/coefficients/consecutive-coefficients-ratio) · [Equal Coefficients](https://ipmatway.com/learn/binomial-theorem/coefficients/equal-coefficients) · [Count Terms, Not Brackets](https://ipmatway.com/learn/binomial-theorem/coefficients/number-of-terms) · [When Is nCr Defined?](https://ipmatway.com/learn/binomial-theorem/coefficients/ncr-defined-values)

## Binomial Applications (Binomial Theorem, Quant)
Source: https://ipmatway.com/learn/binomial-theorem/applications

Idea: The expansion (m+c)^n=m^n+n1m^n-1c+·s+c^n puts every term except the last into multiples of m - the engine for remainders and divisibility. Adding or alternating binomial coefficients gives closed forms; comparing consecutive terms finds the largest one.
Exam method: 1. Small remainder first. 5^99 mod 13: 5^2=26-1, so 5^995(-1)^49=8. 2. End-term removal. for partial sums; hockey stick for diagonal sums. 3. Ratio test. with the formula r≤((n+1)t)/(1+t), t=|(bx)/(a)|. 4. Integral terms. count multiples of the denominator that keep the other exponent whole.
Traps: Odd powers of negative remainders; Tr vs Tr+1; r=0 in counts; too few terms in approximations.

Lessons: [Binomial Applications: start here](https://ipmatway.com/learn/binomial-theorem/applications/start-here) · [Big Powers, Small Remainders](https://ipmatway.com/learn/binomial-theorem/applications/remainder-via-binomial) · [Greatest Term, Not Middle Term](https://ipmatway.com/learn/binomial-theorem/applications/greatest-term) · [Approximate or Compare?](https://ipmatway.com/learn/binomial-theorem/applications/approximation) · [Divisibility Without Big Powers](https://ipmatway.com/learn/binomial-theorem/applications/divisibility-proof-pattern) · [Binomial Sums: Spot the Pattern](https://ipmatway.com/learn/binomial-theorem/applications/binomial-sum-identities) · [Counting Integral Terms](https://ipmatway.com/learn/binomial-theorem/applications/integral-terms-count)

## Matrices (Matrices and Determinants, Quant)
Source: https://ipmatway.com/learn/matrices-determinants/matrices

Idea: A matrix is a rectangular table of numbers with its own arithmetic. Addition and scaling go entry by entry; multiplication combines rows with columns and is not commutative. Inverses undo multiplication, and many exam questions reduce to finding a pattern in powers or using a relation the matrix satisfies.
Exam method: 1. Test with simple matrices. for identities, try A=2I, B=I or diagonal matrices. 2. Patterns in powers. compute A^2, A^3 and generalise. 3. One entry is enough. an unknown entry can be found from a single equation of the product.
Traps: Order of multiplication and of inverses; commuting assumptions.

Lessons: [Matrices: start here](https://ipmatway.com/learn/matrices-determinants/matrices/start-here) · [Matrix Operations: Add and Multiply](https://ipmatway.com/learn/matrices-determinants/matrices/operations-add-multiply) · [Huge Matrix Powers, Small Patterns](https://ipmatway.com/learn/matrices-determinants/matrices/power-of-matrix-pattern) · [Matrix Equations: Match One Entry](https://ipmatway.com/learn/matrices-determinants/matrices/matrix-equation-find-entries) · [Inverse of a 2 by 2 Matrix](https://ipmatway.com/learn/matrices-determinants/matrices/inverse-2x2) · [Inverse from a Matrix Relation](https://ipmatway.com/learn/matrices-determinants/matrices/inverse-element-from-relation) · [Nonsingular Simplification](https://ipmatway.com/learn/matrices-determinants/matrices/nonsingular-simplification) · [Transpose and Symmetry](https://ipmatway.com/learn/matrices-determinants/matrices/transpose-symmetric) · [Counting Matrices](https://ipmatway.com/learn/matrices-determinants/matrices/matrix-counting) · [When Can Matrices Commute?](https://ipmatway.com/learn/matrices-determinants/matrices/commutativity-conditions)

## Determinants (Matrices and Determinants, Quant)
Source: https://ipmatway.com/learn/matrices-determinants/determinants

Idea: The determinant of a square matrix is a single number that measures how the matrix scales volume. It is zero exactly when the rows are dependent, which is when the matrix has no inverse and a linear system has no unique solution.
Exam method: 1. Look for structure. before expanding: equal row sums, a triangular matrix, a known pattern. 2. Concrete examples. a nilpotent matrix such as bmatrix0&1\\0&0bmatrix checks claims instantly. 3. Factor polynomials in A. and multiply determinants.
Traps: Middle cofactor sign; k^n for scalars; polynomial applied to the determinant.

Lessons: [Determinants: start here](https://ipmatway.com/learn/matrices-determinants/determinants/start-here) · [Evaluate a 3 by 3 Determinant](https://ipmatway.com/learn/matrices-determinants/determinants/evaluate-3x3) · [Row Operations, Determinant Changes](https://ipmatway.com/learn/matrices-determinants/determinants/det-properties-row-ops) · [When Is a Determinant Zero?](https://ipmatway.com/learn/matrices-determinants/determinants/det-zero-condition) · [Determinant of a Polynomial in A](https://ipmatway.com/learn/matrices-determinants/determinants/det-of-polynomial-in-matrix) · [Determinants of Sums of Powers](https://ipmatway.com/learn/matrices-determinants/determinants/det-of-sum-of-powers) · [Cyclic Determinants: Mind the Sign](https://ipmatway.com/learn/matrices-determinants/determinants/sign-of-cyclic-det) · [Vandermonde: Spot the Differences](https://ipmatway.com/learn/matrices-determinants/determinants/vandermonde-type) · [Determinants Without Multiplying](https://ipmatway.com/learn/matrices-determinants/determinants/det-of-product-power-scalar) · [Magic Square Determinants](https://ipmatway.com/learn/matrices-determinants/determinants/magic-square-det) · [Nilpotent Determinants](https://ipmatway.com/learn/matrices-determinants/determinants/nilpotent-det) · [Adjoint: Two Powers to Watch](https://ipmatway.com/learn/matrices-determinants/determinants/adjoint-properties) · [Cramer’s Rule and Consistency](https://ipmatway.com/learn/matrices-determinants/determinants/cramer-rule-systems) · [Determinants with Restricted Entries](https://ipmatway.com/learn/matrices-determinants/determinants/entries-constraint-det)

## Lines, Angles and Polygons (Geometry, Quant)
Source: https://ipmatway.com/learn/geometry/lines-angles-polygons

Idea: Every polygon fact comes from two numbers: the angle sum (n-2)· 180^ (cut into triangles) and the exterior-angle sum 360^ (walk once around the polygon). Regular polygons share both equally among n corners.
Exam method: 1. Work with the exterior angle. It is always (360^)/(n) and must divide 360^ - a fast way to reject options (an exterior angle of 50^ is impossible). 2. Ratio forms. interior : exterior =(n-2):2; 'interior =k× exterior' means n=2k+2. 3. Max / min n. divide the bound by 180, take the floor (or the next integer), then add 2 - and check the boundary. 4. Areas. remember the hexagon (3√(3)2a^2) and octagon (2√(2)r^2 in a circle of radius r); others by (n)/(2)r^2(360^)/(n).
Traps: (n-1)· 180^ or (180^)/(n) slips; counting the sides as diagonals; treating co-interior angles as equal; the strict boundary.

Lessons: [Lines, Angles and Polygons: start here](https://ipmatway.com/learn/geometry/lines-angles-polygons/start-here) · [Polygon Interior Angle Sum](https://ipmatway.com/learn/geometry/lines-angles-polygons/angle-sum-polygon) · [Maximum Sides from Angle Sum](https://ipmatway.com/learn/geometry/lines-angles-polygons/max-sides-given-angle-sum) · [Regular Polygon Inside a Circle](https://ipmatway.com/learn/geometry/lines-angles-polygons/regular-polygon-in-circle-area) · [Exterior First, Sides Next](https://ipmatway.com/learn/geometry/lines-angles-polygons/exterior-angles) · [Parallel Lines: Equal or 180?](https://ipmatway.com/learn/geometry/lines-angles-polygons/parallel-lines-angles) · [Diagonals: Count Without Confusion](https://ipmatway.com/learn/geometry/lines-angles-polygons/diagonals) · [Complement or Supplement?](https://ipmatway.com/learn/geometry/lines-angles-polygons/complementary-supplementary) · [Two Polygons, Two Ratios](https://ipmatway.com/learn/geometry/lines-angles-polygons/regular-polygon-two-polygons) · [Star Points, Not Polygon Corners](https://ipmatway.com/learn/geometry/lines-angles-polygons/star-polygon-angles) · [Regular Hexagon Area](https://ipmatway.com/learn/geometry/lines-angles-polygons/regular-hexagon-area)

## Triangles (Geometry, Quant)
Source: https://ipmatway.com/learn/geometry/triangles

Idea: A triangle is fixed by three pieces of data; every question asks you to recover one more length, angle or area. Pick the tool that matches the data: Pythagoras and similarity for lengths, angle chasing for angles, and one of the three area formulas for areas.
Exam method: 1. Coordinates are allowed. Put a right angle or a base on the axes; mid-points, feet of altitudes and centroids become averages. 2. Pythagorean triples. (3-4-5, 5-12-13, 8-15-17, 7-24-25, 20-21-29, 11-60-61) - spot them before computing; check EVERY option in 'which is right-angled' questions (JIPMAT 2024 Q21 had two). 3. Angle chases. name one unknown base angle and write every angle in terms of it - the answer usually does not depend on . 4. Symbolic options. test a special case (equilateral, right angle, n=1) to eliminate.
Traps: Flat triangles, ordered triples, the non-longest side, linear instead of squared area ratios, R vs r, AG vs AD.

Lessons: [Triangles: start here](https://ipmatway.com/learn/geometry/triangles/start-here) · [Triangle Area: Pick the Right Tool](https://ipmatway.com/learn/geometry/triangles/area-formulas) · [Median, Angle and Area](https://ipmatway.com/learn/geometry/triangles/median-and-angle-area) · [Isosceles Angle Chase](https://ipmatway.com/learn/geometry/triangles/isosceles-angle-chase) · [Counting Integer Triangles](https://ipmatway.com/learn/geometry/triangles/integer-sides-perimeter-count) · [Acute, Right or Obtuse?](https://ipmatway.com/learn/geometry/triangles/acute-obtuse-from-sides) · [Which Third Sides Are Possible?](https://ipmatway.com/learn/geometry/triangles/triangle-inequality-valid-side) · [Similar Triangles: Length to Area](https://ipmatway.com/learn/geometry/triangles/similar-triangles-ratio) · [Largest Rectangle in a Triangle](https://ipmatway.com/learn/geometry/triangles/inscribed-rectangle-max-area) · [Incircle and Circumradius](https://ipmatway.com/learn/geometry/triangles/incircle-circumradius) · [Angle Bisector: Divide in Ratio](https://ipmatway.com/learn/geometry/triangles/angle-bisector-theorem) · [Centroid: Which Distance?](https://ipmatway.com/learn/geometry/triangles/centroid-distance) · [Right Triangle Check](https://ipmatway.com/learn/geometry/triangles/right-triangle-check) · [Midpoints: Half and Parallel](https://ipmatway.com/learn/geometry/triangles/midpoint-theorem) · [Median Length: Pick the Right Tool](https://ipmatway.com/learn/geometry/triangles/median-length) · [Incentre and Excentre Angles](https://ipmatway.com/learn/geometry/triangles/incentre-excentre-angles) · [Altitude on the Hypotenuse](https://ipmatway.com/learn/geometry/triangles/altitude-on-hypotenuse) · [Crossing Wires: Find the Height](https://ipmatway.com/learn/geometry/triangles/crossing-poles-height) · [Angle Ratios and Exterior Angles](https://ipmatway.com/learn/geometry/triangles/angle-ratio-exterior-angle)

## Circles (Geometry, Quant)
Source: https://ipmatway.com/learn/geometry/circles

Idea: A circle is all points at distance r from the centre, so almost everything reduces to a right triangle made of a radius, a half-chord or a tangent, and a distance from the centre. Angles reduce to the inscribed-angle theorem.
Exam method: 1. Draw the right triangle first. (radius, half-chord, distance) - it gives chord, distance or radius in one line. 2. Use coordinates. for circles touching sides of squares or rectangles: centre (r,r), then substitute the side's equation. 3. Ratios. areas scale with the square of lengths; circumferences with the lengths. 4. Paths round polygons. sides + one full circle of radius d - the shape of the polygon does not matter.
Traps: Full chord for half chord; wrong configuration (same/opposite side, direct/transverse, inside/outside); radii ratio for area ratio; the wrong arc.

Lessons: [Circles: start here](https://ipmatway.com/learn/geometry/circles/start-here) · [Chord Distance](https://ipmatway.com/learn/geometry/circles/chord-distance) · [Tangents from an External Point](https://ipmatway.com/learn/geometry/circles/tangent-from-external-point) · [Angle Between Tangents](https://ipmatway.com/learn/geometry/circles/angle-between-tangents) · [Inscribed Shapes: Area Ratios](https://ipmatway.com/learn/geometry/circles/inscribed-circles-area-ratio) · [Circle Meets Square](https://ipmatway.com/learn/geometry/circles/circle-meets-square) · [Nearest and Farthest from a Circle](https://ipmatway.com/learn/geometry/circles/shortest-longest-distance-from-point) · [Arc, Sector or Segment?](https://ipmatway.com/learn/geometry/circles/arc-length-sector) · [Cyclic Quadrilateral: Spot the Right Angle](https://ipmatway.com/learn/geometry/circles/cyclic-quadrilateral) · [Intersecting Chords](https://ipmatway.com/learn/geometry/circles/intersecting-chords) · [Paths Around Polygons](https://ipmatway.com/learn/geometry/circles/path-around-polygon-at-distance) · [Centre Angle and Circle Angles](https://ipmatway.com/learn/geometry/circles/angle-at-centre) · [Common Tangent Length](https://ipmatway.com/learn/geometry/circles/common-tangent-length) · [Touching Circles](https://ipmatway.com/learn/geometry/circles/touching-circles) · [Common Chord: Join the Centres](https://ipmatway.com/learn/geometry/circles/common-chord) · [Tangent secant](https://ipmatway.com/learn/geometry/circles/tangent-secant) · [Two Chords, One Straight Distance](https://ipmatway.com/learn/geometry/circles/chords-in-sequence) · [Triangle–Circle Overlap](https://ipmatway.com/learn/geometry/circles/circle-triangle-overlap-area) · [Circle Through Rectangle Points](https://ipmatway.com/learn/geometry/circles/circle-through-rectangle-points) · [Circle Terms Without the Traps](https://ipmatway.com/learn/geometry/circles/circle-terms)

## Quadrilaterals (Geometry, Quant)
Source: https://ipmatway.com/learn/geometry/quadrilaterals

Idea: Every quadrilateral splits into triangles - by a diagonal, by both diagonals, or by cutting off corners. Area questions become triangle-area questions; angle questions use the 360^ sum.
Exam method: 1. Take numbers. for ratio answers set a side to a convenient value (1+n, m+n). 2. AM-GM. for least areas: product fixed ⇒ sum least when equal. 3. Similar triangles in trapeziums. the diagonals cut each other in the ratio of the parallel sides.
Traps: Equal side triangles only in a trapezium; squares of ratios; which special quadrilateral the mid-point figure is.

Lessons: [Quadrilaterals: start here](https://ipmatway.com/learn/geometry/quadrilaterals/start-here) · [Inner Quadrilateral Area Ratios](https://ipmatway.com/learn/geometry/quadrilaterals/area-ratio-inner-quadrilateral) · [Minimum Area from Diagonal Triangles](https://ipmatway.com/learn/geometry/quadrilaterals/min-area-from-triangle-areas) · [Rhombus, Parallelogram, Trapezium](https://ipmatway.com/learn/geometry/quadrilaterals/parallelogram-rhombus-trapezium) · [Join Midpoints, Follow Diagonals](https://ipmatway.com/learn/geometry/quadrilaterals/midpoint-quadrilateral) · [Trapezium Diagonal Triangles](https://ipmatway.com/learn/geometry/quadrilaterals/trapezium-diagonal-triangles) · [Quadrilateral Angles](https://ipmatway.com/learn/geometry/quadrilaterals/quadrilateral-angles) · [Rectangle diagonal perimeter](https://ipmatway.com/learn/geometry/quadrilaterals/rectangle-diagonal-perimeter)

## Mensuration 2D (Mensuration, Quant)
Source: https://ipmatway.com/learn/mensuration/2d

Idea: Two-dimensional mensuration is about splitting a figure into rectangles, triangles and pieces of circles whose areas and perimeters are known, then adding or subtracting.
Exam method: 1. Use =(22)/(7) when radii are multiples of 7. answers come out whole. 2. Scale factors. a length factor k multiplies areas by k^2; use this for percentage changes and similar figures. 3. Collect circle pieces. quarter circles at four corners, sectors at the vertices of a triangle - add their angles first. 4. Order by roundness. for equal-area / equal-perimeter comparisons; no computation needed.
Traps: Diameter for radius, missing straight edges, double-counted road crossings, linear percentage for areas, unit slips.

Lessons: [Mensuration 2D: start here](https://ipmatway.com/learn/mensuration/2d/start-here) · [Area, Perimeter and Hidden Sides](https://ipmatway.com/learn/mensuration/2d/area-perimeter-basic) · [Shaded Regions: Collect the Pieces](https://ipmatway.com/learn/mensuration/2d/shaded-region) · [Equal Area, Different Boundaries](https://ipmatway.com/learn/mensuration/2d/perimeter-ordering-equal-area) · [Circle Differences and Boundaries](https://ipmatway.com/learn/mensuration/2d/circle-circumference-minus-radius) · [Square in Circle in Square](https://ipmatway.com/learn/mensuration/2d/square-in-circle-in-square) · [Paths and Crossing Roads](https://ipmatway.com/learn/mensuration/2d/paths-and-roads) · [Same Wire, Different Areas](https://ipmatway.com/learn/mensuration/2d/wire-bent-into-shapes) · [Circular Rings and Tracks](https://ipmatway.com/learn/mensuration/2d/circular-ring-track) · [Wheel Revolutions](https://ipmatway.com/learn/mensuration/2d/wheel-revolutions) · [Length Change to Area Change](https://ipmatway.com/learn/mensuration/2d/area-change-percent) · [Fencing or Paving: What to Charge?](https://ipmatway.com/learn/mensuration/2d/cost-of-fencing-paving) · [Grazing Area: Follow the Rope](https://ipmatway.com/learn/mensuration/2d/grazing-area)

## Mensuration 3D (Mensuration, Quant)
Source: https://ipmatway.com/learn/mensuration/3d

Idea: Solids are measured by volume (space inside) and surface area (skin). Most questions conserve one of them - melting keeps the volume, rolling a sheet keeps the area - or scale a solid, which multiplies areas by k^2 and volumes by k^3.
Exam method: 1. Ratios before numbers. for 'two cones / two cubes' questions compare r^2h or edges directly. 2. =(22)/(7) with radii in multiples of 7. gives whole answers; cancel when it appears on both sides. 3. Scale factors. for percentage changes and similar solids. 4. Brute-force small integer searches. (cube triples, whole tiles, box cuts) instead of algebra.
Traps: Hemisphere faces, the cone's (1)/(3), squares vs cubes, unit conversions, partial submersion.

Lessons: [Mensuration 3D: start here](https://ipmatway.com/learn/mensuration/3d/start-here) · [Cube & Cuboid: Surface and Volume](https://ipmatway.com/learn/mensuration/3d/cube-cuboid-sa-volume) · [Cylinder, Cone, Sphere](https://ipmatway.com/learn/mensuration/3d/cylinder-cone-sphere) · [Melting and Recasting](https://ipmatway.com/learn/mensuration/3d/melting-recasting) · [Surface Area: Percent Change](https://ipmatway.com/learn/mensuration/3d/surface-area-change-percent) · [Surface Given, Volumes Wanted](https://ipmatway.com/learn/mensuration/3d/volume-sums-from-surface) · [Earth Dug, Earth Spread](https://ipmatway.com/learn/mensuration/3d/earth-dug-platform) · [Cubes Joined or Cut](https://ipmatway.com/learn/mensuration/3d/cubes-joined-cuboid) · [Room Height from Areas](https://ipmatway.com/learn/mensuration/3d/room-dimensions-from-areas) · [Space Diagonal and Face Areas](https://ipmatway.com/learn/mensuration/3d/space-diagonal) · [Cone Cuts and Frustums](https://ipmatway.com/learn/mensuration/3d/cone-cut-parallel-base) · [Water Rise: Count What Is Underwater](https://ipmatway.com/learn/mensuration/3d/displacement-water-rise) · [Flow Through a Pipe](https://ipmatway.com/learn/mensuration/3d/flow-through-pipe) · [Cut Corners, Fold a Box](https://ipmatway.com/learn/mensuration/3d/open-box-from-sheet) · [Sector Rolled into a Cone](https://ipmatway.com/learn/mensuration/3d/sector-rolled-into-cone) · [Painted Cubes: Count by Position](https://ipmatway.com/learn/mensuration/3d/painted-cube-counting) · [Inscribed Solids: Find the Fit](https://ipmatway.com/learn/mensuration/3d/inscribed-solids-ratio) · [Hollow Solids: Count Only Metal](https://ipmatway.com/learn/mensuration/3d/hollow-solids) · [Composite Solids: What Counts?](https://ipmatway.com/learn/mensuration/3d/composite-solids)

## Straight Lines (Coordinate Geometry, Quant)
Source: https://ipmatway.com/learn/coordinate-geometry/lines

Idea: A straight line is fixed by two facts: two points, or a point and a slope (direction). Every line question is either reading those facts off an equation (slope -(a)/(b), intercepts -(c)/(a) and -(c)/(b)) or building an equation from them. Lengths come from Pythagoras, areas from the shoelace formula, and angles from slopes.
Exam method: 1. Options first. for "equation of the line" questions, substitute the given point into each option - usually only one or two survive (Indore 2020 Q13: only 10y-8x=80 contains (-5,4)). 2. Normal-vector trick. perpendicular line bx-ay=k, parallel ax+by=k; one substitution gives k. 3. Midpoint picture. a point bisecting the intercept segment means intercepts 2h, 2k; any ratio m:n gives a=((m+n)h)/(n), b=((m+n)k)/(m). 4. Squared lengths. for triangle type and for comparing distances; Pythagorean triples (3-4-5, 5-12-13, 8-15-17) appear constantly. 5. Right-triangle centres. without formulas: orthocentre at the right angle, circumcentre at the hypotenuse midpoint, inradius (a+b-c)/(2). 6. Euler line. O=(3G-H)/(2) when the orthocentre and centroid are given.
Traps: Reversed section ratio; parallel vs perpendicular slope; un-normalised parallel lines; one root of a modulus dropped; 'equal intercepts' through the origin; two true options in classification questions.

Lessons: [Straight Lines: start here](https://ipmatway.com/learn/coordinate-geometry/lines/start-here) · [Distance Between Two Points](https://ipmatway.com/learn/coordinate-geometry/lines/distance-formula) · [Section Formula: Weights Cross Over](https://ipmatway.com/learn/coordinate-geometry/lines/section-formula) · [Slope and Equation Forms](https://ipmatway.com/learn/coordinate-geometry/lines/slope-and-equation-forms) · [Angles Between Lines](https://ipmatway.com/learn/coordinate-geometry/lines/slope-angle-between-lines) · [Perpendicular Line Intercept](https://ipmatway.com/learn/coordinate-geometry/lines/perpendicular-line-intercept) · [Concurrent Lines: Find k](https://ipmatway.com/learn/coordinate-geometry/lines/concurrent-lines-parameter) · [Collinearity: Find the Parameter](https://ipmatway.com/learn/coordinate-geometry/lines/collinearity-parameter) · [Area from Vertices](https://ipmatway.com/learn/coordinate-geometry/lines/polygon-area-from-vertices) · [Triangle Area from Three Lines](https://ipmatway.com/learn/coordinate-geometry/lines/triangle-area-from-lines) · [Intercepts Make a Triangle](https://ipmatway.com/learn/coordinate-geometry/lines/intercept-form-triangle) · [Equal Intercepts: Check the Signs](https://ipmatway.com/learn/coordinate-geometry/lines/equal-intercepts) · [Triangle Centres: Pick the Right One](https://ipmatway.com/learn/coordinate-geometry/lines/triangle-centres) · [Find the Fourth Vertex](https://ipmatway.com/learn/coordinate-geometry/lines/parallelogram-fourth-vertex) · [Point and Parallel-Line Distance](https://ipmatway.com/learn/coordinate-geometry/lines/point-line-distance) · [Image, Foot and Origin Shift](https://ipmatway.com/learn/coordinate-geometry/lines/image-and-shift) · [Triangle Type from Points](https://ipmatway.com/learn/coordinate-geometry/lines/triangle-type-from-points) · [Pair of Lines: Coincidence](https://ipmatway.com/learn/coordinate-geometry/lines/pair-of-lines-coincide)

## Circles in the Plane (Coordinate Geometry, Quant)
Source: https://ipmatway.com/learn/coordinate-geometry/circles

Idea: A circle is all points at a fixed distance r from a centre. Almost every question reduces to one comparison: a distance from the centre (to a point, a line, an axis or another centre) against the radius.
Exam method: 1. Draw the centre and the radius. nearest/farthest, touching an axis, missing the axes are all one-line pictures. 2. S1 is the workhorse. position, tangent length and the 'not outside' condition in one substitution. 3. Half-angle. angle between tangents from P: ()/(2)=(r)/(L) in the right triangle formed by radius, tangent and the line to the centre. 4. Options. for 'which pair of lines are tangents', check the distance of one line in each option - sign patterns usually kill three options at once. 5. Symmetry. the parabolas y^2=kx and x^2=ky meet on y=x; circles touching both axes have centres on y=± x.
Traps: Sign of the centre; sign of c in the radius; the inside case; nearer vs farther axis; degenerate triangles.

Lessons: [Circles in the Plane: start here](https://ipmatway.com/learn/coordinate-geometry/circles/start-here) · [Circle Equation, Centre and Radius](https://ipmatway.com/learn/coordinate-geometry/circles/equation-centre-radius) · [Point to Circle: Min and Max](https://ipmatway.com/learn/coordinate-geometry/circles/distance-point-to-circle-min-max) · [Circle Missing Both Axes](https://ipmatway.com/learn/coordinate-geometry/circles/circle-not-meeting-axes) · [Inside, On, or Outside?](https://ipmatway.com/learn/coordinate-geometry/circles/point-position-wrt-circle) · [Tangents: Distance Equals Radius](https://ipmatway.com/learn/coordinate-geometry/circles/tangent-lines-to-circle) · [Tangent Length and Angle](https://ipmatway.com/learn/coordinate-geometry/circles/tangent-length-angle) · [Circles Touching the Axes](https://ipmatway.com/learn/coordinate-geometry/circles/circle-touching-axis-through-point) · [Chord Length from a Line](https://ipmatway.com/learn/coordinate-geometry/circles/chord-length-line-circle) · [Two Circles: Position and Tangents](https://ipmatway.com/learn/coordinate-geometry/circles/two-circles-position) · [Count Lattice Points Without Repeats](https://ipmatway.com/learn/coordinate-geometry/circles/lattice-points-on-circle) · [Circle Points with Integer Area](https://ipmatway.com/learn/coordinate-geometry/circles/points-on-circle-with-condition) · [Circle Through Given Points](https://ipmatway.com/learn/coordinate-geometry/circles/circle-through-given-points) · [Circle Intercepts on Axes](https://ipmatway.com/learn/coordinate-geometry/circles/circle-intercepts-on-axes) · [Concentric Circles: Rings and Ratios](https://ipmatway.com/learn/coordinate-geometry/circles/concentric-ratio)

## Regions, Areas and Loci (Coordinate Geometry, Quant)
Source: https://ipmatway.com/learn/coordinate-geometry/regions-loci

Idea: A region is a set of points cut out by inequalities; a locus is a set of points obeying one condition. Draw the boundary, read its shape (rhombus, triangle, circle, conic), then measure it - area by geometry, number of lattice points by counting rows or Pick's theorem.
Exam method: 1. Shape first, then numbers. 2|x|+3|y|6 is a rhombus with diagonals 6 and 4 - area 12 in one step. 2. Symmetry halves the work. curves in |x| or x^2 intersect at ± pairs; the segment between them is horizontal. 3. Strict vs non-strict. 'interior' means strict; on a triangle with legs on the axes the interior points need x,y1 and the strict hypotenuse inequality. 4. Classification by option elimination. a ratio of distances to two points is never a parabola or hyperbola; a sum of squares =0 is a point.
Traps: Boundary vs interior; one quadrant only; ratio vs difference loci; coefficients vs denominators.

Lessons: [Regions, Areas and Loci: start here](https://ipmatway.com/learn/coordinate-geometry/regions-loci/start-here) · [Modulus Curves: Find the Area](https://ipmatway.com/learn/coordinate-geometry/regions-loci/area-abs-x-plus-abs-y) · [Lattice Points Inside a Triangle](https://ipmatway.com/learn/coordinate-geometry/regions-loci/lattice-points-in-triangle) · [Counting Points in a Diamond](https://ipmatway.com/learn/coordinate-geometry/regions-loci/manhattan-distance-count) · [Read the Equation, Name the Shape](https://ipmatway.com/learn/coordinate-geometry/regions-loci/conic-classification) · [Distance Ratio Loci](https://ipmatway.com/learn/coordinate-geometry/regions-loci/locus-distance-ratio) · [Distance Between Intersections](https://ipmatway.com/learn/coordinate-geometry/regions-loci/intersection-of-curves-distance) · [Locus: Read the Condition](https://ipmatway.com/learn/coordinate-geometry/regions-loci/locus-basic) · [Inequalities to Areas](https://ipmatway.com/learn/coordinate-geometry/regions-loci/area-of-region-inequalities)

## Trigonometric Identities (Trigonometry, Quant)
Source: https://ipmatway.com/learn/trigonometry/identities

Idea: Every trigonometric ratio of any angle comes from a point on the unit circle, so all of them are tied together by ^2+^2=1 and by the addition formulas. Identities questions ask you to turn what is given (one ratio, a sum, a quadrant) into what is asked, with as little computing as possible.
Exam method: 1. Substitute a value. for identity options put =0, 30^ or 45^ and compare numbers. 2. Square and add. whenever two sums like + and + are given. 3. Pair angles. that add to 90^ or 180^ before evaluating anything. 4. Tan-only. if the ratio ()/() is fixed, rewrite the target as a function of t=.
Traps: Quadrant signs; (A+B) is not A+ B; P versus P^2 in power sums; degrees in arc formulas.

Lessons: [Trigonometric Identities: start here](https://ipmatway.com/learn/trigonometry/identities/start-here) · [Standard Values in Radians](https://ipmatway.com/learn/trigonometry/identities/standard-values-radians) · [Allied Angles: Reduce, Then Sign](https://ipmatway.com/learn/trigonometry/identities/allied-angles-reduction) · [One Ratio, All the Others](https://ipmatway.com/learn/trigonometry/identities/ratios-from-one-ratio) · [Spot the Hidden One](https://ipmatway.com/learn/trigonometry/identities/pythagorean-simplification) · [Sin Plus Cos to Powers](https://ipmatway.com/learn/trigonometry/identities/sin-plus-cos-to-expression) · [Sixth Powers, One Simple Product](https://ipmatway.com/learn/trigonometry/identities/sixth-power-sum) · [Sine and Cosine: Fourth Powers](https://ipmatway.com/learn/trigonometry/identities/sin-n-cos-n) · [Squared Sums: Pair Before You Calculate](https://ipmatway.com/learn/trigonometry/identities/sum-of-squared-cosines) · [Compound Angles: Spot the Pattern](https://ipmatway.com/learn/trigonometry/identities/compound-angle) · [Double and Triple Angles](https://ipmatway.com/learn/trigonometry/identities/double-angle) · [Sum–Product Transformations](https://ipmatway.com/learn/trigonometry/identities/sum-product-transformations) · [Two Sums, One Shortcut](https://ipmatway.com/learn/trigonometry/identities/sums-of-sines-cosines) · [Tan Given? Keep It Tan](https://ipmatway.com/learn/trigonometry/identities/tan-given-expression) · [Two Squares, One Variable](https://ipmatway.com/learn/trigonometry/identities/linear-in-sin2-cos2) · [Radians: Arc, Angle and Area](https://ipmatway.com/learn/trigonometry/identities/radian-arc-length)

## Trigonometric Equations and Ranges (Trigonometry, Quant)
Source: https://ipmatway.com/learn/trigonometry/equations-ranges

Idea: Trigonometric functions are bounded and periodic. Ranges come from the bound ||1 after rewriting the expression as one sine (or as a quadratic in one ratio); equations are solved by factoring into simple pieces and then counting angles in the interval.
Exam method: 1. Bound first. the answer to a range question is usually c±a^2+b^2 - read it off. 2. Vertex test. in g(t)=-at^2+bt+c the vertex t=(b)/(2a) decides whether the end points are enough. 3. Sketch a turn. draw y= x over the interval and mark the horizontal lines for each root. 4. Plug the options. when the stem gives a few candidate angles.
Traps: Impossible roots, closed versus open intervals, the vertex inside [-1,1], one solution per turn at x=±1.

Lessons: [Trigonometric Equations and Ranges: start here](https://ipmatway.com/learn/trigonometry/equations-ranges/start-here) · [Trig Maximum and Minimum](https://ipmatway.com/learn/trigonometry/equations-ranges/max-min-of-trig-expression) · [Trig Ranges Under a Constraint](https://ipmatway.com/learn/trigonometry/equations-ranges/range-under-constraint) · [When Does the Equation Have a Solution?](https://ipmatway.com/learn/trigonometry/equations-ranges/equation-parameter-single-solution) · [Solve Trig Equations in an Interval](https://ipmatway.com/learn/trigonometry/equations-ranges/solve-in-interval) · [Factor First, Count Pairs](https://ipmatway.com/learn/trigonometry/equations-ranges/product-form-equation-count) · [Compare Without Calculating](https://ipmatway.com/learn/trigonometry/equations-ranges/compare-trig-expressions) · [Log Trig: Domain Before Counting](https://ipmatway.com/learn/trigonometry/equations-ranges/log-trig-equation) · [When Sine Equals Cosine](https://ipmatway.com/learn/trigonometry/equations-ranges/sin-cos-equal-condition)

## Trigonometry in Triangles (Trigonometry, Quant)
Source: https://ipmatway.com/learn/trigonometry/triangles

Idea: Inside a triangle the angles and sides are linked by the sine rule (each side over the sine of its opposite angle equals the circumcircle's diameter) and by the cosine rule (Pythagoras corrected by -2bc A). Area is half the product of two sides and the sine of the angle between them.
Exam method: 1. Standard triangles. 30-60-90 (1:√(3):2), 45-45-90 (1:1:√(2)), and integer triangles with a 60^ or 120^ angle (3,5,7 / 5,7,8). 2. AP angles. always B=60^ first. 3. Right triangle with a difference. use (h-a)(h+a)=b^2.
Traps: Angle ratio is not side ratio; the ambiguous case; sign in the cosine rule.

Lessons: [Trigonometry in Triangles: start here](https://ipmatway.com/learn/trigonometry/triangles/start-here) · [Sine Rule and Circumradius](https://ipmatway.com/learn/trigonometry/triangles/sine-rule-circumradius) · [Cosine Rule: Sides and Angles](https://ipmatway.com/learn/trigonometry/triangles/cosine-rule) · [Isosceles Triangle: Side to Radius](https://ipmatway.com/learn/trigonometry/triangles/isosceles-circumradius-relation) · [Area from Two Sides and an Angle](https://ipmatway.com/learn/trigonometry/triangles/area-half-ab-sin) · [AP Angles: Fix the Middle](https://ipmatway.com/learn/trigonometry/triangles/angles-in-ap-triangle) · [Right Triangles: Sum and Difference](https://ipmatway.com/learn/trigonometry/triangles/right-triangle-ratios) · [Triangle Nature from Sides](https://ipmatway.com/learn/trigonometry/triangles/triangle-nature-from-sides)

## Heights and Distances (Trigonometry, Quant)
Source: https://ipmatway.com/learn/trigonometry/heights-distances

Idea: Every heights problem is one or two right triangles sharing a vertical side. The height h and the horizontal distance x are tied by h=x, so two observations give two equations in h and x.
Exam method: 1. Cotangent bookkeeping. write the distances directly as h√(3), h, h√(3). 2. Approximate at the end. √(3)1.732 separates options like 273 and 173. 3. Ratios of times. for moving observers come from ratios of cotangents, not of angles.
Traps: versus , same side versus opposite sides, unit conversion.

Lessons: [Heights and Distances: start here](https://ipmatway.com/learn/trigonometry/heights-distances/start-here) · [Two Angles, One Height](https://ipmatway.com/learn/trigonometry/heights-distances/two-angles-elevation) · [Angles to Speed and Time](https://ipmatway.com/learn/trigonometry/heights-distances/angle-of-depression-speed) · [Tower and Shadow](https://ipmatway.com/learn/trigonometry/heights-distances/tower-and-shadow) · [Moving Observer: Time Ratios](https://ipmatway.com/learn/trigonometry/heights-distances/moving-observer) · [Opposite Sides or Same Side?](https://ipmatway.com/learn/trigonometry/heights-distances/two-objects-opposite-sides) · [Broken Tree, Kite and Ladder](https://ipmatway.com/learn/trigonometry/heights-distances/broken-tree-kite) · [Flagstaff on a Tower](https://ipmatway.com/learn/trigonometry/heights-distances/flagstaff-on-tower) · [Tower Views in 3D](https://ipmatway.com/learn/trigonometry/heights-distances/three-d-elevation)

## Two-Set Venn Problems (Set Theory and Venn Diagrams, Quant)
Source: https://ipmatway.com/learn/set-theory/two-sets

Idea: Two overlapping groups split the population into four non-overlapping parts: only A, only B, both, neither. Every question gives some of these (directly or as totals) and asks for another - or asks how large or small the overlap can be.
Exam method: 1. 2x2 table. rows A / not A, columns B / not B; fill what is given, the rest is subtraction. 2. Extremes in one line. least overlap a+b-N (if positive), greatest (a,b) - Indore 2021 Q10: 60+68-100=28. 3. Two-way splits. (stream x team, Indore 2023 Q24): the overlap is at least m-(N-s) - everyone outside the stream absorbs as many as possible. 4. Linear systems. name only the unknown parts; combine the equations so the unknowns you do not need cancel (Indore 2025: 2×Math - English gives 3e=120).
Traps: Missing 'neither'; least vs greatest; wrong base for a percentage; giving up on a system that does determine the asked quantity.

Lessons: [Two-Set Venn Problems: start here](https://ipmatway.com/learn/set-theory/two-sets/start-here) · [Both, Neither, and the Missing Total](https://ipmatway.com/learn/set-theory/two-sets/both-neither) · [How Small Can Both Be?](https://ipmatway.com/learn/set-theory/two-sets/min-max-both) · [Range of the Overlap Percentage](https://ipmatway.com/learn/set-theory/two-sets/percent-range-both) · [Only A, Only B](https://ipmatway.com/learn/set-theory/two-sets/only-a-only-b) · [Two Exams, One Fixed Answer](https://ipmatway.com/learn/set-theory/two-sets/venn-linear-system) · [Extra Condition, Minimum or Maximum](https://ipmatway.com/learn/set-theory/two-sets/min-max-with-extra-condition)

## Three-Set Venn Problems (Set Theory and Venn Diagrams, Quant)
Source: https://ipmatway.com/learn/set-theory/three-sets

Idea: Three overlapping sets create eight regions. Totals of single sets count the 'exactly two' people twice and the 'all three' people three times; inclusion-exclusion and the region-by-region picture undo that double counting. Extreme-value questions ask how the regions can be arranged.
Exam method: 1. Count extras. n(Ai)-N tells how many 'extra' memberships exist; each exactly-two person uses 1, each all-three person uses 2. 2. Minimum all three. misses add up: 100-(100-pi). 3. Divisibility Venn. count multiples with floors and LCMs; exactly one =S1-2S2+3T (Indore 2026: 50). 4. Statements. build the full region table once - three statements then cost seconds.
Traps: Sign of the triple term; exactly vs at least two; products vs LCMs; caps vs totals.

Lessons: [Three-Set Venn Problems: start here](https://ipmatway.com/learn/set-theory/three-sets/start-here) · [Three Sets, Count Everyone Once](https://ipmatway.com/learn/set-theory/three-sets/inclusion-exclusion-three) · [Exactly One, Two or Three](https://ipmatway.com/learn/set-theory/three-sets/exactly-one-two-three) · [Maximum Passing All Three](https://ipmatway.com/learn/set-theory/three-sets/max-all-three) · [Minimum Common to All](https://ipmatway.com/learn/set-theory/three-sets/min-all-three) · [Maximum Liking More Than One](https://ipmatway.com/learn/set-theory/three-sets/max-liking-multiple) · [Divisibility Counts with Venn](https://ipmatway.com/learn/set-theory/three-sets/divisibility-counting-venn) · [Read the Region, Not Just the Set](https://ipmatway.com/learn/set-theory/three-sets/venn-region-reading)

## Set Algebra and Power Sets (Set Theory and Venn Diagrams, Quant)
Source: https://ipmatway.com/learn/set-theory/sets-algebra

Idea: Set algebra is bookkeeping: how many subsets a set has, how sets combine under union, intersection, difference and complement, and how many elements a set described by a rule contains.
Exam method: 1. Track sizes, not sets,. for nested power sets: 012416. 2. Complement counting. for 'at least one' conditions on subsets: all minus those that avoid the condition. 3. Test identities on tiny sets. two elements per set expose a wrong option immediately. 4. AP of the three Venn parts. middle part =(1)/(3) of the union.
Traps: Proper subsets; P(); \\; strict inequalities in set-builder form.

Lessons: [Set Algebra and Power Sets: start here](https://ipmatway.com/learn/set-theory/sets-algebra/start-here) · [Counting Subsets Quickly](https://ipmatway.com/learn/set-theory/sets-algebra/power-set-cardinality) · [Nested Power Sets](https://ipmatway.com/learn/set-theory/sets-algebra/nested-power-sets) · [Set Builder Counting](https://ipmatway.com/learn/set-theory/sets-algebra/set-builder-counting) · [Three Venn Parts in AP](https://ipmatway.com/learn/set-theory/sets-algebra/cardinality-in-ap) · [Counting Subsets with Conditions](https://ipmatway.com/learn/set-theory/sets-algebra/subset-counting-with-condition) · [Set Operations Without Confusion](https://ipmatway.com/learn/set-theory/sets-algebra/set-operations-identities)

## Counting Numbers and Words (Permutations and Combinations, Quant)
Source: https://ipmatway.com/learn/pnc/counting-numbers

Idea: A number is a string of digits with one extra rule: the first digit is not 0. Every question adds conditions on some places (last digit even, odd digits at odd places, digit sum fixed). Count by filling places one at a time and multiplying the choices.
Exam method: 1. Last digit first, then the first digit. even/divisible by 5 from a set with 0: (ends in 0)+(ends in other); check one case with ^m-1Pk-1. 2. Bounds. below 3000000 with digits 1, 3: all lengths 1-6 (126) plus 7-digit starting with 1 (64): 190. 3. Odd digits at odd places. the first place is odd, so 0 is no problem: ^5P3×^7P2=2520. 4. Digit sum s for 3-digit numbers. s+12 for s≤ 9; above 9 subtract the cases where a digit exceeds 9 (or count by the hundreds digit). 5. Sum of all numbers formed. (n-1)!×(digit sum)× 111.
Traps: A leading 0; one case of the last digit forgotten; the boundary digit in 'greater than'; numbers of other lengths.

Lessons: [Counting Numbers and Words: start here](https://ipmatway.com/learn/pnc/counting-numbers/start-here) · [Digits with Conditions](https://ipmatway.com/learn/pnc/counting-numbers/digits-with-conditions) · [Divisible by 5: Last Digit First](https://ipmatway.com/learn/pnc/counting-numbers/divisible-by-5-from-set) · [Count Beyond the Boundary](https://ipmatway.com/learn/pnc/counting-numbers/greater-than-threshold) · [Digit Sum and Product](https://ipmatway.com/learn/pnc/counting-numbers/digit-sum-condition) · [Two Digits, One Upper Bound](https://ipmatway.com/learn/pnc/counting-numbers/binary-digit-numbers) · [Repeat or Remove?](https://ipmatway.com/learn/pnc/counting-numbers/repetition-vs-no-repetition) · [Divisibility by 3 or 4](https://ipmatway.com/learn/pnc/counting-numbers/divisibility-by-3-or-4) · [Sum Without Listing Every Number](https://ipmatway.com/learn/pnc/counting-numbers/sum-of-numbers-formed) · [Monotone Digits](https://ipmatway.com/learn/pnc/counting-numbers/monotone-digits)

## Arrangements (Permutations and Combinations, Quant)
Source: https://ipmatway.com/learn/pnc/arrangements

Idea: An arrangement is an ordering. Distinct objects in a row: n!. Identical objects reduce the count (divide by their factorials), a round table removes rotations (fix one person), and conditions are handled by blocks (together), gaps (apart) or complements.
Exam method: 1. Gap method in one line. consonants (6!)/(2!2!)=180, gaps 74=35, vowels (4!)/(2!2!)=6: 37800. 2. Two couples at a round table. one couple together 2·6!, minus both together 4·5!: 960. 3. Rank. blocks of (n-1)! per first letter; with repeats divide each block by the repeats left. 4. Option check. the answer for a round table must divide (n-1)! times the inner arrangements - quickly rejects linear counts.
Traps: Repeats ignored; n! at a round table; blocks not arranged internally; end gaps forgotten; 'not all together' confused with 'no two together'.

Lessons: [Arrangements: start here](https://ipmatway.com/learn/pnc/arrangements/start-here) · [Words with Restrictions](https://ipmatway.com/learn/pnc/arrangements/words-with-restrictions) · [Vowels Together or Apart?](https://ipmatway.com/learn/pnc/arrangements/vowels-together-separated) · [Circles with Conditions](https://ipmatway.com/learn/pnc/arrangements/circular-with-constraints) · [No Two Together](https://ipmatway.com/learn/pnc/arrangements/seating-not-adjacent) · [Dictionary Rank: Count the Blocks](https://ipmatway.com/learn/pnc/arrangements/rank-of-word) · [Repeated Letters, Distinct Words](https://ipmatway.com/learn/pnc/arrangements/identical-objects-permutations) · [Together Means Make a Block](https://ipmatway.com/learn/pnc/arrangements/block-arrangement) · [Relative Order, Not Together](https://ipmatway.com/learn/pnc/arrangements/relative-order) · [Derangements: Nobody Correct](https://ipmatway.com/learn/pnc/arrangements/derangements) · [Signals: Any Number of Flags](https://ipmatway.com/learn/pnc/arrangements/signals-any-number) · [Alternate seating](https://ipmatway.com/learn/pnc/arrangements/alternate-seating)

## Selections (Permutations and Combinations, Quant)
Source: https://ipmatway.com/learn/pnc/selections

Idea: A selection ignores order. nr counts the ways to pick r of n distinct items. Conditions are handled by splitting into exact cases, by fixing the forced items, or by subtracting the selections that break the rule.
Exam method: 1. Complement first. at least one black shirt from 2 white, 3 black, 4 red, drawing 3: 93-63=64. 2. Symmetry. 2016=204=4845. 3. Identical items. p identical give p+1 choices (0 to p), each distinct item 2 choices. 4. Divisibility of a product. count the selections that fail (too few factors of 2) and subtract.
Traps: 'One forced item, then anything' double counts; order used for unordered choices; identical items treated as distinct; the empty selection kept.

Lessons: [Selections: start here](https://ipmatway.com/learn/pnc/selections/start-here) · [Committees: At Least and Majority](https://ipmatway.com/learn/pnc/selections/committee-with-inclusion-exclusion) · [At Least One: Count the Opposite](https://ipmatway.com/learn/pnc/selections/at-least-one-of-type) · [Selecting Identical Items](https://ipmatway.com/learn/pnc/selections/indistinguishable-selection) · [Valid Values in n C x](https://ipmatway.com/learn/pnc/selections/ncx-valid-values) · [Subsets With Number Conditions](https://ipmatway.com/learn/pnc/selections/subsets-with-product-condition) · [Selection from Groups](https://ipmatway.com/learn/pnc/selections/selection-from-groups) · [Particular People in Selections](https://ipmatway.com/learn/pnc/selections/particular-included-excluded) · [Total Selections: Two Choices Each](https://ipmatway.com/learn/pnc/selections/total-selections-2n) · [Select, Then Arrange](https://ipmatway.com/learn/pnc/selections/select-then-arrange) · [NPR NCR equations](https://ipmatway.com/learn/pnc/selections/npr-ncr-equations) · [Choose or Assign Roles?](https://ipmatway.com/learn/pnc/selections/basic-combinations)

## Distribution and Partitions (Permutations and Combinations, Quant)
Source: https://ipmatway.com/learn/pnc/distribution

Idea: Distributing n identical items among k people is the same as writing n stars and k-1 bars in a row: n+k-1k-1 ways. Lower bounds are removed by handing them out first; upper bounds by subtracting the cases that exceed them.
Exam method: 1. Shift then count. x11, x22, sum 50, four variables: 47+33=19600. 2. Ranges. 21≤ a+b+c25 in positive integers: s-12=1160, or 253-203 by the hockey stick. 3. Identical boxes. Rohtak 2020 racquets: patterns (3,1,1) and (2,2,1): 10+15=25. 4. Odd parts. x=2a+1 turns 'odd positive' into 'non-negative'.
Traps: Lower index off by one; 'at least one' vs 'zero allowed'; equal groups counted twice; a bound forgotten.

Lessons: [Distribution and Partitions: start here](https://ipmatway.com/learn/pnc/distribution/start-here) · [Non-negative Integer Solutions](https://ipmatway.com/learn/pnc/distribution/non-negative-integer-solutions) · [Minimum Shares: Shift Then Count](https://ipmatway.com/learn/pnc/distribution/positive-solutions-bounded) · [Distinct Items, Identical Boxes](https://ipmatway.com/learn/pnc/distribution/distinct-into-identical-boxes) · [Identical Objects, Upper Caps](https://ipmatway.com/learn/pnc/distribution/identical-into-distinct-with-caps) · [Counting Under Inequalities](https://ipmatway.com/learn/pnc/distribution/inequality-constrained-distribution) · [Different Prizes, Different Students](https://ipmatway.com/learn/pnc/distribution/distinct-into-distinct) · [Identical Bags, Unique Splits](https://ipmatway.com/learn/pnc/distribution/identical-into-identical) · [Coin Combinations](https://ipmatway.com/learn/pnc/distribution/coin-combinations) · [Ordered Factorisations](https://ipmatway.com/learn/pnc/distribution/ordered-factorisations) · [Distinct Items, Unlabelled Groups](https://ipmatway.com/learn/pnc/distribution/grouping-distinct-items)

## Counting in Geometry and Grids (Permutations and Combinations, Quant)
Source: https://ipmatway.com/learn/pnc/geometry-counting

Idea: Geometric figures are chosen sets of points or lines: a triangle is 3 non-collinear points, a line is 2 points, a parallelogram is 2+2 lines from two families. Count the choices and remove the degenerate ones.
Exam method: 1. Collinear points. triangles n3-m3; lines n2-m2+1. 2. Grids. lattice paths m+nm; with a blocked point subtract the paths through it. 3. Stairs. write the Fibonacci list 1,2,3,5,8, up to the required step.
Traps: The collinear line not added back; grid lines vs squares; the recursion read one step off.

Lessons: [Counting in Geometry and Grids: start here](https://ipmatway.com/learn/pnc/geometry-counting/start-here) · [Triangles: Reject Straight Triples](https://ipmatway.com/learn/pnc/geometry-counting/triangles-from-collinear-points) · [Lines from Points](https://ipmatway.com/learn/pnc/geometry-counting/lines-from-points) · [Rectangles from Parallel Lines](https://ipmatway.com/learn/pnc/geometry-counting/rectangles-from-parallel-lines) · [Lattice Paths: Through or Avoid](https://ipmatway.com/learn/pnc/geometry-counting/lattice-paths) · [Staircase Steps](https://ipmatway.com/learn/pnc/geometry-counting/staircase-steps) · [Chessboard Rooks](https://ipmatway.com/learn/pnc/geometry-counting/chessboard-rooks) · [Polygon Diagonals and Crossings](https://ipmatway.com/learn/pnc/geometry-counting/diagonals-of-polygon) · [Squares and Rectangles in Grids](https://ipmatway.com/learn/pnc/geometry-counting/squares-in-grid) · [Intersections, Regions, Triangles](https://ipmatway.com/learn/pnc/geometry-counting/intersection-points) · [Triangles from Polygon Vertices](https://ipmatway.com/learn/pnc/geometry-counting/polygon-triangles)

## Tournaments and Handshakes (Permutations and Combinations, Quant)
Source: https://ipmatway.com/learn/pnc/tournaments

Idea: Tournament counts are pair counts. In a league every pair of teams is one match (or two), in a knockout every match removes one player, and handshakes are unordered pairs while gifts and cards are ordered pairs.
Exam method: 1. Withdrawal. n-12+k (the others' league plus the k matches played). 2. Inverse problems. n2=M means n(n-1)=2M; spot consecutive factors. 3. Different multiplicities between groups. within-group pairs gn2, cross-group pairs n^2 per pair of groups times the number of meetings.
Traps: n(n-1) for a single league; dropping the matches a withdrawn team did play; byes counted as matches.

Lessons: [Tournaments and Handshakes: start here](https://ipmatway.com/learn/pnc/tournaments/start-here) · [Round Robin Match Counts](https://ipmatway.com/learn/pnc/tournaments/round-robin-total) · [Round Robin with Withdrawal](https://ipmatway.com/learn/pnc/tournaments/round-robin-with-withdrawal) · [Knockout Matches, Rounds and Byes](https://ipmatway.com/learn/pnc/tournaments/knockout-matches) · [Minimum Teams from Match Counts](https://ipmatway.com/learn/pnc/tournaments/min-teams-for-match-count) · [Handshakes, Gifts and Couples](https://ipmatway.com/learn/pnc/tournaments/handshakes-gifts)

## Classical Probability (Probability, Quant)
Source: https://ipmatway.com/learn/probability/classical

Idea: When all outcomes of an experiment are equally likely, the probability of an event is (number of favourable outcomes) / (number of all outcomes). Most exam items are counting problems in disguise.
Exam method: 1. Complement first. at least one head in n tosses =1-(1)/(2^n); neither 3 nor 4 =1-P(3 or 4). 2. Selections. probability =····Nk (JIPMAT 2025: exactly 2 children =(10)/(21)). 3. Symmetry. without replacement, the k-th draw behaves like the first. 4. Odds. convert to probabilities before combining events.
Traps: Unordered outcomes treated as equally likely; overlap counted twice; wrong sample space; replacement confused.

Lessons: [Classical Probability: start here](https://ipmatway.com/learn/probability/classical/start-here) · [Two Dice: Count the Right Outcomes](https://ipmatway.com/learn/probability/classical/dice-two) · [Cards: Count Without Double Counting](https://ipmatway.com/learn/probability/classical/cards) · [Balls Without Replacement](https://ipmatway.com/learn/probability/classical/balls-without-replacement) · [Divisibility: Count the Overlap](https://ipmatway.com/learn/probability/classical/digit-divisibility) · [Digit Conditions Decide the Denominator](https://ipmatway.com/learn/probability/classical/three-digit-number-conditions) · [At Least One: Count None First](https://ipmatway.com/learn/probability/classical/at-least-one) · [Three Dice: Count the Orders](https://ipmatway.com/learn/probability/classical/dice-three-sum) · [Position Symmetry](https://ipmatway.com/learn/probability/classical/position-symmetry) · [Selection Probability](https://ipmatway.com/learn/probability/classical/selection-probability) · [Odds Are Not Probabilities](https://ipmatway.com/learn/probability/classical/odds-conversion)

## Conditional Probability and Bayes (Probability, Quant)
Source: https://ipmatway.com/learn/probability/conditional

Idea: Knowing that something happened shrinks the set of possible outcomes. Conditional probability counts inside that smaller set; Bayes' theorem turns 'probability of the evidence given the cause' into 'probability of the cause given the evidence'.
Exam method: 1. Shrink, then count. three dice with sum 10: 27 outcomes, 18 with distinct numbers. 2. Reporter problems. two branches report the event — 'true and he tells the truth' and 'false and he lies'. 3. Independence. multiply; for 'neither' multiply the complements.
Traps: Reversed conditionals; the missing denominator; exclusive mistaken for independent; ignoring the given information.

Lessons: [Conditional Probability and Bayes: start here](https://ipmatway.com/learn/probability/conditional/start-here) · [Truthful Reporter: Which Branch?](https://ipmatway.com/learn/probability/conditional/bayes-truthful-reporter) · [Dice: Given the Sum](https://ipmatway.com/learn/probability/conditional/conditional-on-sum) · [Conditional Cards](https://ipmatway.com/learn/probability/conditional/conditional-cards) · [Neither, Overlap and Independence](https://ipmatway.com/learn/probability/conditional/independent-events-neither) · [Bayes: Which Source?](https://ipmatway.com/learn/probability/conditional/total-probability-bayes) · [When Two Witnesses Contradict](https://ipmatway.com/learn/probability/conditional/contradiction-independent)

## Sequential Events and Games (Probability, Quant)
Source: https://ipmatway.com/learn/probability/sequential

Idea: Repeated independent trials multiply. A specific sequence of successes and failures has probability p^k(1-p)^n-k; how many such sequences there are is a counting question. Games that go on until someone succeeds are geometric series.
Exam method: 1. Rounds. P(A first)=(a)/(1-(1-a)(1-b)). 2. Thresholds. (12)^3=0.125<0.2 but (12)^2=0.25: three tosses. 3. Solvers. list the 2^3 patterns only for the ones asked.
Traps: Rate comparison instead of rounds; missing nk; exactly vs at least; threshold one step short.

Lessons: [Sequential Events and Games: start here](https://ipmatway.com/learn/probability/sequential/start-here) · [Alternating Turns: Who Wins First?](https://ipmatway.com/learn/probability/sequential/alternating-shooters) · [Minimum Trials, Maximum Clarity](https://ipmatway.com/learn/probability/sequential/min-trials-for-threshold) · [First Success and No Consecutive Heads](https://ipmatway.com/learn/probability/sequential/geometric-trials) · [Exactly k and Best of Three](https://ipmatway.com/learn/probability/sequential/binomial-exactly-k) · [Independent Solvers](https://ipmatway.com/learn/probability/sequential/independent-solvers)

## Probability with Numbers (Probability, Quant)
Source: https://ipmatway.com/learn/probability/number-theory-probability

Idea: Choosing a divisor of N at random is choosing each prime exponent independently and uniformly. Properties of the divisor become conditions on the exponents, so the probability is a ratio of counts of exponent choices.
Exam method: 1. Powers of ten. divisors of 10^n that are multiples of 10^m: ((n-m+1)/(n+1))^2. 2. Unit digits. 7^m+7^n divisible by 5 for m,n from 1 to 100: 4 of the 16 cycle pairs, 14. 3. Matrices. count ad=bc directly; the rest are non-singular.
Traps: e instead of e+1; forgetting the divisor 1; number sets instead of placements.

Lessons: [Probability with Numbers: start here](https://ipmatway.com/learn/probability/number-theory-probability/start-here) · [Random Divisors, Counted Fast](https://ipmatway.com/learn/probability/number-theory-probability/factor-of-power-multiple) · [Perfect Square Divisors](https://ipmatway.com/learn/probability/number-theory-probability/perfect-square-factor) · [Singular Matrices from Digits](https://ipmatway.com/learn/probability/number-theory-probability/singular-matrix-from-digits) · [Divisors: Count Exponent Choices](https://ipmatway.com/learn/probability/number-theory-probability/divisor-property) · [Unit Digit Probability](https://ipmatway.com/learn/probability/number-theory-probability/unit-digit-probability)

## Probability of Arrangements (Probability, Quant)
Source: https://ipmatway.com/learn/probability/arrangements-probability

Idea: For random seatings or random arrangements of letters, the probability is (favourable arrangements) / (all arrangements), using exactly the counting tools of permutations: blocks for 'together', gaps for 'apart', and (n-1)! for round tables.
Exam method: 1. Fix a person. at a round table the probability that A and B are adjacent is (2)/(n-1). 2. Gap method. boys first, girls into gaps — then divide by all seatings. 3. Words. glue the letters that must be together; identical letters in a block have one order.
Traps: Row vs round table; block not arranged internally; identical letters arranged.

Lessons: [Probability of Arrangements: start here](https://ipmatway.com/learn/probability/arrangements-probability/start-here) · [Seating: Together or Apart?](https://ipmatway.com/learn/probability/arrangements-probability/seating-separation) · [Round Table Probability](https://ipmatway.com/learn/probability/arrangements-probability/circular-seating) · [Word Arrangement Probability](https://ipmatway.com/learn/probability/arrangements-probability/word-arrangement-probability)

## Mean, Median and Mode (Statistics, Quant)
Source: https://ipmatway.com/learn/statistics/central-tendency

Idea: Mean, median and mode are three ways to summarise a list by one number. The mean responds to every value (so totals are what matter in combined-group and correction questions); the median depends only on order (so tables of counts and medians are really ordering puzzles); the mode is a frequency count.
Exam method: 1. Indore 2024 Q10. N=245, median position 123; cumulative 32,60,103,142 puts it at D's 20th place, D's median: 45. 2. Indore 2024 Q3. A's maximum = B's median -1=29 (B's lower half can all be 30). 3. Indore 2024 Q11. F's ages 50; 14×50+54+14×54=1510. 4. Indore 2025 Q11. m-(15+m)/(3)=2⇒ m=10.5. 5. JIPMAT 2023 Q8. 13·32+13·39-25·36=23. 6. Indore 2026. test x=1,5,13 in 5,8,3x+2,15,27,29,36,5x-2: mean = median for 5 and 13.
Traps: Unsorted median; unweighted combined mean; wrong n after a correction; swapped empirical relation; non-strict bounds in ordered tables.

Lessons: [Mean, Median and Mode: start here](https://ipmatway.com/learn/statistics/central-tendency/start-here) · [Mean, Median, Mode: Pick the Method](https://ipmatway.com/learn/statistics/central-tendency/mean-median-mode-basic) · [Median from Frequency Tables](https://ipmatway.com/learn/statistics/central-tendency/median-from-grouped-counts) · [Median, Mean and Mode: Connect](https://ipmatway.com/learn/statistics/central-tendency/median-mean-relation) · [Median Bounds: Max and Min](https://ipmatway.com/learn/statistics/central-tendency/max-min-under-median) · [Combined Means: Think Totals](https://ipmatway.com/learn/statistics/central-tendency/mean-of-combined-groups) · [Expected Value: Use the Weights](https://ipmatway.com/learn/statistics/central-tendency/expected-value-stratified) · [Median Tables: Order Sets the Bounds](https://ipmatway.com/learn/statistics/central-tendency/median-table-constraints) · [Correct the Total, Check the Count](https://ipmatway.com/learn/statistics/central-tendency/corrected-observation)

## Range, Variance and Deviation (Statistics, Quant)
Source: https://ipmatway.com/learn/statistics/dispersion

Idea: Dispersion measures how far the data spread around the centre. The range looks only at the extremes; the variance averages squared deviations from the mean, and the standard deviation brings that back to the original units. Shifting data does nothing to the spread; scaling it scales the spread.
Exam method: 1. PW HM: SD 10, every item decreased by 1: SD still 10. 2. Variance 16, every observation tripled: 16×9=144. 3. x=60, x^2=400, n=10: variance 40-36=4. 4. First 11 natural numbers: (120)/(12)=10. 5. SD of 2,3,a,11 is 3.5: 3a^2-32a+84=0, a=6.
Traps: n-1; shift added to SD; k vs k^2; variance vs SD; sign of a.

Lessons: [Range, Variance and Deviation: start here](https://ipmatway.com/learn/statistics/dispersion/start-here) · [Range: Watch the Extremes](https://ipmatway.com/learn/statistics/dispersion/range) · [Variance and SD: The Core Methods](https://ipmatway.com/learn/statistics/dispersion/variance-sd-basic) · [Shift Changes Centre, Not Spread](https://ipmatway.com/learn/statistics/dispersion/effect-of-shift-scale)

## Main idea and primary purpose (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/main-idea

Idea: Main-idea questions ask what the whole passage is doing: its central claim, its purpose, or the summary that covers all of it. They appear in almost every IPMAT RC set ("The passage is chiefly concerned with", "The main point the passage makes is", "The objective of the passage is to"). The right answer must cover the whole passage and match the author's attitude. It cannot be a single example, and it cannot claim more than the passage does.
Exam method: 1. Write your own one-liner first. (topic + claim). Example: "Sleep is a part of fitness, and losing it harms health." 2. Classify each option. too narrow (one paragraph, one example), too broad (bigger than the passage), distorted (right words, wrong claim), reversed (the view the author rejects), or just right. 3. Check the verb for purpose questions. "argue / defend / criticise" need an author with a stance; "describe / explain" need a neutral author. A balanced passage cannot have the purpose "to criticise". 4. Extreme-word rule. if an option says always, never, entirely, only, solved, proved and the passage hedges (may, some, often, begun to), eliminate it.
Traps: True but narrow: the most common wrong answer, because it is in the passage. Ask whether it covers every paragraph. Topic without claim: "about sleep" is not "sleep matters for fitness". The rejected view: passages often open with a view they then attack ("Publishers defend..."). That view is not the main idea. Extreme words that the passage never earns.

Lessons: [Main idea and primary purpose: start here](https://ipmatway.com/learn/reading-comprehension/main-idea/start-here) · [Central theme](https://ipmatway.com/learn/reading-comprehension/main-idea/central-theme) · [Primary purpose](https://ipmatway.com/learn/reading-comprehension/main-idea/primary-purpose) · [Best summary](https://ipmatway.com/learn/reading-comprehension/main-idea/best-summary)

## Inference (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/inference

Idea: An inference question ("It can be inferred that", "The passage suggests", "What can be concluded about...") asks for something the passage does not state outright but that must be true, or is very strongly supported, given what it does state. IPMAT setters build most wrong options from the passage's own words pushed too far. Inference boundaries. A valid inference: 1. rests on specific sentences you can point to; 2. takes one short step (combining two facts, or reading an implication); 3. never needs outside knowledge; 4. never says more than the evidence (degree words matter).
Exam method: 1. Locate. find the stem's key phrase in the passage and read two lines either side. 2. Predict. say in your own words what follows. Example: "Treated as a curiosity, then marketed as one, then sells little, then seems to justify the caution" predicts "the caution creates its own evidence". 3. Prove or kill. for each option, find the sentence that makes it true. Kill any option that needs outside knowledge (out of scope), upgrades the degree (extreme), joins unconnected facts (logic gap), or flips the relation (reversal). 4. Last two standing. choose the one that claims less and is still fully supported.
Traps: "Sounds true" is not "follows". Out-of-scope options are often sensible real-world statements. Degree inflation: "may lower" becomes "eliminates"; "some" becomes "most". Two mentions are not a link: "endorphins" and "therapy" both appear, so "endorphins make therapy work" is a logic gap. The passage's words, flipped: reversals reuse the exact vocabulary, so check the direction of the claim.

Lessons: [Inference: start here](https://ipmatway.com/learn/reading-comprehension/inference/start-here) · [Implied claim](https://ipmatway.com/learn/reading-comprehension/inference/implied-claim) · [Author would agree](https://ipmatway.com/learn/reading-comprehension/inference/author-would-agree) · [Not stated](https://ipmatway.com/learn/reading-comprehension/inference/not-stated) · [Apply to new case](https://ipmatway.com/learn/reading-comprehension/inference/apply-to-new-case)

## Specific detail (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/specific-detail

Idea: Detail questions ("According to the passage", "The passage states that", "Which of the following is NOT mentioned") test whether you can find and correctly read a specific sentence. They are the most common RC type in IPMAT Indore PYQs and the easiest to get right, as long as you check the text and do not answer from memory.
Exam method: 1. Keyword scan. pick the most distinctive word in the stem (a name, number, technical term) and scan for it. 2. Read the whole sentence plus one either side. Many traps live in the next sentence ("not because they are poor credit risks but because..."). 3. Match the meaning, not the words. The correct option is usually a paraphrase ("in a graded way" becomes "gradually"). 4. For NOT/EXCEPT questions. confirm three options in the passage and the fourth is the answer. Mark each "S" (stated) as you confirm it. 5. For sequence or cause-effect details. write the chain in short form (e.g. rules eased 2019, first iPhone made in India 2017, stores opened 2023) before reading the options.
Traps: Distortion: "alienate" moves from "partner sellers" to "competitors". Number swap: "42 of the 50 most polluted cities" becomes "all 50". Hasty NOT answers: an option worded differently but meaning the same thing ("penalties" and "punished") is still stated. Memory answers: always re-check the sentence. Detail questions punish "I think it said...".

Lessons: [Specific detail: start here](https://ipmatway.com/learn/reading-comprehension/specific-detail/start-here) · [Locate detail](https://ipmatway.com/learn/reading-comprehension/specific-detail/locate-detail) · [Except not true](https://ipmatway.com/learn/reading-comprehension/specific-detail/except-not-true) · [Sequence of facts](https://ipmatway.com/learn/reading-comprehension/specific-detail/sequence-of-facts)

## Tone and attitude (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/tone-attitude

Idea: Tone questions ask how the author feels about the subject ("The author's attitude towards X is best described as") or why a sentence is there ("In the last sentence, the writer is", "What is the writer's intention in pointing this out?"). IPMAT RC passages are usually analytical or argumentative, so the right answer is typically measured: sceptical, cautiously supportive, critical, concerned, balanced.
Exam method: 1. Collect the evidence words. adjectives and verbs carrying the author's judgement ("weaker than it looks", "sound medicine but ruinous commerce", "None of these problems is a reason to dismiss the idea"). 2. Direction. positive, negative, neutral, or mixed (supports with reservations). 3. Strength. mild or strong. Exam authors rarely shout, so eliminate the extreme words. 4. Author or subject?. "Negative" may describe the news, while the author's intention is to criticise or to warn. 5. Intent-of-sentence. ask what job the sentence does here (opens with irony, rallies the reader, concedes a point, illustrates a claim).
Traps: Extreme tone words. Ask whether a single sentence actually shows contempt or euphoria. Subject vs author. A passage about a grim subject can have a hopeful author. Mixed passages. If the author concedes and then criticises, look for "qualified", "balanced" or "cautious". Unknown words. Learn the core tone vocabulary (ambivalent = mixed feelings; didactic = instructive; sardonic = mocking).

Lessons: [Tone and attitude: start here](https://ipmatway.com/learn/reading-comprehension/tone-attitude/start-here) · [Tone word](https://ipmatway.com/learn/reading-comprehension/tone-attitude/tone-word) · [Attitude to subject](https://ipmatway.com/learn/reading-comprehension/tone-attitude/attitude-to-subject) · [Intent of sentence](https://ipmatway.com/learn/reading-comprehension/tone-attitude/intent-of-sentence)

## Vocabulary in context (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/vocab-in-context

Idea: These questions ask what a word, phrase or idiom means as used in the passage ("The phrase 'that kicks in' (para 3) means", "The synonym for 'stranglehold' is", "The antonym for 'unbounded' is"). IPMAT Indore PYQs use them in almost every set. The context nearly always gives the meaning away, and the traps are the dictionary meanings that don't fit.
Exam method: 1. Find the word and read the full sentence. (and the next one, which often explains it: "a sliver of what is published... three in every hundred books"). 2. Blank it out. and predict a replacement from the context. 3. Match. choose the option closest to your prediction, then put it back into the sentence to check it reads naturally. 4. For antonym questions. fix the meaning in context, then choose its opposite.
Traps: Literal reading of figurative language. Sound-alikes: piety/pity, posterity/prosperity, pedantry/pedestrian. Right meaning, wrong sentence: "gamed" can mean "played", but here it means "manipulated". Synonym in an antonym question: the most common careless error.

Lessons: [Vocabulary in context: start here](https://ipmatway.com/learn/reading-comprehension/vocab-in-context/start-here) · [Word meaning](https://ipmatway.com/learn/reading-comprehension/vocab-in-context/word-meaning) · [Phrase meaning](https://ipmatway.com/learn/reading-comprehension/vocab-in-context/phrase-meaning) · [Idiom in passage](https://ipmatway.com/learn/reading-comprehension/vocab-in-context/idiom-in-passage) · [Antonym in passage](https://ipmatway.com/learn/reading-comprehension/vocab-in-context/antonym-in-passage)

## Suitable title (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/title

Idea: "Which of the following would be the most suitable title for the passage?" is a main-idea question in disguise. The best title captures the passage's subject and its angle in a few words, and it must hold for every paragraph.
Exam method: 1. Use your one-line summary from the main-idea step. 2. For each option, ask: (a) Does it cover all paragraphs? (b) Does it reflect the author's claim, not just the topic? (c) Is it no stronger than the passage? 3. If two titles survive, prefer the one using the passage's own concluding idea (often the last sentence).
Traps: Catchy but wrong: titles that sound good but distort the claim. Too narrow: the most vivid example becomes the title. Too broad: a textbook-chapter title for a focused argument.

Lessons: [Suitable title: start here](https://ipmatway.com/learn/reading-comprehension/title/start-here) · [Title choice](https://ipmatway.com/learn/reading-comprehension/title/title-choice)

## Structure and function (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/structure-function

Idea: Structure questions ask why something is in the passage or how the passage is built: the role of a paragraph, the purpose of an example or analogy, how information is organised, and what the next paragraph would discuss. IPMAT PYQs include all four ("how is the information about treatments organised", "the instance of the shoemaker is an example of", "the writer calls social media the present-day Forum because").
Exam method: 1. Map while skimming. P1 myth, P2 correction, P3 why it matters, P4 second case. 2. Example or analogy questions. find the claim it serves (usually the sentence right before or after). The right option names that claim ("to show that paying for readiness is a familiar idea"), not the content of the example ("fire brigades cost money"). 3. Paragraph-role questions. decide whether the paragraph introduces, supports, objects, concedes, replies, illustrates or concludes, and whether that role is qualified (concede and qualify). 4. Organisation questions. list the sequence of moves (define, then evidence, then cause, then remedy, then resistance) and match the option with the same order. 5. Next-paragraph questions. extend the last sentence's direction.
Traps: Content instead of function: "the example describes a fire brigade" is not "the example shows paying for readiness is familiar". Wrong paragraph: options often describe a neighbouring paragraph accurately. Over-reading a rebuttal: "qualifies" is not "rejects outright". Going backwards in next-paragraph questions.

Lessons: [Structure and function: start here](https://ipmatway.com/learn/reading-comprehension/structure-function/start-here) · [Paragraph role](https://ipmatway.com/learn/reading-comprehension/structure-function/paragraph-role) · [Organisation](https://ipmatway.com/learn/reading-comprehension/structure-function/organisation) · [Next paragraph](https://ipmatway.com/learn/reading-comprehension/structure-function/next-paragraph) · [Example purpose](https://ipmatway.com/learn/reading-comprehension/structure-function/example-purpose)

## Strengthen / weaken (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/strengthen-weaken

Idea: These questions bring critical-reasoning logic into RC: "Which of the following, if true, would most strengthen / weaken the author's argument (or the critics' objection)?" or "What is a limitation of the study?". Treat the options as new facts and ask what each does to the specific claim named in the stem.
Exam method: 1. Name the target claim. and whose it is. 2. Write its logic. "time freed from unpaid work leads to more paid work"; "mixing styles leads to incoherent singing". 3. Strengthen. find new evidence that the link holds (time freed, then more paid work observed). 4. Weaken. find evidence that breaks the link (styles mixed, yet coherent singing). 5. Limitation. what makes the evidence less reliable than it looks (a skewed sample, unequal survival, missing variables)? Use what the passage itself admits first.
Traps: Wrong claim: stems often specify "the critics' first objection" or "the author's argument". Read them twice. Direction errors: circle STRENGTHEN or WEAKEN in the stem. Restatements: "girls' schooling has improved" is already in the passage and adds no support.

Lessons: [Strengthen / weaken: start here](https://ipmatway.com/learn/reading-comprehension/strengthen-weaken/start-here) · [Strengthen](https://ipmatway.com/learn/reading-comprehension/strengthen-weaken/strengthen) · [Weaken](https://ipmatway.com/learn/reading-comprehension/strengthen-weaken/weaken) · [Limitation](https://ipmatway.com/learn/reading-comprehension/strengthen-weaken/limitation)

## Author would agree / disagree (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/author-agree

Idea: "The author would be LEAST likely to agree with..." is a favourite IPMAT stem (full-length mocks and PYQs). Three options are statements the author makes or would accept; one clashes with the text, usually through an absolute word or a reversal. The MOST-agree version asks for the option that follows from the author's own position.
Exam method: 1. Write down the author's position, including concessions ("translators deserve credit, though not co-authorship"). 2. For LEAST. test each option against a specific sentence; the clash is usually explicit ("not... alone" vs "entirely"; "there are none" vs "can be trusted unaided"). 3. For MOST. prefer options that extend the author's stated test or recommendation (an app that lets users freeze a streak passes the author's "free to stop" test). 4. Mark the stem: write L or M beside the question so you don't flip it.
Traps: Reported vs held views: "Critics point out..." is not the author's opinion. Concessions: authors often grant a point to their opponents (the plot belongs to the author; there is "truth" in the designers' defence). Flipping the stem under pressure.

Lessons: [Author would agree / disagree: start here](https://ipmatway.com/learn/reading-comprehension/author-agree/start-here) · [Least likely agree](https://ipmatway.com/learn/reading-comprehension/author-agree/least-likely-agree) · [Most likely agree](https://ipmatway.com/learn/reading-comprehension/author-agree/most-likely-agree)

## Conversation passages (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/conversation-analysis

Idea: Since 2025, one of the three Indore RC passages has been a conversation: an interview, podcast or debate between two or three speakers (2025: podcast and start-ups; 2026: a conversation about the Nile and Egypt, according to coaching analyses). The questions check whether you can track who holds which view, where speakers agree and differ, and what a remark implies in context.
Exam method: 1. Label the speakers. in a margin note (e.g. Rhea = quick commerce, Suresh = kirana). 2. Two-column claims map. note each speaker's main claims in 2–3 words. 3. Mark concessions. every "I agree", "fair point", "you're right that" goes on an agree line. Agreement questions are built on these. 4. Attribution questions. tag every option as A, B, both or neither. "Expressed by X but not Y" eliminates the both options. 5. Implication questions. read the remark with the line before it. Most remarks answer the previous speaker ("you're trying to make it profitable, which isn't the same thing" answers "we're making that service available to everyone").
Traps: Misattribution is the number-one error. Tag before you choose. "Both said it" options in "X but not Y" questions. Host summaries are not agreed positions; speakers often add to them ("And about who got paid..."). Polite openings ("With respect...") often introduce disagreement.

Lessons: [Conversation passages: start here](https://ipmatway.com/learn/reading-comprehension/conversation-analysis/start-here) · [Speaker stance](https://ipmatway.com/learn/reading-comprehension/conversation-analysis/speaker-stance) · [Who said what](https://ipmatway.com/learn/reading-comprehension/conversation-analysis/who-said-what) · [Dialogue inference](https://ipmatway.com/learn/reading-comprehension/conversation-analysis/dialogue-inference) · [Agreement disagreement](https://ipmatway.com/learn/reading-comprehension/conversation-analysis/agreement-disagreement)

## Reading strategy (Reading Comprehension, VARC)
Source: https://ipmatway.com/learn/reading-comprehension/reading-strategy

Idea: RC is the biggest block of the IPMAT Indore VA section: 18 of 45 questions in 2025 and 2026 (three passages of about 6 questions each), with one of the passages written as a conversation. Rohtak sets three shorter passages (about 8–10 questions) and JIPMAT one or two. Reading strategy decides three things: how you read (skim or close-read), which passage you attempt first, and how long you allow each one.
Exam method: Step 1: preview (15 seconds). Glance at the length, the topic and the question stems. Concrete topics (business, health, news) with "according to the passage" questions go first. Abstract topics (philosophy, art theory) with inference and "least likely to agree" questions go later. Step 2: skim for structure (about 60–90 seconds for 400 words). Read the first and last sentence of every paragraph and note one or two words per paragraph (e.g. P1 problem, P2 cause, P3 fix, P4 limits). Watch the signal words: but, however, yet (turn), therefore, so (conclusion), for example (support), some argue (a view the author may reject). Step 3: answer, going to the paragraph each question points to. Main-idea and tone questions come from your skim map. Detail, vocabulary and inference questions need the actual sentence, so read the two lines either side of the key phrase. Step 4: time budget. A good working formula is tpassage (w)/(r) + q · tq where w is the word count, r your reading speed (about 180–220 words per minute in an exam) and tq about 45–60 s per question. For a 450-word, six-question passage: (450)/(200) + 6 × 50 s 7 minutes. In Indore, after about 10 minutes for the 5 TITA para-jumbles and about 15 minutes for the 22 short questions, roughly 15 minutes remain for three passages, about 5 each. So you must skim, not read twice. Step 5: when to cut losses. If, after 90 seconds, you cannot say in one line what the passage is arguing, mark it, do the next passage, and come back with whatever time is left. Answer only the questions you can prove from the text. Leave the rest blank rather than guessing at −1.
Traps: Same speed for every passage. News-style passages reward speed; abstract ones punish it. Adjust your reading speed to the passage. Rereading the whole passage per question. Use your paragraph map and go straight to the relevant paragraph. Sunk-cost reading. Having spent 3 minutes on a passage is no reason to spend 6 more. Move on and come back. Late blind guessing. With negative marking, an unprovable guess has a negative expected score unless you can eliminate at least two options.

Lessons: [Reading strategy: start here](https://ipmatway.com/learn/reading-comprehension/reading-strategy/start-here) · [Skim](https://ipmatway.com/learn/reading-comprehension/reading-strategy/skim) · [Select passage](https://ipmatway.com/learn/reading-comprehension/reading-strategy/select-passage) · [Time budget](https://ipmatway.com/learn/reading-comprehension/reading-strategy/time-budget)

## 4-sentence TITA (Indore) (Para Jumbles, VARC)
Source: https://ipmatway.com/learn/para-jumbles/four-sentence-tita

Idea: In Indore's para-jumbles you type the order of four (sometimes five) numbered sentences, for example 3142. There are no options to eliminate, so the order must be built from the sentences themselves. Every well-made jumble has a few locks: a sentence that can only open, a pair that must sit together, and a sentence that can only close.
Exam method: 1. Mark the dependents. Underline every word that points backwards: this, that, these, he, she, it, they, such, the same, also, however, but, therefore, then, later. A sentence full of these cannot open. 2. Pick the opener. from what is left: a definition, a proper noun introduced in full, a general claim, a date that starts a story. 3. Lock one pair. Find the word with only one possible antecedent ("the three engines" → the sentence that names three engines). Write the pair down, e.g. 4-2. 4. Place the last sentence. Usually only one position remains; check that it reads as an ending (summary, consequence, latest date). 5. Read the whole order once. If a pointer word points to nothing, or "however" contrasts with nothing, change it.
Traps: Two openers: prefer the sentence that introduces a name or term in full; the other sentence will use a short form or pronoun. Floating transitions: "also" needs a first item of the same kind; "however" needs the opposite claim right before it. Hidden time order: dates, "later", "by then", "within a few years" give the order even without pronouns. The reversed answer: a sequence that is the exact reverse of the printed order is almost never correct; recheck it.

Lessons: [4-sentence TITA (Indore): start here](https://ipmatway.com/learn/para-jumbles/four-sentence-tita/start-here) · [Mandatory pair](https://ipmatway.com/learn/para-jumbles/four-sentence-tita/mandatory-pair) · [Opener](https://ipmatway.com/learn/para-jumbles/four-sentence-tita/opener) · [Closer](https://ipmatway.com/learn/para-jumbles/four-sentence-tita/closer) · [Pronoun link](https://ipmatway.com/learn/para-jumbles/four-sentence-tita/pronoun-link) · [Transition link](https://ipmatway.com/learn/para-jumbles/four-sentence-tita/transition-link)

## 5-sentence TITA (Indore) (Para Jumbles, VARC)
Source: https://ipmatway.com/learn/para-jumbles/five-sentence-tita

Idea: Five-sentence TITA items (Indore 2019-2025) need the same skills as four-sentence ones, but random checking no longer works. The method is to build blocks: pairs or triples that must stay together. Then arrange the blocks.
Exam method: 1. Mark backward-pointing words in all five sentences. 2. Build block 1 from the strongest lock ("This means…" + the sentence it explains). 3. Build block 2 from the next lock (a name introduced in full + the sentence that uses its short form; "A study…" + "The study…"). 4. You now have at most three units. Find the opener among them, then the closer. 5. Check the joints between blocks: each joint needs its own reason (time order, cause and effect, contrast).
Traps: Fixing the opener too early. In 2019 Q40 the hook "Incredible as it may sound, we are now told…" opens, not the general sentence about the study. Splitting a block. "A study spanning 170 countries" must come before both "The study…" sentences. Ignoring time words. "Decades later", "by then" and "in the same year" are as strong as pronouns.

Lessons: [5-sentence TITA (Indore): start here](https://ipmatway.com/learn/para-jumbles/five-sentence-tita/start-here) · [Mandatory pair](https://ipmatway.com/learn/para-jumbles/five-sentence-tita/mandatory-pair) · [Opener](https://ipmatway.com/learn/para-jumbles/five-sentence-tita/opener) · [Closer](https://ipmatway.com/learn/para-jumbles/five-sentence-tita/closer) · [Chronology](https://ipmatway.com/learn/para-jumbles/five-sentence-tita/chronology) · [Cause effect](https://ipmatway.com/learn/para-jumbles/five-sentence-tita/cause-effect)

## MCQ with first/last sentence fixed (Rohtak/JIPMAT) (Para Jumbles, VARC)
Source: https://ipmatway.com/learn/para-jumbles/fixed-first-mcq

Idea: Rohtak (and sometimes JIPMAT) gives the first sentence (S1) and the last sentence (S6) of a six-sentence paragraph and jumbles the four in between (P, Q, R, S). Four options are offered, so the task is elimination rather than construction.
Exam method: 1. Read S1 and ask what must come next (an answer to a question, the person just named, the next event). 2. Find that sentence among P, Q, R, S and strike out every option that does not start with it. 3. Among the remaining options, find the one mandatory pair that differs (e.g. "They" in R needs Q) and choose. 4. Check the last sentence leads into S6.
Traps: Stopping at the first match: two options often start with the same sentence; check the next pair. Ignoring S6: the sentence before S6 is as constrained as the one after S1.

Lessons: [MCQ with first/last sentence fixed (Rohtak/JIPMAT): start here](https://ipmatway.com/learn/para-jumbles/fixed-first-mcq/start-here) · [Anchor sentence](https://ipmatway.com/learn/para-jumbles/fixed-first-mcq/anchor-sentence) · [Option elimination](https://ipmatway.com/learn/para-jumbles/fixed-first-mcq/option-elimination)

## MCQ without anchor (Rohtak/JIPMAT 'logical sequence') (Para Jumbles, VARC)
Source: https://ipmatway.com/learn/para-jumbles/mcq-options

Idea: JIPMAT and Rohtak ask jumbles as multiple choice: either a short paragraph (four or five sentences labelled A-E) or a single sentence split into four parts (P, Q, R, S). Because the options are given, the fastest route is elimination.
Exam method: 1. Opener test. Cross out every option whose first label starts with a pointer word ("It", "This", "However", "For instance", "such"). 2. Pair test. Among the survivors, find one pair that must be adjacent ("For that we need…" after the aim it refers to) and choose the option that keeps it. 3. Sentence parts. Put the subject and verb first, attach objects and phrases in grammatical order, and check that the last part can end a sentence.
Traps: Reading all options in full: usually the first label decides. Ignoring grammar in sentence parts: "the art and science a geographical area" is ungrammatical however logical the meaning looks.

Lessons: [MCQ without anchor (Rohtak/JIPMAT 'logical sequence'): start here](https://ipmatway.com/learn/para-jumbles/mcq-options/start-here) · [Option elimination](https://ipmatway.com/learn/para-jumbles/mcq-options/option-elimination) · [Mandatory pair](https://ipmatway.com/learn/para-jumbles/mcq-options/mandatory-pair) · [Sentence parts](https://ipmatway.com/learn/para-jumbles/mcq-options/sentence-parts)

## Missing opening sentence (Para Completion, VARC)
Source: https://ipmatway.com/learn/para-completion/opening-sentence

Idea: Here the first sentence is missing. Indore set this in 2019 (flooding), 2022 (shopping habits), 2023 (river disputes) and 2024 (stolen tomatoes), so expect about one a year. There are two kinds: - Topic sentence. The rest of the paragraph explains, illustrates or proves one general claim, and the blank is that claim. Clue words come after the blank: "for example", a list of causes, or a story that teaches a lesson. - Reference anchor. The second sentence points back to something: "This happened after…", "Such shops…", "These were not the poorest households", "The answer, it turned out, was…". The opener must supply exactly that thing (an event, a kind of shop, a group, a question).
Exam method: 1. Read the sentence right after the blank, slowly. Circle any pointer: this, that, these, such, the answer, for example, also, yet, but. 2. If there is a pointer, name what it needs. "This happened" needs an event. "The answer" needs a question. "For example" needs a general claim. "Such a view" needs a view. Reject every option that does not supply it. 3. If there is no pointer, find the common thread. Ask what every remaining sentence is about. In 2019 every sentence is about infrastructure making floods worse, so the opener must be about infrastructure. 4. Check the scope. The opener should be as wide as the paragraph: not one example (too narrow) and not a sweeping claim the paragraph never supports (too wide). 5. Read the join aloud. Your option plus the second sentence must read naturally without a missing "also" or "another".
Traps: Out of scope: a topic that never comes back (climate change, rainfall amounts). Right point, wrong place: the claim of a later sentence ("men hunt, women gather"). The rejected explanation: after "This was not because…", the option that gives that very reason. True but idle: a correct fact that the paragraph does not develop (record rainfall, an award won). Scope: too narrow (one example) or too wide (sweeping and unsupported).

Lessons: [Missing opening sentence: start here](https://ipmatway.com/learn/para-completion/opening-sentence/start-here) · [Topic sentence](https://ipmatway.com/learn/para-completion/opening-sentence/topic-sentence) · [Reference anchor](https://ipmatway.com/learn/para-completion/opening-sentence/reference-anchor)

## Missing sentence in the middle (Para Completion, VARC)
Source: https://ipmatway.com/learn/para-completion/missing-middle

Idea: A sentence is missing between two others, so the answer has to fit both neighbours. This is the most common Indore position: 9 of the 19 located PYQs (2019 old age, 2020 diseases, 2021 Tokyo Olympics, 2022 Goa and exams, 2023 Indian poetry and the Lucknow villas, 2024 Riken Yamamoto and sports careers). There are three kinds: - Bridge (link-before-after): the blank carries the thought from one sentence to the next (troubles → the pandemic → "Yet Japan is a safe choice"). - Sequence slot: the paragraph is a list or a series of steps (Firstly… Equally important… [blank]… Above all), and the blank is the next item. - Reference link: a word after the blank points back to it: "They become ill more easily", "several causes for this situation", "Villas, hence, provided an ideal substitute". The blank must supply that referent.
Exam method: 1. Start after the blank. Read the next sentence and circle its first few words: pronouns, labels (this situation, the savings), connectors (Yet, But, therefore, Then, In fact). 2. Name what the blank must give. A referent for "They"; a negative for "Yet" to turn against; a cause for "therefore"; a situation for "this situation"; the next list item for "Equally important… Above all". 3. Check the sentence before. The blank must also follow from it (2023: "centred in Calcutta" → the blank must still be about Calcutta, because "Then, gradually, it moved…" comes next). 4. Eliminate in this order. fits one side only → repeats an earlier point → jumps ahead (conclusion, last step) → new topic. 5. Read three sentences together. before + your option + after.
Traps: Half-fit: links to the sentence before but not to the one after (or the other way round). Repeat: restates a point already made (2019 old age: physical problems were covered earlier). Too early: the conclusion or the last step slipped into the middle. Wrong referent: makes "They", "it", "the journey" or "the savings" point to the wrong thing, or to nothing. Wrong direction before "Yet/But": a positive point where a negative one is needed, or the reverse.

Lessons: [Missing sentence in the middle: start here](https://ipmatway.com/learn/para-completion/missing-middle/start-here) · [Link before after](https://ipmatway.com/learn/para-completion/missing-middle/link-before-after) · [Sequence slot](https://ipmatway.com/learn/para-completion/missing-middle/sequence-slot) · [Reference link](https://ipmatway.com/learn/para-completion/missing-middle/reference-link)

## Missing last sentence (Para Completion, VARC)
Source: https://ipmatway.com/learn/para-completion/last-sentence

Idea: The last sentence is missing, and the answer must finish the paragraph in three ways at once: - Logic (logical-close): it follows from what came before: a result, a lesson, what happened instead, or the open question that remains (Indore 2022: a two-script text lets scholars decode the Indus script; 2023: Correa avoided high-rises, so low-rise homes on a human scale). - Scope (scope-match): it covers the whole paragraph, not one part (2021: herbivores help, predators harm → it depends on eating habits; 2024: the paragraph ends on a creativity debate, so the close must be about creativity, not ethics). - Tone (tone-match): it keeps the paragraph's attitude and degree of certainty (2019: every cause is hedged, so the close adds one more possible cause, not "the main reason").
Exam method: 1. Summarise first. In 6-8 words: topic + direction + certainty. ("Arab Spring: several possible causes, all hedged.") 2. Look hard at the last sentence. The close usually responds to it. "Yet it took fifty years" needs a comment on the delay; "avoided high-rise housing" needs what he did instead. 3. Predict the kind of close. a result, a lesson, an open question, a balance of two sides, or one more item in a list. 4. Eliminate. new topic → one side only → extreme words (only, proves, always, never, main) → tone flip → true but idle fact → a "To sum up" that does not sum up. 5. Read the last two sentences together. with your choice.
Traps: Half the picture: the close covers one side of a two-sided paragraph. Overclaiming: "proves", "the main reason", "only", "always" after a hedged paragraph. A false summary: "To sum up…" followed by something the paragraph did not discuss. True but idle: a correct fact that does not close the argument (awards, chemical causes, dates). Tone flip: praise after criticism, a harsh verdict after affection, a solemn statistic after irony.

Lessons: [Missing last sentence: start here](https://ipmatway.com/learn/para-completion/last-sentence/start-here) · [Logical close](https://ipmatway.com/learn/para-completion/last-sentence/logical-close) · [Scope match](https://ipmatway.com/learn/para-completion/last-sentence/scope-match) · [Tone match](https://ipmatway.com/learn/para-completion/last-sentence/tone-match)

## Best summary of the paragraph (Para Summary, VARC)
Source: https://ipmatway.com/learn/para-summary/best-summary

Idea: A para-summary question gives one paragraph and four one-sentence summaries. The best summary is the one a careful reader would write: it keeps the paragraph's main claim, its key qualification, and nothing extra. JIPMAT asked two in 2023 ("determine carefully the main idea"); Indore lists the type in its syllabus.
Exam method: 1. Summarise first. Before looking at the options, write about 15 words: topic + claim + turn. 2. Check coverage. Does the option cover the start and the "but/however" part? If it covers only one, it is too narrow. 3. Check strength. Match the hedges: "can be", "often", "may". An option with "always", "only", "best", "must" is usually too strong. 4. Check additions. Strike out anything not in the paragraph: advice, blame, numbers, comparisons. 5. Choose. the option that survives; if two do, prefer the one that keeps the paragraph's own conclusion.
Traps: The vivid detail (one example, one statistic) is rarely the summary. The missing "but": summaries that keep only the first half of a "but" sentence are too narrow. The extra opinion: "should", "must", "is to blame" usually come from the option writer, not the paragraph.

Lessons: [Best summary of the paragraph: start here](https://ipmatway.com/learn/para-summary/best-summary/start-here) · [Scope](https://ipmatway.com/learn/para-summary/best-summary/scope) · [Extreme word](https://ipmatway.com/learn/para-summary/best-summary/extreme-word) · [Distortion](https://ipmatway.com/learn/para-summary/best-summary/distortion)

## Pick the sentence that does not belong (Odd Sentence Out, VARC)
Source: https://ipmatway.com/learn/odd-sentence-out/odd-sentence

Idea: Five sentences are given; four form a paragraph and one does not belong. Indore has not set this type in 2019-2026 but lists it in the syllabus; it is common in CAT and in coaching tests. Here it is set as a four-option MCQ (the options name four of the five sentences).
Exam method: 1. Name the topic. in three or four words from the sentences that clearly belong together. 2. Link the four. opener, pronoun links, "therefore/also/however". Usually four sentences lock into one chain. 3. Test the leftover. it may share a keyword but shift the theme (a different subject) or the scope (the same subject, a different question, e.g. history instead of how it works). 4. Confirm. reading the four in order should make a complete paragraph without the leftover.
Traps: Same word, different topic (railway, honey, Alexandria). True and interesting is not the same as belonging. A conclusion is not odd: a closing sentence with "therefore" or "this" links back and belongs.

Lessons: [Pick the sentence that does not belong: start here](https://ipmatway.com/learn/odd-sentence-out/odd-sentence/start-here) · [Theme shift](https://ipmatway.com/learn/odd-sentence-out/odd-sentence/theme-shift) · [Scope shift](https://ipmatway.com/learn/odd-sentence-out/odd-sentence/scope-shift)

## Replace the underlined part (Indore style) (Sentence Correction / Improvement, VARC)
Source: https://ipmatway.com/learn/sentence-correction/underlined-part

Idea: Indore has used one sentence-correction format every year from 2019 to 2024: the incorrect part of the sentence is underlined; choose the alternative that makes the sentence correct (27 questions in those six papers). The underlined part always contains at least one error, and the options try to fix it. Some fix it and add a new error, some fix only half, one often repeats the original, and one is right. Almost every item tests one of six families: subject-verb agreement, verb forms (tense, conditionals, verb patterns), pronouns, structure (modifiers, parallelism, comparison, word order), usage (prepositions, idioms, confusable words, redundancy) and nouns/articles.
Exam method: 1. Read the whole sentence. , not just the underlined part. The error is often caused by a word outside it ("yesterday", "the city of Kundapur", "Besides offering…"). 2. Name the error and its rule. in two or three words ("each = singular", "if-clause: no would", "dangling modifier"). 3. Predict the fix. , then scan for it. 4. Eliminate in pairs. Where options split on a point (best/better, who/whom, its/their), settle that point and cut half of them. Then check the survivors for a second error. 5. Re-read the full sentence. with your choice. It must be grammatical and keep the meaning.
Traps: Half fixes: one error corrected, another kept or added. The original wording offered again as an option. Meaning changes: cause and effect reversed, a new person added. Wordy or passive versions of a correct idea, when a direct option exists. Spoken English vs exam English: "If I was", "whoever you are assigned", "taller than me". Exams follow the formal rule (see the rule note in each solution).

Lessons: [Replace the underlined part (Indore style): start here](https://ipmatway.com/learn/sentence-correction/underlined-part/start-here) · [Subject verb](https://ipmatway.com/learn/sentence-correction/underlined-part/subject-verb) · [Verb form](https://ipmatway.com/learn/sentence-correction/underlined-part/verb-form) · [Pronoun](https://ipmatway.com/learn/sentence-correction/underlined-part/pronoun) · [Structure](https://ipmatway.com/learn/sentence-correction/underlined-part/structure) · [Usage](https://ipmatway.com/learn/sentence-correction/underlined-part/usage) · [Noun article](https://ipmatway.com/learn/sentence-correction/underlined-part/noun-article)

## Improve the bold part, with a "No improvement" option (Rohtak/JIPMAT style) (Sentence Correction / Improvement, VARC)
Source: https://ipmatway.com/learn/sentence-correction/sentence-improvement

Idea: This is the Rohtak/JIPMAT (and SSC/bank) format: part of a sentence is in bold (or underlined), three replacements are offered, and (D) "No improvement" is the fourth option. Unlike the Indore format, the bold part may already be correct, so you must first decide whether there is an error, then choose the right fix.
Exam method: 1. Read the full sentence. and look at the words just before and after the bold part. 2. Test the bold part against a short checklist. subject and verb agree? tense fits the time words? pronoun in the right case? fixed partners (no sooner… than, hardly… when, prefer… to, discuss + no preposition) correct? 3. If a rule is broken, predict the fix. and find it among (A)-(C). 4. If no rule is broken, choose (D). Do not swap a correct form for an equally correct one; the question asks for an improvement. 5. Re-read. your choice in the sentence.
Traps: Over-correction: about a quarter of these sentences are already correct. Look-alike partners: than/then/when after "no sooner" and "hardly". Local fixes that clash elsewhere: a right-sounding verb that breaks agreement with the subject. (D) out of doubt: if a rule is clearly broken, (D) is wrong.

Lessons: [Improve the bold part, with a "No improvement" option (Rohtak/JIPMAT style): start here](https://ipmatway.com/learn/sentence-correction/sentence-improvement/start-here) · [Subject verb](https://ipmatway.com/learn/sentence-correction/sentence-improvement/subject-verb) · [Verb form](https://ipmatway.com/learn/sentence-correction/sentence-improvement/verb-form) · [Pronoun](https://ipmatway.com/learn/sentence-correction/sentence-improvement/pronoun) · [Structure](https://ipmatway.com/learn/sentence-correction/sentence-improvement/structure) · [Usage](https://ipmatway.com/learn/sentence-correction/sentence-improvement/usage) · [Noun article](https://ipmatway.com/learn/sentence-correction/sentence-improvement/noun-article) · [No improvement](https://ipmatway.com/learn/sentence-correction/sentence-improvement/no-improvement)

## Pick the correct sentence among four (Sentence Correction / Improvement, VARC)
Source: https://ipmatway.com/learn/sentence-correction/choose-correct-sentence

Idea: Four complete sentences are given; three contain one clear error each and one is correct. This appears in Rohtak and JIPMAT practice sets and older Indore mocks. It tests the same rules as the other two formats, but you must find the error yourself, with no bold part to point at it.
Exam method: 1. Read sentence (A) with the checklist. subject-verb, tense and time words, pronoun case, opening phrase, comparison or pair, preposition or look-alike word, noun or article. 2. Strike it when you find an error;. move to the next. 3. The survivor is usually clear by (C). Check it once more against the checklist. 4. If two survive,. reread both slowly, especially "along with / as well as", "each / neither", "than any", "whom… thought", and every opening "-ing" phrase.
Traps: Sounds right, breaks a rule: "between you and I", "whom they thought had won". Dangling openings hidden in long sentences. Unlike comparisons: a rate compared with a country, a camera with a phone. Look-alikes: affect/effect, principle/principal, loose/lose, it's/its.

Lessons: [Pick the correct sentence among four: start here](https://ipmatway.com/learn/sentence-correction/choose-correct-sentence/start-here) · [Subject verb](https://ipmatway.com/learn/sentence-correction/choose-correct-sentence/subject-verb) · [Verb form](https://ipmatway.com/learn/sentence-correction/choose-correct-sentence/verb-form) · [Pronoun](https://ipmatway.com/learn/sentence-correction/choose-correct-sentence/pronoun) · [Structure](https://ipmatway.com/learn/sentence-correction/choose-correct-sentence/structure) · [Usage](https://ipmatway.com/learn/sentence-correction/choose-correct-sentence/usage) · [Noun article](https://ipmatway.com/learn/sentence-correction/choose-correct-sentence/noun-article)

## Find the erroneous part: three parts + (D) No error (Rohtak/SSC format) (Spot the Error, VARC)
Source: https://ipmatway.com/learn/spot-the-error/part-error

Idea: This is the Rohtak and SSC/bank format: the sentence is cut into three parts, (A), (B) and (C), and (D) is No error. At most one part is wrong. Rohtak printed exactly this format in 2019 and 2020 ("no errors" / "No error" as (D)); JIPMAT 2021 used a different format (see underlined-error). Every item in this bank names its rule (xruleid), and every rule is explained in shared/grammarrules.json.
Exam method: 1. Subject → verb. find the real subject (cross out "of…", "as well as…", "along with…") and check its verb. 2. Time words → tense. ago/yesterday (simple past), since/for (present perfect), by the time (past perfect), by next year (future perfect), if/when (no "will"). 3. Pairs and fixed words. no sooner… than, hardly/scarcely… when, although (no but), unless/lest (no extra not), superior/senior/prefer + to, comply with, accused of, discuss (no about). 4. Nouns and articles. advice/information/furniture (no plural), a/an by sound, "the" with epics, rivers and unique things, one of the + plural noun. 5. Pronouns. object form after prepositions and verbs (between you and me), who/whom by its own clause. 6. Nothing breaks?. Choose (D). Do not "fix" a correct sentence.
Traps: Nearest noun: the verb agrees with the head of the subject, not the noun beside it. Look-wrong-but-right: bread and butter is; the news was; the police have; a number of… are; neither… nor + nearer subject. Partner words: than/then/when after no sooner and hardly. Contested points: "one of those who + plural verb" is the exam rule, though informal English often uses the singular (the solutions say so when an item depends on it).

Lessons: [Find the erroneous part: three parts + (D) No error (Rohtak/SSC format): start here](https://ipmatway.com/learn/spot-the-error/part-error/start-here) · [Subject verb](https://ipmatway.com/learn/spot-the-error/part-error/subject-verb) · [Verb form](https://ipmatway.com/learn/spot-the-error/part-error/verb-form) · [Pronoun](https://ipmatway.com/learn/spot-the-error/part-error/pronoun) · [Structure](https://ipmatway.com/learn/spot-the-error/part-error/structure) · [Usage](https://ipmatway.com/learn/spot-the-error/part-error/usage) · [Noun article](https://ipmatway.com/learn/spot-the-error/part-error/noun-article) · [No error](https://ipmatway.com/learn/spot-the-error/part-error/no-error)

## Pick the wrong underlined word or phrase (JIPMAT 2021 format) (Spot the Error, VARC)
Source: https://ipmatway.com/learn/spot-the-error/underlined-error

Idea: JIPMAT 2021 printed a sentence with four underlined words or phrases and asked which one contains the error; the four options were those phrases, in a shuffled order. There is no "No error" option, so the question is only where the error is. The rules are the same as in part-error; this bank shows the underlined parts in bold.
Exam method: 1. Read the whole sentence once. and locate the subject and main verb. 2. Check the bold verb forms first. (agreement, tense, -ing vs to), then pronouns, then the small words (prepositions, articles, conjunctions). 3. Name the fix. ("have → has"). If you cannot name a fix for a part, it is probably correct. 4. Match to the option. (they may be shuffled).
Traps: Noun vs verb: in "The bunch of keys were found", the wrong word is "were", not "keys". Deletion fixes: "Although… but", "Unless you don't", "discussed about": the extra word is the error. Shuffled options: do not assume (A) is the first underlined part.

Lessons: [Pick the wrong underlined word or phrase (JIPMAT 2021 format): start here](https://ipmatway.com/learn/spot-the-error/underlined-error/start-here) · [Subject verb](https://ipmatway.com/learn/spot-the-error/underlined-error/subject-verb) · [Verb form](https://ipmatway.com/learn/spot-the-error/underlined-error/verb-form) · [Pronoun](https://ipmatway.com/learn/spot-the-error/underlined-error/pronoun) · [Structure](https://ipmatway.com/learn/spot-the-error/underlined-error/structure) · [Usage](https://ipmatway.com/learn/spot-the-error/underlined-error/usage) · [Noun article](https://ipmatway.com/learn/spot-the-error/underlined-error/noun-article)

## Single blank, vocabulary (Fill in the Blanks, VARC)
Source: https://ipmatway.com/learn/fill-in-the-blanks/single-vocab

Idea: One word is missing, and the sentence itself tells you what kind of word it is. Indore tested single blanks in most years from 2019 to 2023, often as phrase blanks (2021: "domineer over her children", "affects the citizen"), and the 2026 paper leaned on hard words. Rohtak and JIPMAT use plain single-blank vocabulary items. Every item is one of five sub-skills: a context clue, a collocation (the word's fixed partner), connotation (positive vs negative shade), a confusable look-alike, or a hard-word set where only one option is defined by the clue.
Exam method: 1. Find the clue. Underline the words that define the blank: a phrase after a colon or dash, a "so… that" result, or an example. 2. Find the signal. Contrast (although, but, unlike, far from, rather than) flips the clue; support (and, colon) keeps it; cause (so… that, because) makes the blank cause the result. 3. Predict. your own word, even a plain one ("careful", "harmless"). 4. Match and eliminate. Cut options of the wrong direction first, then the wrong shade, then the wrong part of speech. 5. Re-read the full sentence. with your choice. For hard-word sets, you only need to know one or two words: cut the ones you know are wrong.
Traps: Reversal: the option describes the other side of a contrast (the quiet brother, the old temper). Shade trap: stingy/thrifty, obstinate/firm, cramped/cosy. Same idea, wrong attitude. Look-alikes: wreck/wreak, allay/ally, invalid/invaluable, discreet/discrete. Fancy-word trap: a rare word that sounds impressive but is not defined by the clue. Double negative: "not… hardly / never".

Lessons: [Single blank, vocabulary: start here](https://ipmatway.com/learn/fill-in-the-blanks/single-vocab/start-here) · [Context clue](https://ipmatway.com/learn/fill-in-the-blanks/single-vocab/context-clue) · [Collocation](https://ipmatway.com/learn/fill-in-the-blanks/single-vocab/collocation) · [Connotation](https://ipmatway.com/learn/fill-in-the-blanks/single-vocab/connotation) · [Confusables](https://ipmatway.com/learn/fill-in-the-blanks/single-vocab/confusables) · [Rare word](https://ipmatway.com/learn/fill-in-the-blanks/single-vocab/rare-word)

## Double blank, vocabulary (Fill in the Blanks, VARC)
Source: https://ipmatway.com/learn/fill-in-the-blanks/double-vocab

Idea: Two blanks in one sentence (or two short sentences), and the two words must work together. Indore used two-blank items in 2019 and 2023 (dementia: "indistinguishable … reversible"; Cairo: "ubiquitous … immortalised"), and mock series list "2 blanks, vocab" as a regular block. The extra blank makes the question easier if you use it: each blank is a filter.
Exam method: 1. Read the whole sentence and mark the signal. that links the blanks: and / colon (same direction), but / though / for all its / rather than (opposite), so… that / because (cause and result). 2. Pick the easier blank,. the one with the clearer clue, and predict a word for it. 3. Strike. every option whose word for that blank fails. Usually two options die. 4. Test the survivors on the other blank. against the signal. 5. Read the finished sentence once. Watch for the right words in the wrong order.
Traps: Half-true: one word perfect, the other wrong. Always check both blanks. Order swap: in "X rather than Y" and "once X, now Y" items, the trap is the right pair reversed. No contrast: after "but / though", two words of the same direction are wrong even if each word fits alone.

Lessons: [Double blank, vocabulary: start here](https://ipmatway.com/learn/fill-in-the-blanks/double-vocab/start-here) · [Pair consistency](https://ipmatway.com/learn/fill-in-the-blanks/double-vocab/pair-consistency) · [Contrast signal](https://ipmatway.com/learn/fill-in-the-blanks/double-vocab/contrast-signal) · [Cause effect](https://ipmatway.com/learn/fill-in-the-blanks/double-vocab/cause-effect)

## Three or four blanks (Indore 2019–2025 style) (Fill in the Blanks, VARC)
Source: https://ipmatway.com/learn/fill-in-the-blanks/triple-vocab

Idea: Three (sometimes four) blanks spread over one to three sentences, often lifted from an editorial or a non-fiction book. Indore has set them almost every year: 2019 (assiduous/querulous, multiculturalism, quantum physics), 2020 (coral reefs, privilege, cohesive team, CIF), 2021 (listening, events, appraisal, Aravalli), 2022 (two four-blank items: philosophy and spaceflight), 2023 (influencers, work from home, 21st-century culture) and a full set of six in 2024. 2025 again had double and triple items. The words are rarely obscure; the skill is elimination.
Exam method: 1. Read the whole passage once. for its direction (positive or negative, cause or contrast, technical or general). 2. Hunt for the anchor blank. a fixed phrase ("without in history", "orally as well as in "), a defined term ("collective investment fund" → pooled), or the clearest clue. 3. Eliminate on the anchor. Typically two or three options die. 4. Test survivors on the next-easiest blank,. including grammar (is it a verb, an adjective, a superlative?). 5. Stop as soon as one option survives,. then read it through once.
Traps: Partial fit: two words excellent, one wrong (outstanding events, sentinel to events, reject a function). Check the weakest-looking word in each surviving option. Look-alikes inside a set: stereotypes/archetypes, discerningly/discreetly. Right word, wrong blank: an option uses the key words but swaps them (prioritise … compromised). Register misfit: technical words from another field (nominal scale, tectonic landscape).

Lessons: [Three or four blanks (Indore 2019–2025 style): start here](https://ipmatway.com/learn/fill-in-the-blanks/triple-vocab/start-here) · [Pair consistency](https://ipmatway.com/learn/fill-in-the-blanks/triple-vocab/pair-consistency) · [Elimination by one blank](https://ipmatway.com/learn/fill-in-the-blanks/triple-vocab/elimination-by-one-blank) · [Four blank](https://ipmatway.com/learn/fill-in-the-blanks/triple-vocab/four-blank)

## Single blank, grammar (Indore 2025 style) (Fill in the Blanks, VARC)
Source: https://ipmatway.com/learn/fill-in-the-blanks/grammar-single

Idea: A one-blank sentence where the options differ only in grammar: a preposition, a verb form, a tense, an article, a conjunction, a pronoun, or the clause that follows an opening phrase. Indore's 2023 paper had "It grieved me my friend's serious illness" (to hear of), and analyses of 2025 report about two grammar items next to the vocabulary FIBs. The old Indore pattern ("single blank, grammar-based" × 5) and Rohtak/JIPMAT grammar items use the same format. These are the fastest marks in the section, provided you apply rules rather than "what sounds right".
Exam method: 1. Spot what the options vary in. (prepositions? tenses? a/an/the?). That tells you which rule is being tested. 2. Find the trigger in the sentence. a time marker, a verb that needs a partner, "neither / hardly / such", "of the…" before the verb, an opening phrase. 3. Apply the rule. and predict the form. 4. Pick it, and check one trap. is the "natural-sounding" option an Indian-English habit (discuss about, suggested to)?
Traps: Indian-English habits: discuss about, return back, suggested to + verb, "am living since", "is closed since". Nearest-noun agreement: cross out "of…" phrases and "along with / as well as" phrases first. Correlative pairs: hardly/scarcely… when; no sooner… than; neither… nor; such… that. Conditionals: if + present → will; if + past → would; if + had + p.p. → would have + p.p.; wish about the past → had + p.p.

Lessons: [Single blank, grammar (Indore 2025 style): start here](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/start-here) · [Preposition](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/preposition) · [Tense](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/tense) · [Article](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/article) · [Conjunction](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/conjunction) · [Verb form](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/verb-form) · [Agreement](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/agreement) · [Modal conditional](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/modal-conditional) · [Pronoun determiner](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/pronoun-determiner) · [Modifier](https://ipmatway.com/learn/fill-in-the-blanks/grammar-single/modifier)

## Cloze passage (JIPMAT/Rohtak) (Fill in the Blanks, VARC)
Source: https://ipmatway.com/learn/fill-in-the-blanks/cloze-test

Idea: A short passage (100–200 words) with five numbered blanks and one question per blank. JIPMAT sets one cloze passage of five blanks every year, and Rohtak has used single passages too. Indore's multi-blank items are separate sentences, not a cloze. Blanks test four things: meaning in context, collocation (fixed partners), connectors (but, instead of, rather than, before) and grammar form (participles, prepositions, no double negatives).
Exam method: 1. Skim the passage once. for topic and direction (is it praising, warning, explaining?). 2. For each blank, name its type. and apply the matching test: - Context: predict a word from the clue around the blank, including the next sentence. - Collocation: which option is the fixed partner (steady stream, put to good use, make room for)? - Connector: name the relation (contrast → but; replacement → instead of; order → before). - Grammar: part of speech, participle after a comma, no second negative. 3. Answer the easy blanks first;. they make the hard ones clearer. 4. Read the passage through with all five answers. before moving on.
Traps: Sentence-only judgement: always glance at the next sentence. Collocation slips: put to good use, a steady stream, make room for. Reversal of the paragraph's point: a word that fits the sentence but contradicts the passage. Double negatives after "not".

Lessons: [Cloze passage (JIPMAT/Rohtak): start here](https://ipmatway.com/learn/fill-in-the-blanks/cloze-test/start-here) · [Context flow](https://ipmatway.com/learn/fill-in-the-blanks/cloze-test/context-flow) · [Collocation](https://ipmatway.com/learn/fill-in-the-blanks/cloze-test/collocation) · [Connector](https://ipmatway.com/learn/fill-in-the-blanks/cloze-test/connector) · [Grammar form](https://ipmatway.com/learn/fill-in-the-blanks/cloze-test/grammar-form)

## Double blank, grammar (Fill in the Blanks, VARC)
Source: https://ipmatway.com/learn/fill-in-the-blanks/grammar-double

Idea: Two grammar blanks in one sentence: usually two prepositions (grateful to someone for something) or two verb forms that must fit one time line (reached … had left). This format appears in course books and in Rohtak/JIPMAT-style grammar sections. It tests the same rules as single-blank grammar, but the wrong options are built from one correct and one incorrect form.
Exam method: 1. Pick the blank with the firmer rule. (agreement or a fixed preposition beats a tense choice). 2. Eliminate. every option that fails it. 3. Check the survivors on the other blank,. and watch for the correct pair in the wrong order. 4. For verb pairs, draw the time line. mark which event is earlier and whether the time runs up to now.
Traps: Swapped pair: the two right words in the wrong blanks. Half-right: check both blanks every time. Time-frame clash: one clause in the past, the other in the present perfect.

Lessons: [Double blank, grammar: start here](https://ipmatway.com/learn/fill-in-the-blanks/grammar-double/start-here) · [Preposition pair](https://ipmatway.com/learn/fill-in-the-blanks/grammar-double/preposition-pair) · [Verb form pair](https://ipmatway.com/learn/fill-in-the-blanks/grammar-double/verb-form-pair)

## Subject-verb agreement (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/subject-verb

Idea: A verb must agree with its subject in number (singular or plural) and person (I / you / he-she-it / we / they). Most exam items hide the real subject: they put a plural noun between the subject and the verb, add "along with" or "as well as", use a pronoun such as "each" or "neither", or start the sentence with "there". Find the true subject first and the item is solved. Rohtak and JIPMAT test it through spot-the-error and sentence improvement; Indore through underlined-part correction and "choose the correct sentence".
Exam method: 1. Underline the verb. of each clause (in spot-the-error, usually part B or C). 2. Find its subject. Strike out "of…", "along with…", "as well as…" phrases and relative clauses. 3. Classify the subject. each/every/one of/the number of/amount → singular; a number of/X and Y → plural; either…or → nearer noun; there → noun after the verb. 4. Check the pronoun too. a singular collective noun takes "its", not "their". 5. If every verb agrees, look elsewhere (tense, pronoun, preposition), or choose "No error".
Traps: Nearest-noun trap: The results of the survey… shows (results → show); The list of documents… are (list → is). Add-on phrases: as well as, along with, together with, accompanied by, in addition to, like never turn a singular subject into a plural one. Either/neither: "neither of + plural noun" alone is singular (Neither of the answers is correct); "neither X nor Y" goes by the nearer noun. A number / the number: one letter changes the verb. Collective nouns: keep the verb and the pronoun together (has… its or, when members act separately, were… their). Contested points (one of those who + verb; none of + plural) are never the only tested point; if an item depends on one, the solution says so.

Lessons: [Subject-verb agreement: start here](https://ipmatway.com/learn/grammar-rules/subject-verb/start-here) · [Person number](https://ipmatway.com/learn/grammar-rules/subject-verb/person-number) · [Intervening phrase](https://ipmatway.com/learn/grammar-rules/subject-verb/intervening-phrase) · [Either neither](https://ipmatway.com/learn/grammar-rules/subject-verb/either-neither) · [Indefinite pronoun](https://ipmatway.com/learn/grammar-rules/subject-verb/indefinite-pronoun) · [Collective noun](https://ipmatway.com/learn/grammar-rules/subject-verb/collective-noun) · [Compound subject](https://ipmatway.com/learn/grammar-rules/subject-verb/compound-subject) · [Quantity expression](https://ipmatway.com/learn/grammar-rules/subject-verb/quantity-expression)

## Tenses (identification and sequence) (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/tense

Idea: English has twelve tense forms: three times (present, past, future) × four aspects (simple, continuous, perfect, perfect continuous). JIPMAT asks for them in three ways: name the tense of a sentence (2021), match List I with List II (2024, 2025, 2026: four sentences against four tense names), and choose the right tense form in a sentence (2024 Q2, 2025 Q5). Indian books often say indefinite for simple (present indefinite = simple present).
Exam method: 1. First auxiliary → time. is / am / are / has / have / do / does = present; was / were / had / did = past; will / shall = future. 2. Next word → aspect. ing = continuous; have / had + past participle = perfect; been + -ing = perfect continuous; nothing = simple. 3. Check for a passive. be + past participle: read the tense from "be" only. 4. Match-the-list items. fix the pair you are surest of (usually the simple form) and eliminate; one more pair usually decides.
Traps: Passive look-alikes: will be declared, had been postponed, is being repaired: identify from "be", and remember be + past participle is passive. "Been" alone is perfect, not perfect continuous. has vs had: present perfect vs past perfect. Time vs form: a timetable future (leaves tomorrow) is still simple present. Stative verbs (know, believe, own) do not take continuous forms: I have known her, not I have been knowing her.

Lessons: [Tenses (identification and sequence): start here](https://ipmatway.com/learn/grammar-rules/tense/start-here) · [Identify tense](https://ipmatway.com/learn/grammar-rules/tense/identify-tense) · [Time marker](https://ipmatway.com/learn/grammar-rules/tense/time-marker) · [Perfect vs simple](https://ipmatway.com/learn/grammar-rules/tense/perfect-vs-simple) · [Reported tense shift](https://ipmatway.com/learn/grammar-rules/tense/reported-tense-shift)

## Parallel structure (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/parallelism

Idea: Items joined by and / or, items in a list, and the two halves of a correlative pair (not only… but also, either… or, neither… nor, both… and) must have the same grammatical form. A sentence that mixes forms (reading, painting and to cycle) is unbalanced and wrong. Indore 2020 Q18 (not only on the plight of abandoned dogs, but also on that of overworked bulls) tests this.
Exam method: 1. Find the joiner. (and, or, a comma list, or a correlative pair). 2. Write the items one under another. in your head; mark the form of each. 3. Find the odd one out. that part has the error (or that option fixes it). 4. For pairs. , compare the words right after each half.
Traps: Infinitive in an -ing list (or the reverse). A clause in a list of adjectives or nouns (and they inform). Unmatched halves of a pair (not only + adjective, but also + verb). Repeated or missing prepositions: with students, teachers and among retired people.

Lessons: [Parallel structure: start here](https://ipmatway.com/learn/grammar-rules/parallelism/start-here) · [List](https://ipmatway.com/learn/grammar-rules/parallelism/list) · [Correlative conjunction](https://ipmatway.com/learn/grammar-rules/parallelism/correlative-conjunction)

## Misplaced / dangling modifiers (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/modifiers

Idea: A modifier is a word or phrase that describes something. It must sit next to the thing it describes. When an opening phrase has no doer of its own, English reads the first noun after the comma as its doer; if that noun is wrong, the modifier dangles (Walking home, a fox was seen says the fox was walking). A misplaced modifier is in the wrong spot (only, or a describing phrase next to the wrong noun). Indore 2020 Q17 (karate) is a dangling-modifier item.
Exam method: 1. Opening phrase before a comma?. Name its doer. 2. Read the first noun after the comma. If it is not that doer, the sentence dangles. 3. Pick the option. that puts the doer first, or that gives the opener its own subject. 4. Describing phrase in the middle or end?. Check it touches its noun.
Traps: Passive main clauses after an -ing opener. Possessive doers: Walking home, my bag felt heavy (the bag did not walk). -ed and to-openers dangle too, not only -ing ones. Describing phrases at the far end of the sentence (by the owner of five thousand rupees).

Lessons: [Misplaced / dangling modifiers: start here](https://ipmatway.com/learn/grammar-rules/modifiers/start-here) · [Dangling participle](https://ipmatway.com/learn/grammar-rules/modifiers/dangling-participle) · [Misplaced only](https://ipmatway.com/learn/grammar-rules/modifiers/misplaced-only)

## Pronoun agreement / ambiguity / case (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/pronouns

Idea: A pronoun stands for a noun, so it must (1) take the right case for its job (subject I/he/she/we/they/who; object me/him/her/us/them/whom), (2) agree in number and gender with the noun it stands for, and (3) point clearly to one noun. Exams also test reflexives (myself), relative pronouns (who for people, which for things) and reciprocal pronouns (each other). Indore 2019 Q29, 2021 Q17 and 2023 Q29 were pronoun items.
Exam method: 1. Spot every pronoun. in the sentence or the options. 2. Case. subject of a verb → I/he/who; after a verb or preposition → me/him/whom. Use the pair test. 3. Myself/himself. is the same person both doer and receiver? If not, use I/me. 4. Who/whom. cut out the clause, remove "do you think / they said", answer with he/him. 5. Agreement. find the noun the pronoun replaces; singular company/city → its. 6. Ambiguity. two possible nouns of the same gender → the noun must be repeated.
Traps: Polite myself: My father and myself, the results surprised Anil and myself: use I / me. Pairs after prepositions: to Ravi and I, for my sister and I: always me. Inserted clauses: whom do you think will lead → who. Its / it's / their: a firm, school, city or committee acting as one unit is "it". Which / who: people take who (or that), never which. Two-way action: blamed each other (each blamed the other) vs blamed themselves (each blamed himself).

Lessons: [Pronoun agreement / ambiguity / case: start here](https://ipmatway.com/learn/grammar-rules/pronouns/start-here) · [Case](https://ipmatway.com/learn/grammar-rules/pronouns/case) · [Antecedent](https://ipmatway.com/learn/grammar-rules/pronouns/antecedent) · [Who whom](https://ipmatway.com/learn/grammar-rules/pronouns/who-whom) · [Ambiguity](https://ipmatway.com/learn/grammar-rules/pronouns/ambiguity)

## Prepositions and dependent prepositions (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/prepositions

Idea: A preposition links a noun or pronoun to the rest of the sentence. Most preposition questions are about fixed partners: many verbs, adjectives and nouns always take one particular preposition (accused of, comply with), and some verbs take none (discuss the plan, not discuss about). JIPMAT has "fill in the preposition" items and Indore 2023 Q26 (grieved me to hear of) was a preposition FIB.
Exam method: 1. Find the word before the preposition. (verb, adjective or noun) and recall its partner. 2. Is it one of the "no preposition" verbs?. Then the preposition is the error. 3. A comparison with senior / superior / prefer?. It must be "to". 4. Time phrase?. at clock, on day, in month/year. 5. "Between" in the sentence?. Look for "and".
Traps: Extra preposition after discuss, reach, enter, order, describe, approach. "Than" after senior, superior, inferior, prefer. Wrong time preposition: on 10 a.m., in Monday, at 2024. Broken pairs: between… to, from… and. Look-alike partners: angry with a person, angry at/about a thing; different from; comply with.

Lessons: [Prepositions and dependent prepositions: start here](https://ipmatway.com/learn/grammar-rules/prepositions/start-here) · [Fixed preposition](https://ipmatway.com/learn/grammar-rules/prepositions/fixed-preposition) · [Verb preposition](https://ipmatway.com/learn/grammar-rules/prepositions/verb-preposition)

## Articles (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/articles

Idea: English has two articles: a/an (indefinite: one of many, not yet identified) and the (definite: this particular one). Exams test three things: choosing a or an by sound, the rule that a singular countable noun needs an article, and the list of places where the is used or left out (Rohtak 2020 Q19: The war of Mahabharata → The war of the Mahabharata).
Exam method: 1. Find each noun. in the sentence; ask: singular countable? Then it needs a determiner. 2. A or an?. Say the next word aloud. 3. The?. Is the thing unique, superlative, "only", already identified, or a river/sea/range/epic? Then "the". 4. Extra "the"?. General statements, names of people and cities, languages, meals take none.
Traps: Silent h: an hour, an honest, an heir; but a hotel, a house. Yoo- and wun- sounds: a university, a European, a one-way ticket. Abbreviations read as letters: an MLA, an FIR, an SOS. Missing "the": rivers, seas, ranges, epics, superlatives, "only". Missing a/an: become a doctor, buy a laptop.

Lessons: [Articles: start here](https://ipmatway.com/learn/grammar-rules/articles/start-here) · [A an](https://ipmatway.com/learn/grammar-rules/articles/a-an) · [The omission](https://ipmatway.com/learn/grammar-rules/articles/the-omission)

## Conditionals and subjunctive (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/conditionals

Idea: A conditional sentence has a condition (the if-clause) and a result (the main clause). The verb forms of the two clauses must belong to the same pattern, and the pattern depends on whether the situation is real or unreal, and present/future or past. The same "unreal past" logic covers wish and it is time. Rohtak 2019 Q28 (If he had tried), Indore 2022 Q24 (would have driven you there) and Indore 2022 Q25 (provided she has) are conditional items.
Exam method: 1. Find the time. of the condition and of the result (tomorrow / now / yesterday). 2. Real or unreal?. Pick the pattern from the table. 3. Check both clauses. against the pattern; the commonest error is "would" or "will" inside the if-clause. 4. Wish / it is time. move the verb one step into the past.
Traps: will / would in the if-clause: if it will rain, if I would have known. Mixed time words: had… last year + now → would + base, not would have. Unreal present with "will": If I were the principal, I will… → would. Wish + past simple for a past regret: needs had + past participle. It is high time + present: needs the past.

Lessons: [Conditionals and subjunctive: start here](https://ipmatway.com/learn/grammar-rules/conditionals/start-here) · [If clause](https://ipmatway.com/learn/grammar-rules/conditionals/if-clause) · [Wish were](https://ipmatway.com/learn/grammar-rules/conditionals/wish-were)

## Active and Passive Voice (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/voice

Idea: In the active voice the doer is the subject (The cat drank the milk). In the passive the receiver of the action becomes the subject and the doer moves into a "by" phrase or disappears (The milk was drunk by the cat). Only verbs with an object can be made passive. A change of voice changes nothing else: the tense, the modal, the time words and every other word stay the same. JIPMAT asks this in every paper (2 items a year from 2021 to 2026) in both directions, active to passive and passive to active. Rohtak 2025 also had two.
Exam method: 1. Name the tense of the given verb. in two seconds (was + -ing = past continuous; will + base = simple future). 2. Eliminate options with the wrong voice. a "passive" option without be + past participle, or an "active" option that still has one. 3. Eliminate options with the wrong tense. of "be" (the commonest trap: was helped for were helping). 4. Eliminate role swaps. and changed words (modal, article, time phrase). 5. The survivor is the answer; check the past participle (drunk, given, broken).
Traps: Tense drift: was helped for were helping, has been for had been, would for will. Wrong verb form: was drank, was gave, was broke: the passive always takes the past participle. Missing "be" or "been": The results will announce…, My bicycle has stolen: these are active forms with the wrong subject. Role reversal: The police were arrested by the thief. Changed words: a voice change never turns "this" into "the", "can" into "could" or "a fortnight" into "that fortnight". Questions: By who (should be by whom); Whom was elected (should be Who); Did the plan approved (should be Was the plan approved).

Lessons: [Active and Passive Voice: start here](https://ipmatway.com/learn/grammar-rules/voice/start-here) · [Transform](https://ipmatway.com/learn/grammar-rules/voice/transform) · [Passive to active](https://ipmatway.com/learn/grammar-rules/voice/passive-to-active) · [Questions commands](https://ipmatway.com/learn/grammar-rules/voice/questions-commands) · [Identify correct passive](https://ipmatway.com/learn/grammar-rules/voice/identify-correct-passive)

## Direct and Indirect Speech (Narration) (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/narration

Idea: Direct speech gives the speaker's exact words in quotation marks: He said, "I am tired." Indirect (reported) speech reports them from the reporter's point of view: He said that he was tired. JIPMAT asks one or two items a year (2021–2026), mostly direct to indirect, sometimes indirect to direct. Every item tests the same three changes: the reporting verb and joining word, the pronouns, and the tense and time words.
Exam method: 1. Type of sentence?. Pick the reporting verb family (said/told, asked, ordered/requested, proposed, exclaimed). This often removes one or two options at once. 2. Pronouns. find who "I" and "you" are, then strike every option with a wrong person. 3. Structure. strike "said me", "told to", "asked that what", "asked where did I", "requested that let". 4. Tense and time words. check backshift (or no backshift after "says").
Traps: Wrong person: "you" is the listener, not the speaker; "our" said by the fans is "their". Question order and extra words: asked me where did I live, asked me that if…, a question mark in reported speech. "Said" vs "told": said me, told that, told to me are all wrong. Backshift after "says": a present reporting verb keeps the tenses. Wrong reporting verb: requested for a military order, ordered for advice, regretted for self-praise. Meaning changes: had gone for must go, would finish for have finished.

Lessons: [Direct and Indirect Speech (Narration): start here](https://ipmatway.com/learn/grammar-rules/narration/start-here) · [Tense backshift](https://ipmatway.com/learn/grammar-rules/narration/tense-backshift) · [Pronoun shift](https://ipmatway.com/learn/grammar-rules/narration/pronoun-shift) · [Reporting verb](https://ipmatway.com/learn/grammar-rules/narration/reporting-verb) · [Questions](https://ipmatway.com/learn/grammar-rules/narration/questions) · [Commands requests](https://ipmatway.com/learn/grammar-rules/narration/commands-requests) · [Exclamations wishes](https://ipmatway.com/learn/grammar-rules/narration/exclamations-wishes) · [Indirect to direct](https://ipmatway.com/learn/grammar-rules/narration/indirect-to-direct)

## Conjunctions and connectors (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/conjunctions

Idea: Conjunctions join clauses and show how they relate. Exams test (1) correlative pairs whose two halves are fixed (no sooner… than), (2) double conjunctions (although… but), (3) the built-in negatives unless and lest, and (4) choosing a connector whose logic fits the sentence. JIPMAT 2023 Q33 (Hardly had the function got over…) was a correlative item (left out of the bank because its key was faulty; see voice/tense census).
Exam method: 1. Spot the first half of a pair. (no sooner, hardly, both, neither, so/such) and check its partner. 2. Sentence starts with no sooner / hardly / scarcely?. Check for "had + subject". 3. Although / though?. Delete any "but". 4. Unless / lest?. Delete any "not"; lest takes should or the base verb. 5. FIB with connectors. read both clauses, name the relation, then choose.
Traps: Swapped partners: no sooner… when, hardly… than. Missing inversion after a fronted no sooner / hardly / scarcely. Two conjunctions for one link: although… but, because… so. Double negatives with unless / lest. Wrong logic: "because" where the clauses contrast.

Lessons: [Conjunctions and connectors: start here](https://ipmatway.com/learn/grammar-rules/conjunctions/start-here) · [Correlative](https://ipmatway.com/learn/grammar-rules/conjunctions/correlative) · [Although but](https://ipmatway.com/learn/grammar-rules/conjunctions/although-but)

## Adjectives, adverbs, comparison (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/adjectives-adverbs

Idea: Adjectives describe nouns; adverbs describe verbs, adjectives and other adverbs. Exams test two areas: comparison (comparative vs superlative, "any other", like-with-like, double comparatives, "as… as", elder/older) and choosing the right word class (adjective vs adverb, -ed vs -ing, too vs very). Indore 2019 Q28 (Which team has the better record, yours or theirs?) and 2024 Q32 (Hitchcock's thrillers vs those of any other filmmaker) are comparison items.
Exam method: 1. "Than" or "-est" in the sentence?. Count the things compared (two → -er) and check for a double marker. 2. Ask "what is compared with what?". Salary with salary, thrillers with thrillers (that of / those of). 3. Member of its own group?. Add "other". 4. "As" comparison?. Both "as" words, and "than" after the second comparative. 5. Word after the verb. action verb → -ly; linking verb → adjective.
Traps: Two vs many: the better of the two, the best of all. Any vs any other: check whether the subject belongs to the group. Unlike things compared: salary vs manager, thrillers vs filmmaker. Linking verbs: feel bad, look happy, taste good (adjectives, not adverbs). elder than is always wrong.

Lessons: [Adjectives, adverbs, comparison: start here](https://ipmatway.com/learn/grammar-rules/adjectives-adverbs/start-here) · [Comparative superlative](https://ipmatway.com/learn/grammar-rules/adjectives-adverbs/comparative-superlative) · [Adjective vs adverb](https://ipmatway.com/learn/grammar-rules/adjectives-adverbs/adjective-vs-adverb)

## Nouns: number, countability, possessives (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/nouns-number

Idea: English nouns are either countable (a bag, two bags) or uncountable (luggage, advice). The difference decides the plural, the article and the quantity word (fewer bags, less luggage). A second group of rules covers nouns whose form misleads: plural-looking nouns that are singular (news), nouns that are always plural (police), number + noun used as an adjective (a five-rupee note), possessives and "kind of". Rohtak 2020 Q20 (drop little sugar) and Indore 2021 Q19 (less people) are of this type.
Exam method: 1. Circle the nouns. near the quantity words, articles and verbs. 2. Countable?. If not, there can be no -s, no a/an, no "many / few / fewer". 3. Misleading form?. news / mathematics → singular; police / cattle / people → plural. 4. Number + noun before a noun?. Must be singular and hyphenated. 5. One of / each / every / this kind of?. Check the noun's number. 6. Few vs a few. read the meaning: "luckily / so I could" needs the positive "a few".
Traps: Less with countable nouns (less bags, less people). Hidden uncountables: advice, equipment, luggage, scenery, stationery, furniture, information. News is; police are. Compound adjectives: five-rupee, ten-year-old, three-day; two dozen, five hundred. Few vs a few: the sentence's meaning decides. Possessives: children's (not childrens'), principal's office.

Lessons: [Nouns: number, countability, possessives: start here](https://ipmatway.com/learn/grammar-rules/nouns-number/start-here) · [Uncountable](https://ipmatway.com/learn/grammar-rules/nouns-number/uncountable) · [Plural forms](https://ipmatway.com/learn/grammar-rules/nouns-number/plural-forms)

## Verb patterns (gerund, infinitive, bare infinitive) (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/verb-patterns

Idea: When one verb follows another, the second verb's form is fixed by the first: some verbs take the to-infinitive (refuse to sign), some the -ing form (avoid meeting), some the bare infinitive (make him wait), and modals take the base verb (would have accepted). A preposition is always followed by -ing, and the "to" of look forward to and be used to is a preposition. Indore 2023 Q30 (he would have definitely accepted such an offer) was a modal-perfect item.
Exam method: 1. Find the first verb. (or modal, or preposition) and recall its pattern. 2. Is "to" a preposition?. Try a noun after it: look forward to the holiday works, so it is a preposition → -ing. 3. make / let / have?. Active → bare verb; passive → to. 4. Modal?. Base verb, or "have + past participle" for the past.
Traps: Preposition "to": look forward to, object to, be used to, with a view to → -ing. Gerund verbs: avoid, enjoy, suggest, mind, finish, deny, consider. Infinitive verbs: refuse, decide, hope, agree, want, plan. make / let + to in the active is wrong; made + bare verb in the passive is wrong. Modal + past form: must have inform, would accepted.

Lessons: [Verb patterns (gerund, infinitive, bare infinitive): start here](https://ipmatway.com/learn/grammar-rules/verb-patterns/start-here) · [Gerund infinitive](https://ipmatway.com/learn/grammar-rules/verb-patterns/gerund-infinitive)

## Word order (inversion, question tags, indirect questions) (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/word-order

Idea: English normally puts the subject before the verb. Three structures change or test that order: inversion after a fronted negative adverb (the auxiliary jumps before the subject), question tags (a short question that reverses the polarity of the statement), and indirect questions (a question inside a statement goes back to statement order). Indore 2019 Q30, 2022 Q28 (inversion) and 2023 Q28 (question tag) test this.
Exam method: 1. Sentence starts with a negative or limiting word?. Look for auxiliary + subject. 2. Tag at the end?. Decide the polarity of the statement (watch never / nothing / hardly), then flip it; keep the same auxiliary and a pronoun. 3. Question word after asked / wondered / tell me / know?. Subject before verb; drop do / does / did.
Traps: Missing do/did in inversion with a simple tense. Hidden negatives in the statement (never, nothing, hardly, scarcely, seldom, nobody). Fixed tags: aren't I?, shall we? Question order kept inside indirect and embedded questions.

Lessons: [Word order (inversion, question tags, indirect questions): start here](https://ipmatway.com/learn/grammar-rules/word-order/start-here) · [Inversion](https://ipmatway.com/learn/grammar-rules/word-order/inversion) · [Question tag](https://ipmatway.com/learn/grammar-rules/word-order/question-tag) · [Indirect question](https://ipmatway.com/learn/grammar-rules/word-order/indirect-question)

## Usage (redundancy, confusable words, fixed expressions) (Grammar: Voice, Narration, Tenses + Rule Bank, VARC)
Source: https://ipmatway.com/learn/grammar-rules/usage

Idea: Usage items are not about a grammar pattern but about word choice: saying a thing once (no redundancy, no double negative, no roundabout phrasing), choosing between look-alike words, and keeping fixed expressions exactly as they are. Indore tests these heavily in underlined-part correction (2019 Q27, Q31, Q32; 2020 Q16; 2021 Q16; 2022 Q26, Q27; 2023 Q31) and Rohtak 2019 Q27 asked for the natural word ("room").
Exam method: 1. Look for doubled meaning. back, again, together, both… as well as, reason… because. 2. Count the negatives. in each clause. 3. Check look-alike words. against their meaning in the sentence. 4. Fixed phrase?. Recall it exactly, especially its preposition. 5. Among the correct options, prefer the shortest direct one. (Indore keys are often the concise version).
Traps: Back / again after words that already contain them. Reason… because, each and every one of them all. Double negatives with hardly, scarcely, barely, no, never. Look-alikes: affect/effect, its/it's, than/then, lie/lay, principal/principle. Idiom prepositions: hands of, avail of, part in, despite (none).

Lessons: [Usage (redundancy, confusable words, fixed expressions): start here](https://ipmatway.com/learn/grammar-rules/usage/start-here) · [Redundancy](https://ipmatway.com/learn/grammar-rules/usage/redundancy) · [Confusable words](https://ipmatway.com/learn/grammar-rules/usage/confusable-words) · [Collocation idiom](https://ipmatway.com/learn/grammar-rules/usage/collocation-idiom)

## Pick the sentence that uses the word wrongly (Indore format) (Word Usage, VARC)
Source: https://ipmatway.com/learn/word-usage/incorrect-word-usage

Idea: Indore set 5-6 of these every year from 2019 to 2024 (33 located): one word appears in four sentences and one sentence uses it wrongly. Usually the wrong sentence wanted a different word that sounds or looks the same (a homophone such as cord for chord, or a look-alike such as flout for flaunt). Less often the spelling is right but the sense is wrong (a "spot" on a career, jokes that are "cross"), or the word class is wrong (critic for critique). The section was dropped in 2025-26 but could return; the same pairs also appear in FIB and sentence correction.
Exam method: 1. Name the meanings. of the word you know (cord = rope, umbilical cord, measure of wood). 2. Test each sentence. which meaning does it need? If none of the word's meanings fits, the writer meant another word. Say that word to yourself (chord, tide, flaunt). 3. Check the word class. does the slot need a verb, a noun, an adjective? 4. Do not punish rare senses. "A cord of wood", "the Bar", "a stay order", "train of thought" are correct. 5. Ignore unrelated slips. elsewhere in a sentence; the question is only about the word.
Traps: Rare but correct senses (2023 cord of wood; 2019 the Bar barred all bards; 2024 stay order). Unrelated slips in a correct-usage sentence (2024 "The rules… proscribes"). Reading look-alikes too fast: luxuriant/luxurious, climatic/climactic, ordinance/ordnance.

Lessons: [Pick the sentence that uses the word wrongly (Indore format): start here](https://ipmatway.com/learn/word-usage/incorrect-word-usage/start-here) · [Homophone](https://ipmatway.com/learn/word-usage/incorrect-word-usage/homophone) · [Look alike](https://ipmatway.com/learn/word-usage/incorrect-word-usage/look-alike) · [Sense shift](https://ipmatway.com/learn/word-usage/incorrect-word-usage/sense-shift) · [Part of speech](https://ipmatway.com/learn/word-usage/incorrect-word-usage/part-of-speech)

## Best word for the context (near-synonyms) (Word Usage, VARC)
Source: https://ipmatway.com/learn/word-usage/contextual-usage

Idea: Near-synonyms differ in connotation (positive or negative shade: thrifty vs stingy, determined vs stubborn, famous vs notorious) and in register (formal or informal: commence vs kick off, inform vs fill in). This skill underlies Indore's word-usage items and its vocabulary-based fill-in-the-blanks.
Exam method: 1. Mark the attitude clue. admired, praised, delighted (positive) or avoided, disappointed, criticised (negative). 2. Mark the setting. formal letter, notice, court, research paper; or casual speech. 3. Sort the options. into positive/negative or formal/informal and keep the group that matches.
Traps: Right meaning, wrong shade: stubborn/determined, notorious/famous, nosy/curious. Right meaning, wrong register: kick off/commence, grab/obtain, fill in/inform.

Lessons: [Best word for the context (near-synonyms): start here](https://ipmatway.com/learn/word-usage/contextual-usage/start-here) · [Connotation](https://ipmatway.com/learn/word-usage/contextual-usage/connotation) · [Register](https://ipmatway.com/learn/word-usage/contextual-usage/register)

## Pick the sentence that uses the word correctly (Word Usage, VARC)
Source: https://ipmatway.com/learn/word-usage/confusables

Idea: The same confusable pairs that Indore tested in its word-usage section, practised in reverse: four sentences, and only one uses the word or words correctly. Learning the pairs below covers most of what IPMAT has asked. | Pair | Meaning 1 | Meaning 2 | Tested in | |---|---|---|---| | affect / effect | influence (verb) | result (noun) | Indore 2020, 2023 SC | | appraise / apprise | assess value | inform | Indore 2021 | | callus / callous | hard skin | unfeeling | Indore 2024 | | chord / cord | musical notes | rope | Indore 2023 | | climatic / climactic | weather | climax | Indore 2021, 2023 | | defuse / diffuse | calm (a crisis) | spread | Indore 2024 | | flaunt / flout | show off | disobey | Indore 2022 | | further / farther | advance; more | distance | Indore 2023 | | ingenious / ingenuous | clever | naive | Indore 2020 | | intense / intensive | very strong | thorough | Indore 2021 | | ordinance / ordnance | rule | weapons | Indore 2020 | | prescribe / proscribe | lay down | forbid | Indore 2024 | | urbane / urban | polished | of a city | Indore 2020 |
Exam method: 1. Find every pair word. in the four sentences. 2. Check each against its meaning. (or expand it, for contractions). 3. A sentence is right only if every pair word in it is right. 4. Pick the one survivor.
Traps: Half-right sentences: one pair word right, the other wrong (Whether the weather…). Contractions: who's/whose, they're/their/there, it's/its.

Lessons: [Pick the sentence that uses the word correctly: start here](https://ipmatway.com/learn/word-usage/confusables/start-here) · [Homophone](https://ipmatway.com/learn/word-usage/confusables/homophone) · [Look alike](https://ipmatway.com/learn/word-usage/confusables/look-alike)

## Meaning / usage of idioms (Idioms, Phrasal Verbs, Foreign Phrases, One-word Substitution, VARC)
Source: https://ipmatway.com/learn/idioms-phrases/idioms

Idea: Indore has asked 2-8 idiom or phrasal-verb completions every year from 2019 to 2024 (34 located: 28 idioms, 6 phrasal verbs). The format never changes: a sentence with a blank and four phrases, of which only one is the exact, standard idiom with the right meaning. Rohtak and JIPMAT more often ask the meaning of an idiom printed in bold.
Exam method: 1. Read the sentence and name the meaning needed. in plain words ("be lenient", "very rarely", "in trouble"). 2. Cut altered idioms. any option with one word changed from the standard form (beneath the weather, a spoon of her own medicine, past muster). 3. Cut literal phrases. made from the idiom's words (nests and eggs). 4. Check the meaning. of the real idioms left: a real idiom with the wrong meaning is the last trap (face the music vs play it by ear).
Traps: Altered idioms: slice of cake, go to the extra mile, ill at heart. Wrong real idiom: break the ice, face the music, a storm in a teacup when another idiom is needed. Literal readings: nests and eggs; hiding documents craftily.

Lessons: [Meaning / usage of idioms: start here](https://ipmatway.com/learn/idioms-phrases/idioms/start-here) · [Fill idiom](https://ipmatway.com/learn/idioms-phrases/idioms/fill-idiom) · [Meaning](https://ipmatway.com/learn/idioms-phrases/idioms/meaning)

## Phrasal verbs (Idioms, Phrasal Verbs, Foreign Phrases, One-word Substitution, VARC)
Source: https://ipmatway.com/learn/idioms-phrases/phrasal-verbs

Idea: A phrasal verb is a verb plus a particle whose meaning is often not the sum of its parts (put up with = tolerate). Indore 2024 was phrasal-heavy (4 of its 7 idiom items: comes down to, fell through, brought about, puts up with). Options normally keep the same verb and change only the particle, so knowing particle meanings and the grammar of each phrasal verb is the whole game.
Exam method: 1. Name the meaning the blank needs. (fail, cause, tolerate, depend on). 2. Group the options by verb. and compare particles. 3. Run the object test. does the phrasal verb take the following noun, and with the right preposition? 4. Re-read. with your choice.
Traps: Wrong particle: dropped out, brought up, puts her off. Wrong grammar: scrape through (no object), backed down of, come round the flu.

Lessons: [Phrasal verbs: start here](https://ipmatway.com/learn/idioms-phrases/phrasal-verbs/start-here) · [Fill phrasal](https://ipmatway.com/learn/idioms-phrases/phrasal-verbs/fill-phrasal) · [Meaning](https://ipmatway.com/learn/idioms-phrases/phrasal-verbs/meaning)

## Foreign words and phrases (JIPMAT) (Idioms, Phrasal Verbs, Foreign Phrases, One-word Substitution, VARC)
Source: https://ipmatway.com/learn/idioms-phrases/foreign-phrases

Idea: JIPMAT and Rohtak ask the meaning of Latin and French phrases common in English, especially in law and news writing (de jure, alias, bona fide, status quo). The sentence around the phrase is usually enough to work out the meaning even if the phrase is new.
Exam method: 1. If you know the phrase. , answer directly. 2. If not, use the sentence. what must the phrase mean for the sentence to make sense? 3. Beware the partner phrase. (de facto/de jure, per se/per capita) and literal one-word guesses.
Traps: Partner phrases: de facto vs de jure; per se vs per capita. Literal guesses: faux pas as "false step" (close) vs "false promise" (wrong).

Lessons: [Foreign words and phrases (JIPMAT): start here](https://ipmatway.com/learn/idioms-phrases/foreign-phrases/start-here) · [Latin french meaning](https://ipmatway.com/learn/idioms-phrases/foreign-phrases/latin-french-meaning)

## One-word substitution (Rohtak/JIPMAT) (Idioms, Phrasal Verbs, Foreign Phrases, One-word Substitution, VARC)
Source: https://ipmatway.com/learn/idioms-phrases/one-word-substitution

Idea: Rohtak and JIPMAT ask for the single word that replaces a description ("a person who cannot be corrected" → incorrigible). Most answers are built from Greek or Latin roots, and the distractors are usually words from the same family.
Exam method: 1. Split the description. into its key parts ("government" + "by a few"). 2. Map parts to roots. (-cracy/-archy = rule; olig- = few). 3. Check the part of speech. (person, adjective, noun). 4. Separate same-family options. carefully (atheist/agnostic/theist).
Traps: Same family: agnostic/atheist, autocracy/oligarchy, claustrophobia/agoraphobia. Look-alikes: illegible/ineligible.

Lessons: [One-word substitution (Rohtak/JIPMAT): start here](https://ipmatway.com/learn/idioms-phrases/one-word-substitution/start-here) · [Definition to word](https://ipmatway.com/learn/idioms-phrases/one-word-substitution/definition-to-word)

## Nearest meaning (Synonyms, Antonyms, Spelling, VARC)
Source: https://ipmatway.com/learn/synonyms-antonyms/synonyms

Idea: A word is given in capitals and you choose the option nearest to it in meaning. Rohtak sets 2 to 12 such vocabulary items a year (more in 2025-26), JIPMAT 4 to 5; the hard ones use exam words such as obsequious, pusillanimous or perfidious. The options are built to trap you: one is usually the opposite, one looks or sounds like the given word, and one is a related idea that is not the same.
Exam method: 1. Define first. Say the meaning in your own words before you look at the options (ebullient = bubbling with energy). 2. Remove the antonym. Find the option that means the opposite and cross it out. 3. Remove the look-alikes. Options that share letters with the given word (eminent for ebullient) are traps. 4. Check degree and tone. of what is left: the key must match in strength and in approval or disapproval. 5. If stuck, use roots. bene- (good), mal- (bad), loqu- (speak), anim- (spirit), ver- (true), mend- (fault, lie).
Traps: Antonym bait: under time pressure, the opposite feels "related" and gets ticked. Always ask: same or opposite? Look-alikes: ingenious (clever) and ingenuous (innocent), tenacious and tenuous, ostentatious and ostensible. Degree: a synonym must match the strength. Courteous is milder than obsequious; apathetic (no feeling) is not ambivalent (two feelings). Connotation: frugal (approving) and stingy (disapproving) are not interchangeable in a strict question.

Lessons: [Nearest meaning: start here](https://ipmatway.com/learn/synonyms-antonyms/synonyms/start-here) · [Tier1](https://ipmatway.com/learn/synonyms-antonyms/synonyms/tier1) · [Tier2](https://ipmatway.com/learn/synonyms-antonyms/synonyms/tier2) · [Tier3](https://ipmatway.com/learn/synonyms-antonyms/synonyms/tier3)

## Opposite meaning (Synonyms, Antonyms, Spelling, VARC)
Source: https://ipmatway.com/learn/synonyms-antonyms/antonyms

Idea: A word is given and you choose the option most nearly opposite in meaning. The trap is built in: one option is a synonym, which a student who half-knows the word picks because it "goes with" the word. Rohtak and JIPMAT ask antonyms every year, often mixed with synonyms in one block.
Exam method: 1. Define the word and name its opposite. before reading the options (loquacious = talkative, so the opposite is quiet). 2. Cross out the synonym. (garrulous), which is always there. 3. Cross out look-alikes. (luscious) and midpoints (neutral, translucent). 4. Check that the key is on the same scale. as the word: ephemeral is about time, so its opposite is perennial (long-lasting), not trivial.
Traps: Synonym bait: the most common wrong answer in antonym questions. Midpoints: neutral, translucent, lukewarm are between the two ends, not at the other end. Wrong scale: trivial is not the opposite of ephemeral; one is about importance, the other about time. False prefixes: inflammable = flammable; invaluable = very valuable; enervate = weaken.

Lessons: [Opposite meaning: start here](https://ipmatway.com/learn/synonyms-antonyms/antonyms/start-here) · [Tier1](https://ipmatway.com/learn/synonyms-antonyms/antonyms/tier1) · [Tier2](https://ipmatway.com/learn/synonyms-antonyms/antonyms/tier2) · [Tier3](https://ipmatway.com/learn/synonyms-antonyms/antonyms/tier3)

## Correctly / incorrectly spelt word (Rohtak/JIPMAT) (Synonyms, Antonyms, Spelling, VARC)
Source: https://ipmatway.com/learn/synonyms-antonyms/spelling

Idea: Four words are given; you pick the one spelt correctly, or the one spelt wrongly. JIPMAT asked two spelling items a year in 2024-25 and Rohtak includes them in its vocabulary block. The words are standard British spellings of commonly misspelt words.
Exam method: 1. Underline 'correctly' or 'incorrectly'. in the stem. 2. Look for a pattern in the options. If all four are versions of one word, compare them letter by letter at the double letters and the ending. 3. Check the trouble spots. double letters, -ance/-ence, -able/-ible, ie/ei, silent letters (rhythm, mnemonic). 4. Use the related word. definite comes from finite (so definitely, not definately); consensus is linked to consent (s, not c).
Traps: Wrong kind of question: ticking the correct word when the stem asks for the incorrect one. Analogy with a similar word: idiosyncracy (from democracy), concensus (from census), sacreligious (from religious). American spellings are not what these papers test: use manoeuvre, not maneuver.

Lessons: [Correctly / incorrectly spelt word (Rohtak/JIPMAT): start here](https://ipmatway.com/learn/synonyms-antonyms/spelling/start-here) · [Common misspelling](https://ipmatway.com/learn/synonyms-antonyms/spelling/common-misspelling)

## Mixed vocabulary MCQ (Indore 2026 style) (Synonyms, Antonyms, Spelling, VARC)
Source: https://ipmatway.com/learn/synonyms-antonyms/vocab-mcq

Idea: A hard word is used in a sentence and you choose its meaning as used there. IPMAT Indore 2026 asked five such vocabulary items with hard words; Rohtak and JIPMAT use the format too. The test is twofold: knowing rare words (sedulous, anodyne, noisome), and knowing that familiar words have secondary meanings (sanction, pedestrian, temper, close).
Exam method: 1. Read the sentence for its clue. a colon, a contrast (but, far from), a result (so... that), or an example. 2. Predict the meaning in your own words. from the clue. 3. Beware the first meaning you know. if the everyday meaning makes the sentence odd, the word is being used in another sense. 4. Substitute each option. for the word; reject any option that breaks the logic of the sentence.
Traps: Secondary meanings: commute (a sentence), temper (criticism), close (with money), sanction (penalise). Look-alikes: disinterested / uninterested, specious / spacious, noisome / noisy. Topic fit without logic fit: an option that suits the subject of the sentence but contradicts its clue.

Lessons: [Mixed vocabulary MCQ (Indore 2026 style): start here](https://ipmatway.com/learn/synonyms-antonyms/vocab-mcq/start-here) · [Rare word](https://ipmatway.com/learn/synonyms-antonyms/vocab-mcq/rare-word) · [Context sentence](https://ipmatway.com/learn/synonyms-antonyms/vocab-mcq/context-sentence)

## Word pair relationship (Verbal Analogies, VARC)
Source: https://ipmatway.com/learn/analogies/word-analogy

Idea: An analogy question gives a pair of words with a relationship (MAN : HUMANITY) and asks for the pair, or the missing word, with the same relationship (DROP : OCEAN). Rohtak asked two in each of 2019 and 2020; JIPMAT asked two in 2021.
Exam method: 1. Build the bridge. one short sentence linking the two words, with the first word first. "A sedative is something that brings on sleep." 2. Run every option through the bridge. "A mnemonic is something that brings on memory." It fits. "Vocal is something that brings on eloquence." It does not. 3. Check direction and degree. the bridge must work in the same order and with the same strength. 4. Tighten if needed. if two options survive, make the bridge more specific.
Traps: Reversal: clouds cause rain, so CLOUD : RAIN matches FIRE : SMOKE only in that order. Topic bait: an option on the same subject with a different relationship. Double meanings: check both meanings of a word before deciding.

Lessons: [Word pair relationship: start here](https://ipmatway.com/learn/analogies/word-analogy/start-here) · [Synonym antonym pair](https://ipmatway.com/learn/analogies/word-analogy/synonym-antonym-pair) · [Part whole](https://ipmatway.com/learn/analogies/word-analogy/part-whole) · [Degree](https://ipmatway.com/learn/analogies/word-analogy/degree) · [Function](https://ipmatway.com/learn/analogies/word-analogy/function)

## Odd word among four (Odd One Out (words), VARC)
Source: https://ipmatway.com/learn/odd-one-out/odd-word

Idea: Four words are given; three share a category or a shade of meaning, and one does not. Rohtak asked two such questions in 2024 (JIPMAT puts "odd man out" in its LR section).
Exam method: 1. Name the group. that three words clearly share. 2. Check the outsider. it should fail that group for a clear reason (a lake among rivers, a shrub among trees). 3. Look for a rival grouping. origin, region, suffix, positive vs negative meaning. Prefer the most specific, natural category. 4. For near-synonyms, check connotation. one word usually carries disapproval (stingy, nosy, notorious, obstinate).
Traps: Grouping by look: words that share a prefix or suffix may not share a meaning. Two possible outsiders: if you can isolate two different words with two different rules, reread the four and choose the stronger, more specific rule.

Lessons: [Odd word among four: start here](https://ipmatway.com/learn/odd-one-out/odd-word/start-here) · [Category](https://ipmatway.com/learn/odd-one-out/odd-word/category) · [Connotation](https://ipmatway.com/learn/odd-one-out/odd-word/connotation)

## Assumption (four-option CR) (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/assumption

Idea: An argument has a premise (evidence) and a conclusion. The assumption is the unstated link the author needs: if it is false, the conclusion does not follow. Indore tests this inside RC ("the author assumes…"); Rohtak sets standalone CR. Our bank keeps these at difficulty 1-3.
Exam method: 1. Predict the gap. before reading the options. 2. Eliminate. options that are outside the argument (cost, other people, future), too strong ("every", "no other", "only"), or that merely repeat the evidence. 3. Negation test. on the last two: negate each; the one whose negation breaks the argument is the answer.
Traps: Too strong: "Every student owns a smartphone" (the plan works if many do). Helpful but not needed: a statement that would strengthen the argument is not always required by it. Restating evidence: "Students who ate fried snacks were absent more often" is the premise, not the bridge.

Lessons: [Assumption (four-option CR): start here](https://ipmatway.com/learn/critical-reasoning/assumption/start-here) · [Gap between premise conclusion](https://ipmatway.com/learn/critical-reasoning/assumption/gap-between-premise-conclusion) · [Plan will work](https://ipmatway.com/learn/critical-reasoning/assumption/plan-will-work)

## Inference: must be true / cannot be inferred (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/inference

Idea: You are given facts and asked what must be true (or which option cannot be inferred). This is pure reading discipline: no outside knowledge, no likely stories. Rohtak 2019 set both kinds (stuffed toys; family income).
Exam method: 1. Mark the size words. all, most, some, only, none. 2. For each option, try to build a counter-case. that fits the facts but breaks the option. If you can, the option does not have to be true. 3. EXCEPT questions. find the three that follow; the odd one out usually adds a cause or a new comparison. 4. Numbers. list all possibilities (5p + 10q = 35 → three cases) and keep only what holds in all.
Traps: Reversal of "all A are B". Most → all and average → every. Rate → level: faster growth does not mean a higher amount. Correlation → cause in "best supported" questions: stay with "among those studied, X went with Y".

Lessons: [Inference: must be true / cannot be inferred: start here](https://ipmatway.com/learn/critical-reasoning/inference/start-here) · [Must be true](https://ipmatway.com/learn/critical-reasoning/inference/must-be-true) · [Cannot be inferred](https://ipmatway.com/learn/critical-reasoning/inference/cannot-be-inferred)

## Strengthen the argument (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/strengthen

Idea: A strengthener is a new fact that, if true, makes the conclusion more likely. It usually supports the assumption: it closes the gap between evidence and conclusion. For cause-and-effect arguments, the strongest support either rules out another explanation or shows the cause at work.
Exam method: 1. Classify the argument. cause ("X caused Y"), plan ("doing X will achieve Y"), or comparison. 2. Cause. look for a control group ("schools without the change saw no rise") or an intervention ("adding nest boxes brought sparrows back"). 3. Plan. look for evidence that the mechanism works ("shoppers added items to cross ₹499"). 4. Eliminate. options that are about the topic but not the link, and anything that weakens.
Traps: Strengthens the wrong thing: "the path is used by hundreds of joggers" shows the problem matters, not that lights will help. Hidden weakener: "children read to daily also watched less TV" adds another difference between the groups. Partial help vs direct test: "the bird migrates over open sea" rules out landmarks; "magnets disturbed its navigation" tests magnetism directly.

Lessons: [Strengthen the argument: start here](https://ipmatway.com/learn/critical-reasoning/strengthen/start-here) · [Support link](https://ipmatway.com/learn/critical-reasoning/strengthen/support-link) · [Rule out alternative](https://ipmatway.com/learn/critical-reasoning/strengthen/rule-out-alternative)

## Weaken the argument (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/weaken

Idea: A weakener is a new fact that makes the conclusion less likely. It attacks the assumption. With cause claims, the classic weakener is another cause; with plans, it is a reason the plan cannot work. Indore asks this inside RC; Rohtak in standalone CR.
Exam method: 1. Same time, so it caused it?. Look for another change at the same time (monsoon, lockdown, new books). 2. Comparison. the same change where the supposed cause was absent (towns without a factory) is a strong weakener. 3. Reverse cause. keen students choose front seats; the seat does not make them keen. 4. Plan. customers will switch away; illness, not choice, causes absences; litter comes from the sea. 5. Ignore. costs, delays, popularity and other places unless they hit the link.
Traps: Cost ≠ failure: "hundreds of trees will be cut" is a cost, not a reason widening will not cut jams. Strengtheners in disguise: "teachers ask front-row students more questions" suggests the seat helps. Hints vs causes: pick the option that names the other cause.

Lessons: [Weaken the argument: start here](https://ipmatway.com/learn/critical-reasoning/weaken/start-here) · [Break link](https://ipmatway.com/learn/critical-reasoning/weaken/break-link) · [Alternative cause](https://ipmatway.com/learn/critical-reasoning/weaken/alternative-cause)

## Statement-conclusion (I/II follows) (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/conclusion

Idea: Rohtak and JIPMAT print a short statement and two conclusions. Assume the statement is true, even if it sounds odd, and decide which conclusions must follow from it. Options in our bank are always: (A) Only I, (B) Only II, (C) Both (or "Either I or II" in some papers), (D) Neither. Rohtak 2019 printed "Either" instead of "Both"; JIPMAT 2024 printed "Neither" before "Both". Read the options every time. Two kinds of statements appear: - Facts, rules and numbers (deduction): a rule plus a case, a notice, a set of figures. Apply the rule; do the arithmetic. - Proverbs, views and policies: read a proverb as a general truth; a policy tells you what was decided, not why it works or what everyone will do.
Exam method: 1. Read the conclusion first, then hunt for its support. in the statement. No support = does not follow. 2. Watch the size words. all, every, main, only, never, will. A statement about "some" or "a survey" cannot give "all" or "most people". 3. Check direction. "A → B" does not give "B → A". 4. Numbers. compute (e.g. both = 25 + 30 − 40); "at least 15" is true when the value is exactly 15. 5. Either. only for a complementary pair. Two unrelated possibilities are "Neither".
Traps: Outside knowledge: "Non-conventional energy will end the crisis" says nothing about what technology is doing today (JIPMAT 2024). Wrong base: 80 per cent of runs is not 80 per cent of players (Rohtak 2019). Average → every: a higher average does not mean every member scored higher. Cause from correlation: a gap between groups does not prove the cause. Proverbs: read the meaning ("risks bring success"), not the picture.

Lessons: [Statement-conclusion (I/II follows): start here](https://ipmatway.com/learn/critical-reasoning/conclusion/start-here) · [Deduction](https://ipmatway.com/learn/critical-reasoning/conclusion/deduction) · [Opinion or policy](https://ipmatway.com/learn/critical-reasoning/conclusion/opinion-or-policy)

## Flaw in reasoning (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/flaw

Idea: A flaw question asks what is wrong with the reasoning, not whether the conclusion is true. Five flaws cover most IPMAT-level items: | Flaw | Signal | Example | |---|---|---| | Correlation → cause | "X and Y go together, so X causes Y" | More hospitals, more deaths | | Sampling | survey of a self-selected or tiny group | 3 tourists → a whole state | | Circular | reason = conclusion in other words | "trustworthy because reliable" | | False choice | only two options offered | "ban all vehicles or ruin the monuments" | | Part → whole | each part has a property, so the whole has it | excellent players → excellent team |
Exam method: 1. Predict the flaw name. 2. Match. the option that describes this argument's move; ignore options that attack a premise or mention a cost. 3. Check specifics. a correct flaw option usually mentions the argument's own content (respondents, population).
Traps: Attacking a premise ("it assumes pollution damages monuments"): premises are given. Near-miss descriptions: the right option names the real move (self-selected respondents), not a neighbouring idea. Real cost ≠ reasoning flaw.

Lessons: [Flaw in reasoning: start here](https://ipmatway.com/learn/critical-reasoning/flaw/start-here) · [Correlation causation](https://ipmatway.com/learn/critical-reasoning/flaw/correlation-causation) · [Sampling](https://ipmatway.com/learn/critical-reasoning/flaw/sampling) · [Circular](https://ipmatway.com/learn/critical-reasoning/flaw/circular) · [False choice](https://ipmatway.com/learn/critical-reasoning/flaw/false-choice) · [Part whole](https://ipmatway.com/learn/critical-reasoning/flaw/part-whole)

## Statement-assumption (I/II implicit) (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/statement-assumption

Idea: A statement (advice, a decision, a notice, an advertisement) is followed by two assumptions. An assumption is implicit if the speaker has to believe it for the statement to make sense. It is not something the statement says; it is something the statement needs. Rohtak sets two or more of these most years; JIPMAT occasionally.
Exam method: 1. Name the speaker's goal. in five words ("get students to class during rain"). 2. Negation test. for each assumption: if it were false, would the speaker still say this? If the statement becomes pointless, it is implicit. 3. Kill extreme versions. "never", "all", "no one", "only" are rarely needed. 4. Kill reversals. an assumption that says the plan will fail contradicts the speaker. 5. Pick both, one or neither. ; "Either" is almost never right for assumptions.
Traps: True but unneeded (the speaker could say the same thing without it). Too strong ("Students never switch off the lights"). Conditional advice ("If you want to avoid traffic…") does not assume everyone wants to. Convention to remember (Rohtak 2019): a plan that rewards people to improve discipline is taken to assume that "discipline and reward go together", even when the option says "always".

Lessons: [Statement-assumption (I/II implicit): start here](https://ipmatway.com/learn/critical-reasoning/statement-assumption/start-here) · [Advice or plan](https://ipmatway.com/learn/critical-reasoning/statement-assumption/advice-or-plan) · [Notice or advert](https://ipmatway.com/learn/critical-reasoning/statement-assumption/notice-or-advert)

## Strong and weak arguments (I/II) (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/strong-weak-arguments

Idea: A policy question ("Should X be done?") is followed by a Yes argument and a No argument. Mark each as strong or weak. A strong argument is important and directly linked to the question; a weak one is trivial, emotional, irrelevant, sweeping or merely copies others. JIPMAT 2024 had one; Rohtak sets them under "critical reasoning".
Exam method: 1. Strip the argument to its reason. ("because X"). 2. Ask "So what?". if X is minor, it is weak. 3. Flag slogans and copies. "youth are the future", "other countries do it", "people love it" → weak. 4. Flag absolutes. "never", "always" → usually weak. 5. Do not penalise a strong argument for having a counter-argument.
Traps: Your opinion is not the test; the quality of the reason is. "Could be countered" does not make an argument weak. Imitation and tradition (other countries; scientists of the past) are weak. Habit ("used to the present timings") is weak.

Lessons: [Strong and weak arguments (I/II): start here](https://ipmatway.com/learn/critical-reasoning/strong-weak-arguments/start-here) · [Relevance](https://ipmatway.com/learn/critical-reasoning/strong-weak-arguments/relevance) · [Generality](https://ipmatway.com/learn/critical-reasoning/strong-weak-arguments/generality)

## Course of action (I/II) (Critical Reasoning / Verbal Reasoning, VARC)
Source: https://ipmatway.com/learn/critical-reasoning/course-of-action

Idea: A statement describes a problem; two suggested actions follow. An action follows if a sensible authority would take it: it is practical, proportionate and actually reduces the problem (or prevents it from recurring). It is a Rohtak/JIPMAT "decision making" format.
Exam method: 1. Name the problem in a phrase. ("ATMs empty on weekends"). 2. Ask "Does this reduce it?". No → does not follow. 3. Ask "Is it practical and proportionate?". Shutting, banning or punishing everyone → does not follow. 4. Both can follow. short-term relief plus long-term prevention.
Traps: Over-reaction: "expel every student who smokes" for a report about a few. Related but useless: "build more parks" when the issue is evening use of existing parks. Worsening the problem: closing ATMs because they run out of cash.

Lessons: [Course of action (I/II): start here](https://ipmatway.com/learn/critical-reasoning/course-of-action/start-here) · [Feasible and addresses problem](https://ipmatway.com/learn/critical-reasoning/course-of-action/feasible-and-addresses-problem)

## Table-Based DI (Data Interpretation, LR / DI)
Source: https://ipmatway.com/learn/data-interpretation/tables

Idea: A table gives exact numbers; every question asks you to combine a few cells - a change, a share, a ratio, a count or a minimum. The skill is choosing the right base and doing as little arithmetic as the options allow.
Exam method: 1. Rank, do not compute. for 'which month / which stock is highest' compare ratios by cross-multiplication or rough percentages; compute only when two options are within 1%. 2. Read the options first. options 60.87% and 62.58% tell you gross vs net is the trap - compute net directly. 3. Totals keep the order. average spread or average marks are lowest where the total is lowest. 4. Compound, do not add. chained trades multiply growth factors. 5. Boundary words. 'more than', 'at least', 'increase for three consecutive months' - decide the reading once and apply it to every row.
Traps: Later value as the base; absolute change mistaken for percentage change; shares divided by the wrong total. Quotes swapped; brokerage on one leg; returns added instead of compounded. 'No change' counted as a rise; servings rounded down.

Lessons: [Percent change month on month](https://ipmatway.com/learn/data-interpretation/tables/percent-change-month-on-month) · [Contribution share](https://ipmatway.com/learn/data-interpretation/tables/contribution-share) · [Ratio comparison](https://ipmatway.com/learn/data-interpretation/tables/ratio-comparison) · [Consecutive increase pattern](https://ipmatway.com/learn/data-interpretation/tables/consecutive-increase-pattern) · [Net after returns](https://ipmatway.com/learn/data-interpretation/tables/net-after-returns) · [Max min identification](https://ipmatway.com/learn/data-interpretation/tables/max-min-identification) · [Stock transactions return](https://ipmatway.com/learn/data-interpretation/tables/stock-transactions-return) · [Brokerage calculation](https://ipmatway.com/learn/data-interpretation/tables/brokerage-calculation) · [Bid ask spread](https://ipmatway.com/learn/data-interpretation/tables/bid-ask-spread) · [Requirement optimisation](https://ipmatway.com/learn/data-interpretation/tables/requirement-optimisation) · [Count satisfying condition](https://ipmatway.com/learn/data-interpretation/tables/count-satisfying-condition)

## Chart-Based DI (Data Interpretation, LR / DI)
Source: https://ipmatway.com/learn/data-interpretation/charts

Idea: Charts show the same numbers as a table, arranged for the eye: bars for comparison, lines for trends, pies for shares, stacked bars for parts of totals. Read the scale and labels, then treat the values exactly like table data.
Exam method: 1. Eye first, pen second. the longest/shortest bars, steepest segments and largest gaps are visible; compute only to separate close options. 2. Deviation averaging. for long series. 3. Block comparisons. compare block sums - dividing by the same block length keeps the order. 4. Perfect powers. make CAGR a recognition task. 5. Pool, do not average. shares of unequal groups.
Traps: Shares compared across pies with different totals; percentage reported as degrees. Simple average growth taken for CAGR; sign of balance of trade. Averaging shares of unequal groups.

Lessons: [Bar reading](https://ipmatway.com/learn/data-interpretation/charts/bar-reading) · [Line trend](https://ipmatway.com/learn/data-interpretation/charts/line-trend) · [Pie share to value](https://ipmatway.com/learn/data-interpretation/charts/pie-share-to-value) · [Import export balance](https://ipmatway.com/learn/data-interpretation/charts/import-export-balance) · [Average over period](https://ipmatway.com/learn/data-interpretation/charts/average-over-period) · [Percent increase year](https://ipmatway.com/learn/data-interpretation/charts/percent-increase-year) · [Cagr growth](https://ipmatway.com/learn/data-interpretation/charts/cagr-growth) · [Pie central angle](https://ipmatway.com/learn/data-interpretation/charts/pie-central-angle) · [Stacked bar share](https://ipmatway.com/learn/data-interpretation/charts/stacked-bar-share)

## Caselets (Data Interpretation, LR / DI)
Source: https://ipmatway.com/learn/data-interpretation/caselets

Idea: A caselet hides a table inside sentences. Once the relations are written as a table (and checked against every condition), the questions are look-ups.
Exam method: 1. Anchor on the scarcest resource. in Indore 2024, C's 16 votes must win two seats, which forces 8 and 8. 2. Ratios once. one part of the batch ratio, then each group's split. 3. Break-even = fixed / margin. , rounded up to whole units. 4. Missing-data grids. fill single-gap lines repeatedly.
Traps: Relations read backwards; one ratio applied to all groups; costs left out; ties counted as wins.

Lessons: [Text to table](https://ipmatway.com/learn/data-interpretation/caselets/text-to-table) · [Election votes seats](https://ipmatway.com/learn/data-interpretation/caselets/election-votes-seats) · [Ratio based caselet](https://ipmatway.com/learn/data-interpretation/caselets/ratio-based-caselet) · [Business economics caselet](https://ipmatway.com/learn/data-interpretation/caselets/business-economics-caselet) · [Missing data deduction](https://ipmatway.com/learn/data-interpretation/caselets/missing-data-deduction)

## Arrangements and Scheduling (Logical Reasoning Sets (Indore QA-embedded), LR / DI)
Source: https://ipmatway.com/learn/logical-reasoning/arrangements

Idea: An arrangement set has a few slots (seats, days, cells, teams) and a list of conditions. The questions are easy once the arrangement is fixed; all the work is in placing people in the right order of conditions.
Exam method: 1. Count the slots first. (Indore 2022: 2 x 6 + 3 = 15 = 5 x 3) to catch misreadings. 2. Most constrained first. the person with an 'only', the day that needs three people, the drug that is already full. 3. Two-case rule. if two cases survive, read the question - often both cases give the same answer. 4. Answer from the options. for 'which pair never meets' test the four options directly against the arrangement.
Traps: 'Somewhere' read as 'immediately'; directions flipped; a second arrangement missed; the weekly wrap-around ignored.

Lessons: [Linear arrangement](https://ipmatway.com/learn/logical-reasoning/arrangements/linear-arrangement) · [Circular arrangement](https://ipmatway.com/learn/logical-reasoning/arrangements/circular-arrangement) · [Scheduling days](https://ipmatway.com/learn/logical-reasoning/arrangements/scheduling-days) · [Grid matching](https://ipmatway.com/learn/logical-reasoning/arrangements/grid-matching) · [Grouping with conditions](https://ipmatway.com/learn/logical-reasoning/arrangements/grouping-with-conditions) · [Numeric distribution grid](https://ipmatway.com/learn/logical-reasoning/arrangements/numeric-distribution-grid) · [Team selection](https://ipmatway.com/learn/logical-reasoning/arrangements/team-selection)

## Tournaments and Games (Logical Reasoning Sets (Indore QA-embedded), LR / DI)
Source: https://ipmatway.com/learn/logical-reasoning/tournaments-games

Idea: In a round robin every match produces either a winner and a loser or a draw for both. Totals of wins, losses, draws and points therefore balance, and these balances turn a partial table into a complete one.
Exam method: 1. Draws from points. 3-1-0 system: draws =3M- total points (one line). 2. The missing team. its wins = total losses - other wins; draws = games - wins - losses. 3. Score lists. total, then 'two maxima' or 'weakest k too low' kills the impossible option. 4. Test, do not trust. if two result tables fit, any match they disagree on is 'cannot be determined'.
Traps: Draw entries vs drawn matches; wrong points system; a result assumed rather than forced.

Lessons: [Round robin points table](https://ipmatway.com/learn/logical-reasoning/tournaments-games/round-robin-points-table) · [Possible score sequences](https://ipmatway.com/learn/logical-reasoning/tournaments-games/possible-score-sequences) · [Match results deduction](https://ipmatway.com/learn/logical-reasoning/tournaments-games/match-results-deduction)

## Grouping and Grid Puzzles (Logical Reasoning Sets (Indore QA-embedded), LR / DI)
Source: https://ipmatway.com/learn/logical-reasoning/puzzles

Idea: Puzzle items test one clean idea each: how many values a set of weights can make, how a count of true statements identifies the culprit, how 'all' and 'no' statements make groups nest or separate, and how ranks from both ends give a total.
Exam method: 1. Powers of 2 or 3. settle every weights question. 2. Candidate table. four suspects x four statements, tick true, read the row with the required count. 3. Containment first. fix which group sits inside which before any arithmetic.
Traps: Wrong weighing rule; double-counted rank; consistency instead of counting; overlapping groups added.

Lessons: [Weights minimum](https://ipmatway.com/learn/logical-reasoning/puzzles/weights-minimum) · [Truth logic counting](https://ipmatway.com/learn/logical-reasoning/puzzles/truth-logic-counting) · [Set logic puzzle](https://ipmatway.com/learn/logical-reasoning/puzzles/set-logic-puzzle) · [Ordering ranking](https://ipmatway.com/learn/logical-reasoning/puzzles/ordering-ranking)

## Single row, facing one direction (Linear Arrangement, LR / DI)
Source: https://ipmatway.com/learn/linear-arrangement/single-row

Idea: People (or cars, books, bulbs) sit in one row, all facing the same way, usually north, so their left and right are ours. Clues give exact gaps (third to the right, two between), ends and neighbours. Rohtak asked a car row in 2020 (Q18-19) and JIPMAT a nine-friend row in 2026 (Q11) and a stack of books in 2023 (Q23); a stack is a row turned upright (top = right end).
Exam method: 1. Anchor. the end or middle clue first. 2. Blocks. "J is next to O, O is third to the left of K" is one block J O K. 3. Two cases. if a block can sit in two places, draw both rows; the next clue usually removes one. 4. Answer from the final row,. writing it once at the top of the page.
Traps: Between count: persons between seats 2 and 5 are 2, not 3. Direction of the clue: "A is second to the left of B" places A. "If" conditions belong to one question only.

Lessons: [Single row, facing one direction: start here](https://ipmatway.com/learn/linear-arrangement/single-row/start-here) · [Left right count](https://ipmatway.com/learn/linear-arrangement/single-row/left-right-count) · [Adjacency](https://ipmatway.com/learn/linear-arrangement/single-row/adjacency) · [Ends](https://ipmatway.com/learn/linear-arrangement/single-row/ends) · [Count between](https://ipmatway.com/learn/linear-arrangement/single-row/count-between) · [Statement check](https://ipmatway.com/learn/linear-arrangement/single-row/statement-check) · [Conditional change](https://ipmatway.com/learn/linear-arrangement/single-row/conditional-change) · [Cannot be determined](https://ipmatway.com/learn/linear-arrangement/single-row/cannot-be-determined)

## Two rows facing each other (Linear Arrangement, LR / DI)
Source: https://ipmatway.com/learn/linear-arrangement/double-row

Idea: Two rows face each other: one row faces south, the other north, and each person faces the one opposite. The only new idea is direction: the south-facing row has its right on the west side. No JIPMAT or Rohtak PYQ so far uses two rows; these PW sets are practice at d2-d3.
Exam method: 1. One numbering for both rows;. "faces" = same seat number. 2. Flip once. write "R = west" above the south-facing row. 3. Answer chains. ("second to the left of the one who faces B1") in two steps: find who faces B1, then count from that person's facing.
Traps: Flip for the south-facing row. Two-step chains: find the person who faces X first. Between counts people in the same row.

Lessons: [Two rows facing each other: start here](https://ipmatway.com/learn/linear-arrangement/double-row/start-here) · [Opposite pairs](https://ipmatway.com/learn/linear-arrangement/double-row/opposite-pairs) · [Relative position](https://ipmatway.com/learn/linear-arrangement/double-row/relative-position) · [Ends](https://ipmatway.com/learn/linear-arrangement/double-row/ends) · [Count between](https://ipmatway.com/learn/linear-arrangement/double-row/count-between) · [Odd one out](https://ipmatway.com/learn/linear-arrangement/double-row/odd-one-out) · [Attribute grid](https://ipmatway.com/learn/linear-arrangement/double-row/attribute-grid) · [Statement check](https://ipmatway.com/learn/linear-arrangement/double-row/statement-check)

## Row + one or two attributes (Linear Arrangement, LR / DI)
Source: https://ipmatway.com/learn/linear-arrangement/with-attributes

Idea: Each person in the row also has a colour, an age or a similar value. Clues mix seats and values. The Rohtak 2020 paper had such a set (eight girls and eight colours, Q1-2). Note that its clues allow two seatings; the paper's key follows one of them (see the key note on that question).
Exam method: 1. Tokens. write "Y" (yellow) above a seat as soon as its seat is fixed, even before you know who sits there. 2. Seats, then values. settle the row, then the ages by elimination. 3. Two fits. try the other side for the first ambiguous clue before trusting a single row.
Traps: Unforced pairs: fill a person-value cell only when a clue forces it. Second arrangement: test the other side of the first two-way clue. Second youngest is the second-lowest age.

Lessons: [Row + one or two attributes: start here](https://ipmatway.com/learn/linear-arrangement/with-attributes/start-here) · [Attribute grid](https://ipmatway.com/learn/linear-arrangement/with-attributes/attribute-grid) · [Count between](https://ipmatway.com/learn/linear-arrangement/with-attributes/count-between) · [Left right count](https://ipmatway.com/learn/linear-arrangement/with-attributes/left-right-count) · [Value arithmetic](https://ipmatway.com/learn/linear-arrangement/with-attributes/value-arithmetic)

## Single row, some facing north and some south (Linear Arrangement, LR / DI)
Source: https://ipmatway.com/learn/linear-arrangement/mixed-facing

Idea: Some people in the row face north and some face south. Left and right then depend on each person's facing: for a south-facer, right is towards the west (our left). Positions and "between" counts do not change. No JIPMAT or Rohtak PYQ so far mixes facings in a row; these PW sets are d2-d3 practice.
Exam method: 1. Arrows first. for the people named with a facing. 2. Reference person. "Neetu is second to the right of Meena" is counted from Meena. 3. Case split on one unknown facing;. the count clue (three face south) usually ends it.
Traps: South-facer's right is our left. Reference person's facing, not the placed person's. Counts only after every arrow is forced.

Lessons: [Single row, some facing north and some south: start here](https://ipmatway.com/learn/linear-arrangement/mixed-facing/start-here) · [Direction flip](https://ipmatway.com/learn/linear-arrangement/mixed-facing/direction-flip) · [Facing count](https://ipmatway.com/learn/linear-arrangement/mixed-facing/facing-count)

## All facing centre (Circular / Square Arrangement, LR / DI)
Source: https://ipmatway.com/learn/circular-arrangement/facing-centre

Idea: People sit around a round (or square) table, all facing the centre. Clues fix seats relative to one another: k-th to the right or left, opposite, neighbours, between. Once one person is placed, every clue places someone else. JIPMAT asks one circle question most years (2023 Q15 and Q27, 2024 Q7, 2025 Q15, all banked here as PYQs).
Exam method: 1. Right = anticlockwise. when everybody faces the centre. Write an arrow on your circle once. 2. Fixed clues first. opposite and immediately-next clues; conditional and negative clues last. 3. Two cases. if a clue leaves two seats, draw both circles; a later clue usually kills one. If both survive, the question may be "cannot be determined". 4. Distance clues. (metres around a table of known circumference): convert to seats first (50 m for 10 people = 5 m a seat).
Traps: Right and left reversed for centre-facing people: right is anticlockwise. Direction of the clue: "A is second to the left of B" is about A's seat. Question-only conditions: a swap in one question does not carry over to the next.

Lessons: [All facing centre: start here](https://ipmatway.com/learn/circular-arrangement/facing-centre/start-here) · [Left right reversal](https://ipmatway.com/learn/circular-arrangement/facing-centre/left-right-reversal) · [Relative position](https://ipmatway.com/learn/circular-arrangement/facing-centre/relative-position) · [Opposite pairs](https://ipmatway.com/learn/circular-arrangement/facing-centre/opposite-pairs) · [Neighbours](https://ipmatway.com/learn/circular-arrangement/facing-centre/neighbours) · [Count between](https://ipmatway.com/learn/circular-arrangement/facing-centre/count-between) · [Conditional change](https://ipmatway.com/learn/circular-arrangement/facing-centre/conditional-change) · [Cannot be determined](https://ipmatway.com/learn/circular-arrangement/facing-centre/cannot-be-determined) · [Distance on circle](https://ipmatway.com/learn/circular-arrangement/facing-centre/distance-on-circle) · [Square table](https://ipmatway.com/learn/circular-arrangement/facing-centre/square-table)

## Some facing outside (Circular / Square Arrangement, LR / DI)
Source: https://ipmatway.com/learn/circular-arrangement/mixed-facing

Idea: Some people face the centre and some face outward. Left and right then depend on each person's facing: for a person facing outward, right is clockwise. Opposite and neighbour clues are the same either way. No JIPMAT or Rohtak PYQ so far mixes facings; these PW sets are practice above the exam's usual level (d3-d4).
Exam method: 1. Arrows on the circle. draw an inward or outward arrow at each seat as soon as you know it. 2. Reference person. "A is k-th to the right of B" is counted from B, in B's right-hand direction. 3. Case split once. one unknown facing gives two cases; resolve them with the next clue.
Traps: Outward right is clockwise. Use the reference person's facing, not the facing of the person being placed. Counts of facings only after every facing is forced.

Lessons: [Some facing outside: start here](https://ipmatway.com/learn/circular-arrangement/mixed-facing/start-here) · [Direction flip](https://ipmatway.com/learn/circular-arrangement/mixed-facing/direction-flip) · [Facing count](https://ipmatway.com/learn/circular-arrangement/mixed-facing/facing-count) · [Opposite pairs](https://ipmatway.com/learn/circular-arrangement/mixed-facing/opposite-pairs) · [Count between](https://ipmatway.com/learn/circular-arrangement/mixed-facing/count-between)

## Circular + attributes (Circular / Square Arrangement, LR / DI)
Source: https://ipmatway.com/learn/circular-arrangement/with-attributes

Idea: Each person around the table also has one or two attributes (a company, a state, a crown colour, an arrival order, a number of languages). Clues mix seats and attributes. The method is the plain circle method with attribute values treated as extra people who share a seat. No JIPMAT or Rohtak PYQ so far is a circle with attributes; the sets here are PW practice at d2-d4.
Exam method: 1. Anchor clue. begin with the clue that links the most items (person, seat and attribute). 2. Tokens. write attribute values next to seats as you place them; a value with no person yet is still a seat clue. 3. Elimination grid. for the last two or three people, a 3 x 3 grid of person vs attribute settles them fast. 4. Two arrangements. if two fit, answer each question by checking both.
Traps: Unforced links: fill a person-attribute cell only when the clue forces it. Same person, two descriptions: "the Haryana delegate" may be a person already named. Two fits: check both arrangements before answering.

Lessons: [Circular + attributes: start here](https://ipmatway.com/learn/circular-arrangement/with-attributes/start-here) · [Attribute grid](https://ipmatway.com/learn/circular-arrangement/with-attributes/attribute-grid) · [Opposite pairs](https://ipmatway.com/learn/circular-arrangement/with-attributes/opposite-pairs) · [Count between](https://ipmatway.com/learn/circular-arrangement/with-attributes/count-between) · [Neighbours](https://ipmatway.com/learn/circular-arrangement/with-attributes/neighbours) · [Left right reversal](https://ipmatway.com/learn/circular-arrangement/with-attributes/left-right-reversal) · [Statement check](https://ipmatway.com/learn/circular-arrangement/with-attributes/statement-check) · [Value arithmetic](https://ipmatway.com/learn/circular-arrangement/with-attributes/value-arithmetic) · [Cannot be determined](https://ipmatway.com/learn/circular-arrangement/with-attributes/cannot-be-determined)

## Person-attribute grid (3-4 variables) (Matrix / Distribution Puzzles, LR / DI)
Source: https://ipmatway.com/learn/matrix-puzzles/person-attribute

Idea: Each person has one value of each attribute (city, sport, spouse, college), and the clues pair them up. JIPMAT asks a short single-question version almost every year (2021, 2022, 2023, 2024, 2025, 2026: games and subjects, couples, cities and transport). PW sets add a second attribute and four or five questions on one grid.
Exam method: 1. Direct clues first. Neha Tea and Cake, Rohit Hot Chocolate and Pastry. 2. Pairs. Lemonade with Ice Cream, not Barun, so Ankit. 3. Last free cell. Barun has neither Milkshake nor Coffee, so Soft drinks; Sameer has no Coffee, so Milkshake; Priya Coffee. 4. Answer from the grid;. for combination options check every part.
Traps: "Not the Actress, not the Singer" is not yet "Air hostess" until the Models and the Housewife are placed. Count distinct values: two students studying mathematics give one subject, not two. An "if" in one question (if F joined IRMA ...) applies to that question only. Alternators can go false-true-false as well as true-false-true.

Lessons: [Person-attribute grid (3-4 variables): start here](https://ipmatway.com/learn/matrix-puzzles/person-attribute/start-here) · [Grid elimination](https://ipmatway.com/learn/matrix-puzzles/person-attribute/grid-elimination) · [If then chain](https://ipmatway.com/learn/matrix-puzzles/person-attribute/if-then-chain) · [Count attributes](https://ipmatway.com/learn/matrix-puzzles/person-attribute/count-attributes) · [Statement check](https://ipmatway.com/learn/matrix-puzzles/person-attribute/statement-check) · [Truth liar](https://ipmatway.com/learn/matrix-puzzles/person-attribute/truth-liar)

## Days x people/events (Scheduling (days/months/time slots), LR / DI)
Source: https://ipmatway.com/learn/scheduling/day-slot

Idea: Events (plays, meetings, lectures, matches) are placed in day or time slots, one per slot. The slots form a row, so the method is the row method: blocks, gaps and ends. Rohtak asked five plays over Monday to Friday in 2019 (Q9-11, banked here as a PYQ set).
Exam method: 1. Blocks first. "E is followed by C" and "B is after D" make EC and DB. 2. End clues. "D or E not first or last" stops both blocks from starting on Monday. 3. Gap clue last. "one play between A and B" chooses between the two block orders.
Traps: Between vs immediately: "one play between" leaves a gap of one slot. Counting days between: Monday to Thursday has two days between. Conditional questions use their condition only once.

Lessons: [Days x people/events: start here](https://ipmatway.com/learn/scheduling/day-slot/start-here) · [Weekday order](https://ipmatway.com/learn/scheduling/day-slot/weekday-order) · [Time slots](https://ipmatway.com/learn/scheduling/day-slot/time-slots) · [Match slots](https://ipmatway.com/learn/scheduling/day-slot/match-slots)

## Months and dates with constraints (Scheduling (days/months/time slots), LR / DI)
Source: https://ipmatway.com/learn/scheduling/month-date

Idea: People or events are placed on months, dates or years. It is a row ordered by time, sometimes with two levels (month, then date). Clues give gaps ("two persons born between N and Q"), arithmetic ("five years older") and calendar facts (leap years). No JIPMAT or Rohtak PYQ uses a month-date set; JIPMAT's birthday-range items sit in clocks-calendars. The sets here are PW practice plus originals.
Exam method: 1. Arithmetic shortlist. with years 1962, 1967, 1975, 1982, 1987, 1993, 1996, "five years apart" fits 1962-1967 and 1982-1987 only. 2. Leap year. among those years only 1996 is a leap year. 3. Older = earlier. write each "older than" clue as an arrow on the time line.
Traps: Older = earlier on the time line. Between excludes the two end people. Month boundaries: order dates across months, not by the day number alone.

Lessons: [Months and dates with constraints: start here](https://ipmatway.com/learn/scheduling/month-date/start-here) · [Date grid](https://ipmatway.com/learn/scheduling/month-date/date-grid) · [Month order](https://ipmatway.com/learn/scheduling/month-date/month-order) · [Year sequence](https://ipmatway.com/learn/scheduling/month-date/year-sequence)

## Select team under if-then constraints (Selection / Team Formation, LR / DI)
Source: https://ipmatway.com/learn/selection-grouping/conditional-selection

Idea: A team is picked from a pool under rules of the form "A and B not together", "if A then B", "exactly one of X and Y". The set has only a handful of valid teams, and the skill is to list them.
Exam method: 1. Fixed pairs first. "Arpit iff Amal" joins two people into one unit. 2. Exactly-one rules. they give a two-way split at once (Ashwani branch or Arpit branch). 3. Kill branches fast. a branch that cannot fill the team size is dead. 4. Budget sets. list all triples within the limit, tick off the barred pairs, then read the maximum.
Traps: Converse error: "If A then B" does not say "If B then A". Condition leakage: an "if" in one question applies only there. Team size: a branch that cannot reach the size is not a valid branch.

Lessons: [Select team under if-then constraints: start here](https://ipmatway.com/learn/selection-grouping/conditional-selection/start-here) · [Constraint chain](https://ipmatway.com/learn/selection-grouping/conditional-selection/constraint-chain) · [Must cannot](https://ipmatway.com/learn/selection-grouping/conditional-selection/must-cannot) · [Count ways](https://ipmatway.com/learn/selection-grouping/conditional-selection/count-ways) · [Best choice](https://ipmatway.com/learn/selection-grouping/conditional-selection/best-choice)

## Grouping into teams (Selection / Team Formation, LR / DI)
Source: https://ipmatway.com/learn/selection-grouping/grouping

Idea: A set of people is split into teams or cars with rules about who may travel or play together. The splits are few, so enumerate them.
Exam method: 1. Fix the trio. once the team of three is given, only four players remain and each barred pair forces the pairing. 2. Opposite sides. with two groups, "A and B cannot be together" puts them in different groups. 3. Reading the answer. if two splits survive, choose the option that lists both.
Traps: Duplicate splits: the order of the two pairs does not matter. Half-true options: check whether the other listed pair also works.

Lessons: [Grouping into teams: start here](https://ipmatway.com/learn/selection-grouping/grouping/start-here) · [Team split](https://ipmatway.com/learn/selection-grouping/grouping/team-split)

## Rank from left/right/top/bottom (Ordering and Ranking, LR / DI)
Source: https://ipmatway.com/learn/ordering-ranking/rank-position

Idea: Positions in a row, queue or rank list counted from either end. Rohtak 2019–2020 and JIPMAT 2021 / 2026 asked them (Atul twelfth from the right and fourth from the left; 78 celebrities; Chandrika 8 ranks ahead of Jaya; a row of thirty boys). Everything follows from n = L + R − 1.
Exam method: 1. Total. 12th from right, 4th from left → 15 boys. 2. Other end. 18th of 42 from the top → 42 − 18 + 1 = 25th from the last. 3. Between. 25th from left and 59th from left → 33 between. 4. Interchange. Arjun 11th from left, Ravi 17th from right; after the swap Arjun is 13th → Ravi was 13th → 29 in the row.
Traps: ± 1 slips: every wrong option in these items is one away from the key. Between vs difference: 59 − 25 = 34 is not the number between. Missing side: "16 girls between Ananya and Meera" needs the side; here Ananya is nearer the right end, so Meera is to her left.

Lessons: [Rank from left/right/top/bottom: start here](https://ipmatway.com/learn/ordering-ranking/rank-position/start-here) · [Total count](https://ipmatway.com/learn/ordering-ranking/rank-position/total-count) · [Interchange](https://ipmatway.com/learn/ordering-ranking/rank-position/interchange) · [Between count](https://ipmatway.com/learn/ordering-ranking/rank-position/between-count) · [Relative order](https://ipmatway.com/learn/ordering-ranking/rank-position/relative-order) · [Middle position](https://ipmatway.com/learn/ordering-ranking/rank-position/middle-position) · [Mixed groups](https://ipmatway.com/learn/ordering-ranking/rank-position/mixed-groups)

## Comparison of heights/weights/scores (Ordering and Ranking, LR / DI)
Source: https://ipmatway.com/learn/ordering-ranking/comparison

Idea: Comparison clues (taller, heavier, scored more) put people or objects in order. Single questions ask who is first, last or k-th (Rohtak 2020: who scored second highest; JIPMAT 2023: who ran fastest); sets add a few known values and ask which value is possible. Rohtak 2019 asked a tastiness chain with a "not tastier than" clue (ties allowed).
Exam method: 1. Rank clues first. "C weighs 51 kg and is heavier than only one" → C 7th of 8. 2. Chain. D (72) A B G. 3. Fill the top/bottom. the heaviest weighs over 80 kg, so it is not D (72): it is E. 4. Possible values. H lies between D (72) and C (51): 63 kg fits; 84, 50 and 34 do not.
Traps: Open top: two chains that meet only at the bottom do not decide the tallest. Equal values: "all different" rules out a value already used. Ties: "not tastier than" allows equality.

Lessons: [Comparison of heights/weights/scores: start here](https://ipmatway.com/learn/ordering-ranking/comparison/start-here) · [Chain ordering](https://ipmatway.com/learn/ordering-ranking/comparison/chain-ordering) · [Possible value](https://ipmatway.com/learn/ordering-ranking/comparison/possible-value)

## Round robin standings (Games and Tournaments, LR / DI)
Source: https://ipmatway.com/learn/games-tournaments/round-robin

Idea: Every team plays every other team once. Wins, draws and losses add up to n - 1 for each team, and the points add up to 2 per match. A partly erased table is solved by turning each known row into its possible (W, D, L) splits.
Exam method: 1. Split table. 8 points in 5 matches is 4-0-1 or 3-2-0; a loss count of 0 selects 3-2-0. 2. Leftover points. 30 minus the known teams' points is shared by the rest; the "less than 5" clue then decides. 3. Draw count. sum draws per team, then halve.
Traps: Draws count twice in a team-by-team tally. n - 1 matches per team. Condition carry-over between questions.

Lessons: [Round robin standings: start here](https://ipmatway.com/learn/games-tournaments/round-robin/start-here) · [Points table](https://ipmatway.com/learn/games-tournaments/round-robin/points-table) · [Match count](https://ipmatway.com/learn/games-tournaments/round-robin/match-count) · [Result deduction](https://ipmatway.com/learn/games-tournaments/round-robin/result-deduction) · [Rounds schedule](https://ipmatway.com/learn/games-tournaments/round-robin/rounds-schedule)

## Knockout rounds (Games and Tournaments, LR / DI)
Source: https://ipmatway.com/learn/games-tournaments/knockout

Idea: Losers leave; winners advance. Matches = players - 1, rounds = log2 N. Seeding rules decide who can meet whom, and an upset is a win by the worse seed.
Exam method: 1. Halving list. 128, 64, 32, 16, 8, 4, 2, 1 gives every count question in seconds. 2. No-upset rule. seed 45 in a 128-player draw is out in the round where it is in the lower half of those left. 3. Upset minimum. a seed s meets only worse seeds until the field has fewer players than s; every later win is an upset.
Traps: Rounds vs matches (7 rounds, 127 matches for 128 players). Semi-final is round 6 in a 7-round event. Opponent pools have four seeds by round 3, not one.

Lessons: [Knockout rounds: start here](https://ipmatway.com/learn/games-tournaments/knockout/start-here) · [Bracket count](https://ipmatway.com/learn/games-tournaments/knockout/bracket-count) · [Seed path](https://ipmatway.com/learn/games-tournaments/knockout/seed-path) · [Upsets](https://ipmatway.com/learn/games-tournaments/knockout/upsets)

## 2-3 statements, conclusions follow? (Syllogisms, LR / DI)
Source: https://ipmatway.com/learn/syllogisms/two-three-statement

Idea: Two to four statements about classes (All, Some, No, Only a few) are taken as true, and you decide which conclusions must follow. Rohtak asks two or three every year (2019 Q5, Q7; 2020 Q7, Q16, Q17) and JIPMAT one (2021 Q23, 2022 Q9, 2025 Q5, 2026 Q14).
Exam method: 1. Chain the 'All's. All sparrows are birds, all birds are mountains, all mountains are skies: all sparrows (and all birds) are skies. 2. Test the reverse. "All skies are birds" reverses a chain: never forced. 3. Some + All. Some bottles are drinks and all drinks are cups: some bottles are cups, and some cups are drinks. 4. No + Some. No tree is a flower and some trees are fruits: the fruits that are trees are not flowers, but "no fruit is a flower" is not forced. 5. Facts format. "All cats like to run; some cats like to swim": cats that swim also run. 6. 'Does not follow' items. mark each conclusion first, then pick the option listing exactly the ones that fail.
Traps: Possible ≠ certain: "Some yachts are boats" can be drawn, but it can also be undrawn, so it does not follow. Reversed 'All': All A are B does not give All B are A. 'Only a few': it also says some are not; "Some plants are not gardens" follows from "Only a few plants are gardens".

Lessons: [2-3 statements, conclusions follow?: start here](https://ipmatway.com/learn/syllogisms/two-three-statement/start-here) · [All some none](https://ipmatway.com/learn/syllogisms/two-three-statement/all-some-none) · [Venn method](https://ipmatway.com/learn/syllogisms/two-three-statement/venn-method) · [Only a few](https://ipmatway.com/learn/syllogisms/two-three-statement/only-a-few) · [Does not follow](https://ipmatway.com/learn/syllogisms/two-three-statement/does-not-follow) · [Fact based](https://ipmatway.com/learn/syllogisms/two-three-statement/fact-based)

## Possibility cases (Syllogisms, LR / DI)
Source: https://ipmatway.com/learn/syllogisms/possibility

Idea: Possibility conclusions ask whether something can be true, not whether it must be. They follow whenever at least one diagram that fits the statements makes them true. Rohtak 2020 Q17 paired one ("Some WhatsApp are Google is a possibility") with a definite conclusion.
Exam method: 1. Look for a ban. "No pencil is a pen" bans any pen-pencil overlap; "some erasers are pencils" then bans "all erasers are pens". 2. No ban, it follows. All fans are jalebis, all jalebis are laddoos, some laddoos are clocks: some fans being clocks is possible. 3. 'Only a few' blocks 'all'. Only a few colours are cold, so "all colours can be cold" is impossible.
Traps: Treating a possibility as a definite claim: "Some fans being clocks is a possibility" follows even though it is not certain. Missing the ban through an 'All' chain: if all A are B and no B is C, then "some A being C" is impossible.

Lessons: [Possibility cases: start here](https://ipmatway.com/learn/syllogisms/possibility/start-here) · [Possibility check](https://ipmatway.com/learn/syllogisms/possibility/possibility-check)

## Either-or conclusions (Syllogisms, LR / DI)
Source: https://ipmatway.com/learn/syllogisms/either-or

Idea: Sometimes neither of two conclusions is forced, but together they cover every case: if one is false the other is true. Then the answer is "Either I or II follows". It appears in PW and coaching sets in every syllogism chapter and is the classic trap in Rohtak-style statement-conclusion questions.
Exam method: 1. Spot the shape. Some/No, All/Some-not, Some/Some-not with the same subject and predicate. 2. Check that neither follows alone. If one of them is already definite, the answer is that one, not "either". 3. Reject All/No. "All apples are donkeys" and "No apple is a donkey" can both fail.
Traps: One already follows: if "No bead is a gem" is definite, "either no bead is a gem or some beads are gems" is not the answer. All/No is not a pair.

Lessons: [Either-or conclusions: start here](https://ipmatway.com/learn/syllogisms/either-or/start-here) · [Complementary pair](https://ipmatway.com/learn/syllogisms/either-or/complementary-pair)

## Which diagram represents the classes (Venn-based Reasoning, LR / DI)
Source: https://ipmatway.com/learn/venn-reasoning/logical-venn

Idea: A Venn diagram shows how classes relate: one wholly inside another, overlapping, or separate. Rohtak 2019 and JIPMAT ask one or two a year in three forms: choose the diagram for three classes (JIPMAT 2021 Q15, 2022 Q30), match groups with diagrams (JIPMAT 2025 Q13, 2026 Q22), or read the number in the region that fits a description (JIPMAT 2024 Q26, 2025 Q24, 2026 Q20).
Exam method: 1. Deer, lion, animals. both inside "animals", separate from each other → two circles inside a big one. 2. Women, mothers, doctors. mothers inside women; doctors overlap both → a circle inside another, with a third overlapping both. 3. Flowers, cloths, white. some flowers and some cloths are white, no flower is a cloth → a chain with white in the middle. 4. Regions. "uneducated women with government and private jobs" = inside women, triangle and private rectangle, outside the educated circle.
Traps: Too much separation: doctors and teachers can be the same people. Too much overlap: a whale is never a crow; mammals contain the whale only. One condition missed in region questions.

Lessons: [Which diagram represents the classes: start here](https://ipmatway.com/learn/venn-reasoning/logical-venn/start-here) · [Class relation](https://ipmatway.com/learn/venn-reasoning/logical-venn/class-relation) · [List match](https://ipmatway.com/learn/venn-reasoning/logical-venn/list-match) · [Region identification](https://ipmatway.com/learn/venn-reasoning/logical-venn/region-identification) · [Classes for diagram](https://ipmatway.com/learn/venn-reasoning/logical-venn/classes-for-diagram)

## 3-set counting / max-min region values (Venn-based Reasoning, LR / DI)
Source: https://ipmatway.com/learn/venn-reasoning/three-set-counting

Idea: Survey data about two or three groups (newspapers read, gadgets owned, languages learnt) are placed in a Venn diagram with up to eight regions: only A, only B, only C, the three 'only two' regions, all three, and none. Once every region is known, each question is a sum. JIPMAT 2021 Q27 gave a four-circle diagram and asked which subject had the most students.
Exam method: 1. Two sets. car 40%, scooter 55%, both 30 families, neither 40 → 0.95N + 10 = N → N = 200. 2. E-counts. three newspapers read 100 + 70 + 90 = 260 times by 200 people with 20 reading all three → E2 + 2E3 = 60 → E2 = 20, E1 = 160. 3. Region fill. seminar gadgets: laptop & I-pod 25 includes the 10 with all three → 15 only; then only-laptop = 75 − 15. 4. Maximum. detergents 328 + 88 + 60 = 476 = 400 + E2 + 2E3 → E3 ≤ 38.
Traps: Pair totals: "20 like Burger and Taco" includes the 6 who like all three. Bases: 85.18% is only-tea over coffee drinkers, not over everyone. Hidden constraint: the both-group (56) must fit inside the smaller set (40x), which rules out x = 1.

Lessons: [3-set counting / max-min region values: start here](https://ipmatway.com/learn/venn-reasoning/three-set-counting/start-here) · [Union formula](https://ipmatway.com/learn/venn-reasoning/three-set-counting/union-formula) · [Exactly k](https://ipmatway.com/learn/venn-reasoning/three-set-counting/exactly-k) · [Max min](https://ipmatway.com/learn/venn-reasoning/three-set-counting/max-min) · [Two set](https://ipmatway.com/learn/venn-reasoning/three-set-counting/two-set) · [Diagram sums](https://ipmatway.com/learn/venn-reasoning/three-set-counting/diagram-sums)

## DS on ordering, seating and directions (Data Sufficiency, LR / DI)
Source: https://ipmatway.com/learn/data-sufficiency/arrangement-ds

Idea: Arrangement DS items ask who sits where, who is tallest, or in which direction a point lies, and give two statements of clues. You test each statement alone and then together, exactly as in arithmetic DS, but each test is a small puzzle: draw the possible orders and see whether the asked position is the same in all of them.
Exam method: 1. Chains. write comparisons as one chain (A C B). The top of a chain is the tallest only if every person is in the chain. 2. Rows. from-the-right questions need the total; positions from opposite ends give the total (n = left + right − 1). 3. Directions. draw the points with free distances; if moving one distance flips east/west, the statement is not sufficient. 4. Seating. fix the most constrained person first (an end, a corner, a known floor), then test the rest.
Traps: Disconnected chains: two true chains can still leave the top undecided. Mirror seats: "at one end" can be either end. Contradiction check: a DS statement never contradicts the other; if your reading makes them clash, re-read the clue.

Lessons: [DS on ordering, seating and directions: start here](https://ipmatway.com/learn/data-sufficiency/arrangement-ds/start-here) · [Ranking order](https://ipmatway.com/learn/data-sufficiency/arrangement-ds/ranking-order) · [Seating floors](https://ipmatway.com/learn/data-sufficiency/arrangement-ds/seating-floors) · [Directions](https://ipmatway.com/learn/data-sufficiency/arrangement-ds/directions)

## DS on numbers, ages, dates and relations (Data Sufficiency, LR / DI)
Source: https://ipmatway.com/learn/data-sufficiency/arithmetic-ds

Idea: A data-sufficiency (DS) item asks a question and gives two statements. You decide whether statement I alone, statement II alone, either alone, both together, or not even both together fix the answer. JIPMAT 2021 asked one (is a + b odd, with 8 < a < 11 and 7 < b < 10); coaching analyses report two to five a year in recent Rohtak papers. The answer choices are a fixed format: read the option list once, since the order differs between papers.
Exam method: 1. Count unknowns. Turnover = units × price + other products: I gives units and price, II rules out other products → both. 2. Look for a counter-example. "Is the average above 70?" with only the highest and lowest scores: 50, 60, 90 (no) and 50, 90, 90 (yes) → not sufficient. 3. Yes/No. Thomas has 50 books; David has 26 to 49 → always "Yes" → sufficient together. 4. Dates and days. Intersect ranges; "yesterday started with T" leaves two days. 5. Relations. Check that the gender needed for the relation word is given.
Traps: Solving instead of judging: once you know the value is fixed, stop. Leaking a fact: while testing II alone, forget everything I said. "No" is an answer: a statement that proves the answer is No is sufficient. Hidden assumption: a best league record does not mean the title; the same mother is assumed only when the statement says so.

Lessons: [DS on numbers, ages, dates and relations: start here](https://ipmatway.com/learn/data-sufficiency/arithmetic-ds/start-here) · [Numbers](https://ipmatway.com/learn/data-sufficiency/arithmetic-ds/numbers) · [Dates ages](https://ipmatway.com/learn/data-sufficiency/arithmetic-ds/dates-ages) · [Relations](https://ipmatway.com/learn/data-sufficiency/arithmetic-ds/relations)

## Operators replaced by symbols (Mathematical Operations, Coded Inequalities, Missing Number, LR / DI)
Source: https://ipmatway.com/learn/mathematical-operations/symbol-substitution

Idea: The question tells you that the printed signs stand for other operations (+ means ÷, A stands for +). You rewrite the expression with the real operations and evaluate it with BODMAS. JIPMAT asks one almost every year (2021 Q9, 2022 Q32, 2025 Q10, 2026 Q16) and afterboards files them under coding-decoding; Rohtak 2020 Q20 used letters.
Exam method: 1. Rewrite, then compute. 36 × 12 + 4 ÷ 6 + 2 − 3 with + → ÷, − → ×, ÷ → +, × → − becomes 36 − 12 ÷ 4 + 6 ÷ 2 × 3. 2. BODMAS. 12 ÷ 4 = 3, 6 ÷ 2 × 3 = 9, so 36 − 3 + 9 = 42. 3. Equation options. evaluate the cheapest option first; stop when one fits. 4. Interchange items. an interchange swaps both signs everywhere.
Traps: No BODMAS: 36 − 12 ÷ 4 … evaluated left to right gives 6, an option. Double swap: change each sign once. A garbled paper: JIPMAT 2026 Q16 as printed on afterboards gives zero for no option (see the chapter census); in such a case recheck the expression, then pick the option closest to working.

Lessons: [Operators replaced by symbols: start here](https://ipmatway.com/learn/mathematical-operations/symbol-substitution/start-here) · [Bodmas after swap](https://ipmatway.com/learn/mathematical-operations/symbol-substitution/bodmas-after-swap) · [Letter operators](https://ipmatway.com/learn/mathematical-operations/symbol-substitution/letter-operators) · [Find correct equation](https://ipmatway.com/learn/mathematical-operations/symbol-substitution/find-correct-equation)

## Coded inequalities (A@B...) (Mathematical Operations, Coded Inequalities, Missing Number, LR / DI)
Source: https://ipmatway.com/learn/mathematical-operations/coded-inequality

Idea: Statements give a chain of inequalities (directly, or through coded symbols such as A @ B for A B), and you decide which conclusions follow for certain. Rohtak 2019 asked two (Q29, Q30) and JIPMAT 2021 one (Q10). A conclusion follows only if one chain of the statements links its two letters with every sign pointing the same way.
Exam method: 1. Chain. F ≥ V R = L E → F E. 2. Break. H P ≤ E: the sign turns at P, so H and R are not linked. 3. Either-or. R ≥ S → "R = S" or "R S". 4. Symbol-fill. to make B < E definite through "B ? C ≤ D < E", the ? must be ≤ or =; test each option.
Traps: ≥ is not . A chain of ≥ signs never proves a strict conclusion. Wrong turn. Two letters both below a third are not linked. Either-or misuse. It needs the same two letters and neither conclusion true alone.

Lessons: [Coded inequalities (A@B...): start here](https://ipmatway.com/learn/mathematical-operations/coded-inequality/start-here) · [Chain combine](https://ipmatway.com/learn/mathematical-operations/coded-inequality/chain-combine) · [Either or](https://ipmatway.com/learn/mathematical-operations/coded-inequality/either-or) · [Coded symbols](https://ipmatway.com/learn/mathematical-operations/coded-inequality/coded-symbols) · [Symbol fill](https://ipmatway.com/learn/mathematical-operations/coded-inequality/symbol-fill)

## Missing number in figure/grid (Mathematical Operations, Coded Inequalities, Missing Number, LR / DI)
Source: https://ipmatway.com/learn/mathematical-operations/missing-number

Idea: Numbers (or letters) are placed in a grid or a figure and one is missing. Every complete row, column or figure follows the same rule; find it and apply it to the incomplete one. JIPMAT asked these in 2022 (Q29, circle) and 2026 (Q13, triangles).
Exam method: 1. Perfect squares → square roots. 64, 36, 49 with 21 inside: 8 + 6 + 7. 2. Circle → ratio of neighbours. 594, 198, 66: each is one-third of the previous. 3. Grid → combine the first numbers to get the last. (9 + 6) × 4 = 60. 4. Letters → positions. B(2) → E(5) → K(11): × 2 + 1.
Traps: One-row rule: 6 × 7 − 6 = 36 fits nothing else in the grid. Direction: read the circle the way the complete numbers work.

Lessons: [Missing number in figure/grid: start here](https://ipmatway.com/learn/mathematical-operations/missing-number/start-here) · [Row column rule](https://ipmatway.com/learn/mathematical-operations/missing-number/row-column-rule) · [Figure pattern](https://ipmatway.com/learn/mathematical-operations/missing-number/figure-pattern)

## Identify step pattern (Input-Output (machine), LR / DI)
Source: https://ipmatway.com/learn/input-output/step-pattern

Idea: A machine rearranges a line of words and numbers one step at a time by a fixed rule: move the next element into place (sorting), swap two elements, or rewrite elements (digit sums, vowels removed, letters replaced by numbers). Rohtak 2019 asked three questions on one printed arrangement (LR Q24–Q26); JIPMAT lists the topic in its syllabus.
Exam method: 1. Sorting sets. after Step I you usually know the order; count how many elements are out of place to get the number of steps. 2. Word-number sets. handle words and numbers as two separate queues (one of each per step). 3. Position questions. count from the end named in the question; convert with n - k + 1. 4. "Which step is this?". count how many elements are already arranged.
Traps: Wrong end: read "from the right" carefully. Step numbering: check whether the input is counted as Step I. Glued symbols: each symbol is one element.

Lessons: [Identify step pattern: start here](https://ipmatway.com/learn/input-output/step-pattern/start-here) · [Shift per step](https://ipmatway.com/learn/input-output/step-pattern/shift-per-step) · [Swap per step](https://ipmatway.com/learn/input-output/step-pattern/swap-per-step) · [Transform elements](https://ipmatway.com/learn/input-output/step-pattern/transform-elements)

## Number series: missing / wrong term (Series (number / letter / alphanumeric), LR / DI)
Source: https://ipmatway.com/learn/series/number-series

Idea: A number series follows one rule from term to term: a constant or growing gap, a multiplier with a small adjustment, powers (squares, cubes, factorials, primes), or two rules woven together. IPMAT Rohtak asks 2–5 such questions a year and JIPMAT 2–3, as "find the missing term", "find the wrong term" or a match-the-lists set of four short series.
Exam method: 1. Gaps first. Write the differences under the terms. Constant → add it. Growing by a constant → second differences (JIPMAT 2023: 2, 12, 30, 56, 90: gaps 10, 18, 26, 34, +8 each → 132). 2. Big growth → multiply. If terms roughly triple or quadruple, test term × k ± c (Rohtak 2020: 12, 38, 116, 350, 1052 = ×3 + 2 → 3158). 3. Recognise landmarks. 24, 120, 720 are factorials; 121, 169, 289 are prime squares; 8, 27, 125, 343 are cubes of primes. The series is then that sequence plus a small counter. 4. No sense? Split. Read alternate terms (Rohtak 2019: 2, 7, 10, 22, 18, 37, 26, ? → 7, 22, 37, 52). 5. Wrong term. Find the rule from the agreeing terms; the one term off the chain is the answer, and the following term should fit again once the error is corrected. 6. Match-the-lists. Solve the easiest series first and eliminate options after each one; two solved series usually leave a single option.
Traps: Early gap reuse: in 5, 8, 13, ?, 29 the gaps are 3, 5, 7, 9, so 20, not 18 or 22. Sign slips: alternating series (+11, −13, +17, −19 …) are usually spoiled by one dropped minus. Decimal multipliers: 16, 8, 8, 12, 24, ? multiplies by 0.5, 1, 1.5, 2, 2.5: the next multiplier is 2.5, not 3. Wrong-term offset: in 56, 72, 90, 110, 132, 139 the gaps 16, 18, 20, 22 point to 156; the wrong term is 139, the last one, not 132.

Lessons: [Number series: missing / wrong term: start here](https://ipmatway.com/learn/series/number-series/start-here) · [Difference](https://ipmatway.com/learn/series/number-series/difference) · [Ratio](https://ipmatway.com/learn/series/number-series/ratio) · [Square cube](https://ipmatway.com/learn/series/number-series/square-cube) · [Mixed](https://ipmatway.com/learn/series/number-series/mixed)

## Letter / alphanumeric series (Series (number / letter / alphanumeric), LR / DI)
Source: https://ipmatway.com/learn/series/letter-series

Idea: Letter series use the alphabet as a number line (A = 1 … Z = 26). Each position in a term moves by its own fixed or growing step, or a short block of letters repeats or rotates. Alphanumeric series (A2Y, B8V, D33R …) combine a letter column, a number column and a second letter column, each with its own rule. Rohtak and JIPMAT ask one or two a year, and JIPMAT 2025 set a match-the-lists item with four letter series.
Exam method: 1. Columns, not words. For MOQ, SUW, YAC read M → S → Y (+6), O → U → A (+6), Q → W → C (+6): the next term is EGI. 2. Check both ends. In A2Y, B8V, D33R the first letters skip 0, 1, 2, 3 letters and the last letters go back 3, 4, 5, 6; the numbers follow ×2 + 2², ×3 + 3², ×4 + 4². 3. Blank strings. Count the letters: a c ba ca cb has 12, so try blocks of 3: abc / cba / bca / acb. 4. Rotations. AGDLX, GDLXA, DLXAG: the first letter moves to the end each time. 5. Match-the-lists. Solve two of the four series and eliminate.
Traps: Column mix-up: the option that applies the first column's step to every letter is always offered. Wrap errors: Y + 6 is E, not an impossible "letter 31"; C − 16 is M. Half-fit options: in match-the-lists items an option often gets two pairs right; check all four.

Lessons: [Letter / alphanumeric series: start here](https://ipmatway.com/learn/series/letter-series/start-here) · [Alphabet position](https://ipmatway.com/learn/series/letter-series/alphabet-position) · [Skip pattern](https://ipmatway.com/learn/series/letter-series/skip-pattern)

## Letter shifting / reversal (Coding-Decoding, LR / DI)
Source: https://ipmatway.com/learn/coding-decoding/letter-shift

Idea: In a letter-shift code every letter of the word is moved a fixed or patterned number of places (+1, +2; −2 then +2; +1, +2, +3 …), replaced by its opposite letter (A ↔ Z), or the word is first rearranged (reversed, halves swapped, pairs swapped, letters sorted) and then shifted. Rohtak asked three such items in 2019; JIPMAT asks one or two a year.
Exam method: 1. Align and subtract. R O A S T over P Q Y U R gives −2, +2, −2, +2, −2: odd positions −2, even positions +2. 2. Constant shift? Done. TOWEL → UPXFM is +1 throughout. 3. No pattern? Rearrange first. SEQUENCE → FDOFVRFT: reversed, ECNEUQES, then +1. IMTITJU → TMIIUJT: blocks of three reversed around the middle letter. 4. Opposites. FRUITS → UIFRGH pairs each letter with its mirror (F–U, R–I, T–G, S–H). A code that mixes big jumps (+19, −5 …) is usually the opposite-letter rule. 5. Answer by elimination. Code the first two letters of the asked word; usually only one option starts that way.
Traps: Uniform-shift bait: for +1, +2, +3 … codes an option applies +1 everywhere. Reversed order: after reversing, the first shift belongs to the last letter of the original word. Near-miss options: ENQWE vs ENQWF differ only in the last letter; recompute that one position.

Lessons: [Letter shifting / reversal: start here](https://ipmatway.com/learn/coding-decoding/letter-shift/start-here) · [Plus minus k](https://ipmatway.com/learn/coding-decoding/letter-shift/plus-minus-k) · [Reverse](https://ipmatway.com/learn/coding-decoding/letter-shift/reverse)

## Word substitution, sentence codes, word formation (Coding-Decoding, LR / DI)
Source: https://ipmatway.com/learn/coding-decoding/substitution

Idea: Three formats share this subconcept. Sentence codes: a few sentences and their coded forms are given; words that recur pin down their codes by intersection, and the rest follow by elimination (JIPMAT 2021: 'sik' = red). Word swaps: a chain of "X is called Y" statements; the question asks a fact and wants the code word for the true answer (Rohtak 2019: the king of the jungle is told as Goat). Word formation: which word can or cannot be made from the letters of a given word (JIPMAT 2021, 2024).
Exam method: 1. Most frequent word first. 'is' appears in all three sentences and only '9' is in all three codes: is = 9. 2. Pairs of sentences. 'flowers' is in two sentences; their common code is hee. Then the sentence 'red flowers' = 'sik hee' leaves sik for red. 3. Leftovers. In 'fly on painted sky', fly, on and painted are known from other sentences, so sky takes the remaining code. 4. Joined words. bike and 'and' appear only together in two sentences with codes tm and ts: nothing separates them. 5. Swaps. answer the fact (the national fruit is the mango), then read the chain once: Mango is called Papaya. 6. Formation. tick off letters; SOLACE needs an E that MIRACULOUS lacks.
Traps: Word-order reading: 'Life is beautiful' = 289 does not mean Life = 2, is = 8; only the intersection logic is safe. Real word vs code word: the fridge keeps things cold, but the question wants the word used for it ('Bulb'). Repeated letters: FRACTURE needs two R's; INFRASTRUCTURE has three, so it can be formed.

Lessons: [Word substitution, sentence codes, word formation: start here](https://ipmatway.com/learn/coding-decoding/substitution/start-here) · [Common word mapping](https://ipmatway.com/learn/coding-decoding/substitution/common-word-mapping) · [Word swap](https://ipmatway.com/learn/coding-decoding/substitution/word-swap) · [Word formation](https://ipmatway.com/learn/coding-decoding/substitution/word-formation)

## Number / symbol coding (Coding-Decoding, LR / DI)
Source: https://ipmatway.com/learn/coding-decoding/number-symbol

Idea: A word is turned into a number through its letters' alphabet positions (sums, products, squares, counts), or digits are mapped one-to-one to letters or symbols by a table. JIPMAT asks one or two every year (CAT = 6423, HE = 418, GREEN = 1677209, DRIVER = 12); Rohtak 2020 had a digit-to-letter code.
Exam method: 1. Size test. CAT → 6423 has one or two digits per letter: positions with +3. HE → 418 is far too big for a sum: a product (reverse positions 19 × 22). 2. Count test. DRIVER = 12, PEDESTRIAN = 20: twice the letter count. SHOULD = 42, ASPIRANT = 72: n(n + 1). 3. Sum test. TO = 35 = 20 + 15. SINGLE = 72 = 66 + 6 letters. FIRE = 152 = 38 × 4 letters. KITE = 2025 = 45². 4. Direction test. GREEN → 1677209: positions +2 written from the last letter (N 16, E 7, E 7, R 20, G 9). 5. Tables. Map each digit from the examples (15789 = XTZAL), then read the asked number. With exception rules, check the first and last digit first.
Traps: Off-by-one positions: J = 10, S = 19, T = 20; a one-place slip changes every answer. Added vs multiplied count: SINGLE = 66 + 6, but FIRE = 38 × 4; test the example, never assume. Forward vs reverse order: when the code has more digits than letters, check whether it starts from the last letter.

Lessons: [Number / symbol coding: start here](https://ipmatway.com/learn/coding-decoding/number-symbol/start-here) · [Digit sum](https://ipmatway.com/learn/coding-decoding/number-symbol/digit-sum) · [Symbol map](https://ipmatway.com/learn/coding-decoding/number-symbol/symbol-map)

## Number analogy (Analogy, Classification and Word Order, LR / DI)
Source: https://ipmatway.com/learn/analogy-classification/number-analogy

Idea: A number analogy states a rule through one pair (or two) and asks for the number the same rule gives. JIPMAT 2021 set two: 210 : 380 :: 182 : ? and a number-set item. The rule is almost always one of a short list of operations on the whole number or on its digits.
Exam method: 1. Look at the size jump. About × 5 to × 10: a product with a small factor or n(n ± 1). About n^2: a square ± a little. Far larger: a cube or a factorial. 2. Factorise the larger number. 1716 = 11 × 12 × 13 tells you the rule at once (12 → 1716, so 17 → 16 × 17 × 18 = 4896). 3. If the number is small and the other large, try the digits. 429 → (4 + 2 + 9)² = 225. 4. Number sets. divide by the common factor and compare the pattern left over.
Traps: One pair, two rules: when two rules fit the given pair, use the second pair (or the options) to decide. Near misses: options are built from the right base with the wrong adjustment (n^3 - n vs n^3 + n).

Lessons: [Number analogy: start here](https://ipmatway.com/learn/analogy-classification/number-analogy/start-here) · [Operation pattern](https://ipmatway.com/learn/analogy-classification/number-analogy/operation-pattern) · [Number set](https://ipmatway.com/learn/analogy-classification/number-analogy/number-set)

## Letter analogy (Analogy, Classification and Word Order, LR / DI)
Source: https://ipmatway.com/learn/analogy-classification/letter-analogy

Idea: A letter analogy is a code shown by one pair: each letter moves by a fixed number of places, by a growing number of places, or is replaced by its opposite letter. JIPMAT set one each year from 2022 to 2024.
Exam method: 1. Shifts first. LCQJ → METN is +1, +2, +3, +4, so ABDF → B, D, G, J. 2. Mixed signs are common. AFHO → GBDJ is +6, −4, −4, −5, so CHFM → I, D, B, H. 3. If the shifts look random, test opposites. ASHU → ZHSF is A↔Z, S↔H, H↔S, U↔F. 4. Eliminate from one letter. usually the first letter alone rules out two options.
Traps: Position slips: count with EJOTY rather than from A each time. Pattern within a group: in ACBD : JLKM the rule is inside each group (+2, −1, +2), not between the groups.

Lessons: [Letter analogy: start here](https://ipmatway.com/learn/analogy-classification/letter-analogy/start-here) · [Position pattern](https://ipmatway.com/learn/analogy-classification/letter-analogy/position-pattern) · [Opposite letters](https://ipmatway.com/learn/analogy-classification/letter-analogy/opposite-letters)

## Word analogy (Analogy, Classification and Word Order, LR / DI)
Source: https://ipmatway.com/learn/analogy-classification/word-analogy

Idea: A word analogy gives a pair with a fixed relation and asks for the option with the same relation, in the same order. Rohtak 2019 set two and Rohtak 2020 one; JIPMAT sets one to three a year, including 'which of these analogies are correct' (2025, 2026) and a three-word colour mix (2021).
Exam method: 1. Sentence test. "Embarrass, then humiliate: the second is a stronger degree of the first." Only annoy : exasperate fits; enquire : ask is a plain synonym. 2. Order check. drill : bore is tool : action, so sieve : sift, not the reverse. 3. Study of, specialist for. botany : plants, entomology : insects; dermatologist : skin, pulmonologist : lungs. 4. Statement sets. mark each statement true or false, then pick the matching option (JIPMAT 2025: B and D only).
Traps: Half-right options: an option on the same topic with a looser link (fear : tremble is cause and effect, not holder and contents). None of these: pick it only when you have ruled out every listed option on the exact relation.

Lessons: [Word analogy: start here](https://ipmatway.com/learn/analogy-classification/word-analogy/start-here) · [Relation type](https://ipmatway.com/learn/analogy-classification/word-analogy/relation-type) · [Three word relation](https://ipmatway.com/learn/analogy-classification/word-analogy/three-word-relation) · [Statements correct](https://ipmatway.com/learn/analogy-classification/word-analogy/statements-correct)

## Classification / odd one out (Analogy, Classification and Word Order, LR / DI)
Source: https://ipmatway.com/learn/analogy-classification/classification

Idea: Three options share a property and one does not. JIPMAT sets one to three a year: odd months (2021), digit sums (2021), letter-gap groups (2021), jumbled words (2023, 2024), bacterial diseases (2024), rabi crops (2025) and a number-pair rule (2026).
Exam method: 1. Words. name the class (rabi crops: wheat, pea, mustard; rice is kharif). 2. Numbers. quick tests in order: prime, multiple, digit sum, digit relation, power. 5698, 7894, 9865 have digit sum 28; 8793 has 27. 3. Number pairs. relate the two numbers: 483 = 23 × 21, 624 = 26 × 24, 1368 = 38 × 36, but 1023 = 31 × 33. 4. Letter groups. B d E g, K m N p, P r S u all go +2, +1, +2; T w X z goes +3. 5. Jumbled words. EIWNTR, UMRSME, PIGRSN are seasons; LCUOD is CLOUD.
Traps: Primes: 171 = 9 × 19 and 153 = 9 × 17 look prime; 181 and 199 are prime. Capitals vs countries: Luanda, Yerevan, Nassau are capitals; Benin is a country.

Lessons: [Classification / odd one out: start here](https://ipmatway.com/learn/analogy-classification/classification/start-here) · [Odd word](https://ipmatway.com/learn/analogy-classification/classification/odd-word) · [Odd number](https://ipmatway.com/learn/analogy-classification/classification/odd-number) · [Odd letter group](https://ipmatway.com/learn/analogy-classification/classification/odd-letter-group) · [Unscramble odd](https://ipmatway.com/learn/analogy-classification/classification/unscramble-odd)

## Word order (logical sequence, dictionary order) (Analogy, Classification and Word Order, LR / DI)
Source: https://ipmatway.com/learn/analogy-classification/word-order

Idea: Arrange words in a logical order (a process, a life cycle, a ranking) or in dictionary order. JIPMAT set a meaningful sequence in 2021, 2025 and 2026 and dictionary order in 2025 and 2026.
Exam method: 1. Fix the ends. Illness must be first and Recovery last, which leaves only two options to compare. 2. Check one middle step. Consultation comes before Treatment, so B, C, A, D, E. 3. Dictionary order. group by the shared start, then sort on the first letter that differs: Ente-, Enth-, Entr-, Ep-, Ex-.
Traps: Ranks and levels: know the common ladders (constable, sub-inspector, inspector, DSP, SP; troposphere, stratosphere, mesosphere, thermosphere, exosphere). Prefix words: Particle before Particular (l before u at the seventh letter).

Lessons: [Word order (logical sequence, dictionary order): start here](https://ipmatway.com/learn/analogy-classification/word-order/start-here) · [Meaningful sequence](https://ipmatway.com/learn/analogy-classification/word-order/meaningful-sequence) · [Dictionary order](https://ipmatway.com/learn/analogy-classification/word-order/dictionary-order)

## Statement-based relation (Blood Relations, LR / DI)
Source: https://ipmatway.com/learn/blood-relations/statement

Idea: A string of one-line facts ("Sheela is the wife of Arun. Deepak is the brother of Sheela …") describes one family; the question asks how two of its members are related, how many males or sons there are, which statements are true, or whether the data are enough. Rohtak and JIPMAT set one or two of these every year (JIPMAT 2021–2026, Rohtak 2019–2020).
Exam method: 1. One generation per row. Place the question's two people first; add only the facts that connect them. 2. Two conventions do most of the work. A child's parents are a couple ("Q is the mother of R" + "P is the father of R": P and Q are married), and siblings share both parents. 3. Sex last. Name the relation, then check the sex of the person being described: if the clues never fix it, look for "cannot be determined". 4. Counting items. (sons, males, couples): list every person once with a sex mark, then count; for "each daughter has as many brothers as sisters" write the two equations b = g − 1 and g = 2(b − 1). 5. Sufficiency items. test each statement alone on a fresh tree; a statement that never links the two people is not sufficient.
Traps: Unknown sex: "P is the son of Q, and Q is the brother of R": R may be an uncle or an aunt, so answer "nephew and uncle/aunt", not "nephew and uncle". Direction of the relation: if A is B's father-in-law, B is A's son- or daughter-in-law; read the question's order twice. Hidden "only": "M has only two children" is what rules D out as T's father in Example 3.

Lessons: [Statement-based relation: start here](https://ipmatway.com/learn/blood-relations/statement/start-here) · [Family tree](https://ipmatway.com/learn/blood-relations/statement/family-tree) · [Count members](https://ipmatway.com/learn/blood-relations/statement/count-members) · [True statements](https://ipmatway.com/learn/blood-relations/statement/true-statements) · [Sufficiency](https://ipmatway.com/learn/blood-relations/statement/sufficiency)

## Pointing / photograph type (Blood Relations, LR / DI)
Source: https://ipmatway.com/learn/blood-relations/pointing

Idea: Someone points at a photograph or introduces a person and describes them by a chain of relations: "He is the only son of the father of my sister's brother". Collapse the chain one link at a time, starting from the speaker, until it ends at a known person. Every Rohtak and JIPMAT paper since 2019 has at least one such item.
Exam method: 1. Collapse from the inside. "son of the daughter of the father of my uncle": my uncle's father = my grandfather; his daughter = my mother or my aunt. 2. Use the speaker's sex. Mr. Arav's mother's only son is Arav himself; Rani's sister's brother is Rani's brother. 3. Only one option can be true?. When a link has two readings (a boy's grandfather may be paternal or maternal), check which reading the options allow; the key never depends on a reading no option offers. 4. Third-person questions. after collapsing, re-anchor to the person asked about (the husband of the speaker, the man's son, Aman's father).
Traps: Wrong direction: in "How is Mr. Handsome related to the man?" the man is his nephew, so the answer is maternal uncle, not nephew. Speaker's own position: "the only child of the only child of my father's father" is the speaker himself. Two grandfathers: "the grandfather of my brother's son" is my father on the usual reading; his maternal grandfather would be my brother's father-in-law.

Lessons: [Pointing / photograph type: start here](https://ipmatway.com/learn/blood-relations/pointing/start-here) · [Self reference](https://ipmatway.com/learn/blood-relations/pointing/self-reference) · [Third person](https://ipmatway.com/learn/blood-relations/pointing/third-person)

## Coded relations (A@B means...) (Blood Relations, LR / DI)
Source: https://ipmatway.com/learn/blood-relations/coded

Idea: Relations are written as symbols: "A + B means A is the brother of B". An expression such as M × N − C + F strings several relations together. Questions ask what an expression means, how two of its letters are related, or which of four expressions shows a given relation (Rohtak 2020 asked "which means that C is the son of M?").
Exam method: 1. Pair by pair. M × N − C + F: M is N's father; N is C's sister; C is F's brother. 2. Merge siblings. N and C are siblings, so M is C's father too; C + F makes C male: C is M's son. 3. Sex check last. "Definitely true" options often fail only on sex (W may be a grandson or a granddaughter). 4. Eliminate fast in expression-choice items. the target person must stand on the left of a symbol that fixes the needed sex, and the chain must reach the other person.
Traps: Reversed symbols: if "A % B means B is the niece of A", the niece is on the right. Unfixed sex: P & R @ Q (R is P's mother, R married to Q) makes P Q's child, but son or daughter cannot be decided. Distinct letters: without "different letters are different people", E in Example 3 could be B herself.

Lessons: [Coded relations (A@B means...): start here](https://ipmatway.com/learn/blood-relations/coded/start-here) · [Symbol decoding](https://ipmatway.com/learn/blood-relations/coded/symbol-decoding) · [Expression choice](https://ipmatway.com/learn/blood-relations/coded/expression-choice)

## Family tree set with 3-5 Q (Blood Relations, LR / DI)
Source: https://ipmatway.com/learn/blood-relations/family-tree-set

Idea: A short paragraph describes one family of five to eight people, sometimes with professions or other attributes, and 2-5 questions follow. The set rewards one careful drawing. Rohtak puts the set-style items in its LR section (2020: an eight-person family; JIPMAT 2021: niece/nephew of Q).
Exam method: 1. Anchor clue first. the clue with a unique person ("P has only two children", "K has no siblings"). 2. Negative clues. "P is the father of R but not the husband of Q" sends Q to the other side of the family. 3. Attribute sets. "No lady is a Doctor or a Designer" fixes the sexes of the Doctor and the Designer, and then their spouses. 4. Two trees, one answer. "O is the brother-in-law of L" can mean L's wife's brother or L's sister's husband; check that each answer holds in both.
Traps: "How many couples?" Two marriages are stated; an unmarried man and woman who are not siblings could still be a couple, so the count is not determined. Sex left open: "How is P related to E?" when P's sex is never fixed: grandparent, i.e. "cannot be determined". Book sets with a missing link: "D is Z's niece" does not say which sibling of Z is D's parent; avoid questions that depend on it.

Lessons: [Family tree set with 3-5 Q: start here](https://ipmatway.com/learn/blood-relations/family-tree-set/start-here) · [Generation count](https://ipmatway.com/learn/blood-relations/family-tree-set/generation-count) · [Gender unknown](https://ipmatway.com/learn/blood-relations/family-tree-set/gender-unknown) · [Relation query](https://ipmatway.com/learn/blood-relations/family-tree-set/relation-query) · [Family attributes](https://ipmatway.com/learn/blood-relations/family-tree-set/family-attributes)

## Net displacement / final direction (Direction Sense, LR / DI)
Source: https://ipmatway.com/learn/direction-sense/displacement

Idea: A person walks, turns and walks again, or a list of statements places points relative to one another ("F is 15 m north of M"). Questions ask the distance from the start, the direction of the end point (or of one point from another), the final heading, or whether two statements are enough. Every Rohtak and JIPMAT LR paper from 2019 to 2026 has one or two such items.
Exam method: 1. Heading first, distance second. Write the heading before each leg: S, then right = W, then left = S... 2. Two totals. Add the east legs and subtract the west legs; do the same north-south. Cancelling legs often leave a straight line (Rohtak 2020: 140 m). 3. Pythagorean triples. 3-4-5, 6-8-10, 5-12-13, 8-15-17, 7-24-25: if the totals are a triple, the answer is immediate. 4. Relative statements. pick the most connected point as the origin and place the others one by one; for coded statements decode the rule first (sum, average or product of the two numbers). 5. Direction of X from Y. compute X minus Y, never the reverse. 6. Clock face as a compass. if the 3 points north-west, every hour mark is 30° further clockwise; opposite marks (3 and 9) point in opposite directions.
Traps: Wrong reference point: "office from home" is the reverse of "home from office". Heading vs position: "In which direction is she moving?" asks for the last heading (JIPMAT 2021: north), not where she is. Near-axis points: 2 km east and 48 km south is still south-east, not south, under the exam's convention.

Lessons: [Net displacement / final direction: start here](https://ipmatway.com/learn/direction-sense/displacement/start-here) · [Pythagoras](https://ipmatway.com/learn/direction-sense/displacement/pythagoras) · [Turn tracking](https://ipmatway.com/learn/direction-sense/displacement/turn-tracking) · [Final direction](https://ipmatway.com/learn/direction-sense/displacement/final-direction) · [Relative position](https://ipmatway.com/learn/direction-sense/displacement/relative-position) · [Coded direction](https://ipmatway.com/learn/direction-sense/displacement/coded-direction) · [Sufficiency](https://ipmatway.com/learn/direction-sense/displacement/sufficiency) · [Route geometry](https://ipmatway.com/learn/direction-sense/displacement/route-geometry) · [Clock face](https://ipmatway.com/learn/direction-sense/displacement/clock-face)

## Shadow / sunrise based direction (Direction Sense, LR / DI)
Source: https://ipmatway.com/learn/direction-sense/shadow-sun

Idea: The Sun fixes a direction: in the morning it is in the east, so shadows point west; in the evening it is in the west, so shadows point east. Knowing which side of a person the shadow falls tells you which way they face. Book and coaching sets use it often; Rohtak has asked direction items in this style.
Exam method: 1. Fix the shadow's compass direction: morning west, evening east. 2. Convert the side to a heading: front = the shadow's direction; behind = opposite; left = 90° clockwise of the shadow's direction; right = 90° anticlockwise. 3. If a second person faces the first, reverse the heading. Then apply any further turns.
Traps: Second person: "Which direction is Shalini facing?" needs one more reversal after you find Reena's heading. Left/right: a shadow on your left means the shadow's direction is 90° anticlockwise of your heading, so you face 90° clockwise of it.

Lessons: [Shadow / sunrise based direction: start here](https://ipmatway.com/learn/direction-sense/shadow-sun/start-here) · [Shadow rule](https://ipmatway.com/learn/direction-sense/shadow-sun/shadow-rule)

## Angle between hands / coincide / opposite (Clocks and Calendars, LR / DI)
Source: https://ipmatway.com/learn/clocks-calendars/clock-angle

Idea: Clock questions turn on two speeds: the minute hand moves 6° a minute and the hour hand 0.5°, so the minute hand gains 5.5° a minute. From this one fact come the angle at any time, the times when the hands meet, oppose or form a given angle, and how far a hand turns in a given time. JIPMAT 2023 set two (a matching list of angles and times, and the hour hand moving 135°).
Exam method: 1. Angle. |30H - 5.5M|; take 360° minus it if it is more than 180° (or keep the larger one if the reflex angle is asked). 2. When at angle θ. solve |30H - 5.5M| = θ: two answers in most hours (minute hand behind, then ahead). 3. Rotation. hour hand 30° an hour, minute hand 6° a minute. 4. Counts. together 11 and opposite 11 times in 12 hours; any other angle 22 times. 5. Clock as a compass. if one hour mark points in a known direction, every other mark is 30° per hour round from it.
Traps: Hour hand drift: at 6:45 the angle is 67.5°, not 90°. Which angle: "reflex" means the larger angle (360° minus the smaller). Mirror: 4:15 in a mirror reads 7:45, not 7:15.

Lessons: [Angle between hands / coincide / opposite: start here](https://ipmatway.com/learn/clocks-calendars/clock-angle/start-here) · [Angle formula](https://ipmatway.com/learn/clocks-calendars/clock-angle/angle-formula) · [Hand rotation](https://ipmatway.com/learn/clocks-calendars/clock-angle/hand-rotation) · [Coincide opposite](https://ipmatway.com/learn/clocks-calendars/clock-angle/coincide-opposite) · [Mirror time](https://ipmatway.com/learn/clocks-calendars/clock-angle/mirror-time) · [Clock direction](https://ipmatway.com/learn/clocks-calendars/clock-angle/clock-direction) · [Clock strikes](https://ipmatway.com/learn/clocks-calendars/clock-angle/clock-strikes)

## Gaining / losing clock (Clocks and Calendars, LR / DI)
Source: https://ipmatway.com/learn/clocks-calendars/faulty-clock

Idea: A faulty clock runs at a steady wrong rate. Every question reduces to a proportion between shown time and true time, or to the moment when a steadily changing error passes zero. Rohtak 2019 and JIPMAT 2024-2025 each set one.
Exam method: 1. Correct time. from x minutes slow to y minutes fast in T hours, the error changes by x + y; it is zero after x/(x + y) of the interval (JIPMAT 2024: 2 slow, 2.5 fast in 27 h → after 12 h). 2. Shown to true. a clock that gains 15 minutes in 20 hours shows 1215 minutes per 1200 true minutes. 3. Two clocks. read the true time from one, then the other's reading from its own rate. 4. Leap years. count 29 February when the interval crosses it (Rohtak 2019: 163 hours from 25 Feb to 3 March 2008).
Traps: Per true hour vs per shown hour: "gains 5 seconds every minute" is per true minute. Half speed: a clock ticking 30 times a minute shows 15 minutes in 30 true minutes.

Lessons: [Gaining / losing clock: start here](https://ipmatway.com/learn/clocks-calendars/faulty-clock/start-here) · [Rate error](https://ipmatway.com/learn/clocks-calendars/faulty-clock/rate-error) · [Correct time](https://ipmatway.com/learn/clocks-calendars/faulty-clock/correct-time) · [Two clocks](https://ipmatway.com/learn/clocks-calendars/faulty-clock/two-clocks)

## Day of the week / odd days (Clocks and Calendars, LR / DI)
Source: https://ipmatway.com/learn/clocks-calendars/calendar-day

Idea: Weekdays repeat every 7 days, so only the remainder of a day count matters (the "odd days"). From a given date and weekday, the weekday of any other date follows by counting odd days; from a reference point (1 January of year 1 = Monday) any date's weekday follows from the century and leap-year rules. JIPMAT set a calendar item in 2021, 2023 (two), and 2024; Rohtak 2019 asked a sufficiency version.
Exam method: 1. Two dates, one weekday known. count days between, reduce mod 7, move forwards or backwards (JIPMAT 2021: 6 March to 15 August 2014 = 162 days → 1). 2. Same date, later year. add 1 per year, plus 1 for each 29 February crossed. 3. Same calendar. both ordinary or both leap, and the odd days in between total a multiple of 7 (2009 → 2015; 2023 → 2034). 4. Overlapping clues. intersect the date ranges first, then test the weekday (JIPMAT 2023: Wednesday between the 16th and 19th → 18th).
Traps: Leap day position: 1 March to 1 April is 31 days even in a leap year; the extra day is in February. Century years: 1900 is ordinary, 2000 is a leap year (2000-2099 has 25 leap years). Hypothetical calendars: "Suppose 2008 starts on a Monday" changes the days but not the counting.

Lessons: [Day of the week / odd days: start here](https://ipmatway.com/learn/clocks-calendars/calendar-day/start-here) · [Odd days](https://ipmatway.com/learn/clocks-calendars/calendar-day/odd-days) · [Leap rule](https://ipmatway.com/learn/clocks-calendars/calendar-day/leap-rule) · [Same calendar](https://ipmatway.com/learn/clocks-calendars/calendar-day/same-calendar) · [Date reasoning](https://ipmatway.com/learn/clocks-calendars/calendar-day/date-reasoning) · [Date sufficiency](https://ipmatway.com/learn/clocks-calendars/calendar-day/date-sufficiency)

## Painted cube cut into smaller cubes (Cubes and Dice, LR / DI)
Source: https://ipmatway.com/learn/cubes-dice/painted-cube

Idea: A big cube is painted (on all faces, on some faces, or in different colours) and cut into identical small cubes, n along each edge. Every small cube is a corner, an edge cube, a face-centre cube or an inner cube, and that position fixes how many painted faces it has. Rohtak and JIPMAT ask one such item most years (JIPMAT 2024, 2025, 2026: "which of these statements are correct" about a cube cut into 27 or 64 pieces).
Exam method: 1. n first. 216 → 6, 343 → 7, 512 → 8; "125 unpainted" → n − 2 = 5 → n = 7. 2. Read the condition word. exactly / at least / only / no: at least two = 12(n − 2) + 8. 3. Colour edges. Opposite faces in pairs (red, blue, green): a red–blue edge exists for each red face and each blue face: 2 × 2 = 4 edges, n − 2 cubes each. 4. Partial painting. Paint only the faces named; a cube is coloured if it lies on any of them; subtract the shared edge once for adjacent faces. 5. Cuts and surface area. Pieces = (cuts + 1) per direction, multiplied; surface area grows from 6a² to (number of pieces) × 6b².
Traps: Corner double count: 12 × n or 12 × (n − 1) for two-face cubes. Exactly vs at least: "at least two" adds the 8 corners. Slices vs cuts: 7 cubes along an edge need 6 cuts in that direction. Same-colour edges: in "two faces of different colours", edges where two faces of one colour meet do not count.

Lessons: [Painted cube cut into smaller cubes: start here](https://ipmatway.com/learn/cubes-dice/painted-cube/start-here) · [Faces painted count](https://ipmatway.com/learn/cubes-dice/painted-cube/faces-painted-count) · [Colour pattern](https://ipmatway.com/learn/cubes-dice/painted-cube/colour-pattern) · [Partial painting](https://ipmatway.com/learn/cubes-dice/painted-cube/partial-painting) · [Cuts pieces](https://ipmatway.com/learn/cubes-dice/painted-cube/cuts-pieces)

## Dice: views, opposite faces and open nets (Cubes and Dice, LR / DI)
Source: https://ipmatway.com/learn/cubes-dice/dice

Idea: A die (cube) has three pairs of opposite faces. Questions show two to four views of the same die, or an unfolded sheet (net), and ask which face is opposite another, which face is on top when another is at the bottom, or which drawn die can be made from the net. Rohtak 2019–2020 and JIPMAT 2024–2026 each asked one or two (JIPMAT 2025 Q7: four views, opposite of 3).
Exam method: 1. Strike out every face seen next to the asked face; often one option survives. 2. If two remain, use the clockwise reading from a common face (PW and afterboards solutions use the same rule). 3. For nets, mark the opposite pairs on the sheet first (pairs two apart in a row), then reject every option that shows an opposite pair together. 4. Corner order decides the last option: on the sheet, read the three faces round a shared corner clockwise; on a drawn die read top → right → front. A die showing the reverse order is the mirror image.
Traps: Seen together = adjacent: an option that appears next to the asked face in any view is wrong. Mirror corner: a die with the right three faces in the wrong turning order cannot be formed. Over-using 'cannot be determined': with a common face and the clockwise rule, two views usually fix all three pairs.

Lessons: [Dice: views, opposite faces and open nets: start here](https://ipmatway.com/learn/cubes-dice/dice/start-here) · [Opposite face rule](https://ipmatway.com/learn/cubes-dice/dice/opposite-face-rule) · [Open net](https://ipmatway.com/learn/cubes-dice/dice/open-net) · [Standard dice](https://ipmatway.com/learn/cubes-dice/dice/standard-dice)

## Mirror / water image (Non-verbal Reasoning, LR / DI)
Source: https://ipmatway.com/learn/non-verbal/mirror-water-image

Idea: A mirror placed beside a figure swaps left and right; a water surface below it swaps top and bottom. Every option in these questions is one of four things: the true image, the other reflection, the figure turned through 180 degrees (both reflections), or a near copy with one detail wrong. Rohtak 2019 asked the mirror image of a letter-digit group (Q8); JIPMAT 2025 asked a mirror image (Q18) and a water image (Q22) of figures, and JIPMAT 2026 did the same (Q5, Q6).
Exam method: 1. Find the most asymmetric character or part (R, F, G, 4, 7, an arrowhead, a flag, a shaded half). 2. Ask where it must be and which way it must face; strike out every option that disagrees. 3. If two options remain, compare one more part (usually the order of the characters or the side of a shaded half).
Traps: Half the job: order reversed but letters not flipped, or the reverse. Wrong mirror: the water image offered for a mirror question and vice versa. Clocks: both hands are reflected; the two times always add to 12:00.

Lessons: [Mirror / water image: start here](https://ipmatway.com/learn/non-verbal/mirror-water-image/start-here) · [Text mirror](https://ipmatway.com/learn/non-verbal/mirror-water-image/text-mirror) · [Text water](https://ipmatway.com/learn/non-verbal/mirror-water-image/text-water) · [Flip rule](https://ipmatway.com/learn/non-verbal/mirror-water-image/flip-rule) · [Symmetric letters](https://ipmatway.com/learn/non-verbal/mirror-water-image/symmetric-letters) · [Clock mirror](https://ipmatway.com/learn/non-verbal/mirror-water-image/clock-mirror) · [Figure mirror](https://ipmatway.com/learn/non-verbal/mirror-water-image/figure-mirror) · [Figure water](https://ipmatway.com/learn/non-verbal/mirror-water-image/figure-water)

## Count triangles / squares / rectangles (Non-verbal Reasoning, LR / DI)
Source: https://ipmatway.com/learn/non-verbal/figure-counting

Idea: Count the triangles, squares or rectangles whose every side lies on a drawn line. JIPMAT asks one each year: triangles in 2024 (Q23, 21 triangles) and 2026 (Q17, 11 triangles), squares and rectangles in 2025 (Q2).
Exam method: 1. Fan + cross lines. k lines from one corner and t lines crossing all of them give tk2 triangles. 2. Grids. squares size by size (4 × 4: 16 + 9 + 4 + 1 = 30); rectangles m+12n+12. 3. Square with both diagonals and both midlines. 8 + 4 + 4 = 16 triangles. 4. Anything else. split the figure into parts you know and count the triangles that cross between parts separately.
Traps: Big ones missed: the triangle made of two or four pieces is still a triangle. False triangles: a region with a bent side is not a triangle. Double counting: list each triangle once by fixing an order of corners.

Lessons: [Count triangles / squares / rectangles: start here](https://ipmatway.com/learn/non-verbal/figure-counting/start-here) · [Triangles](https://ipmatway.com/learn/non-verbal/figure-counting/triangles) · [Squares](https://ipmatway.com/learn/non-verbal/figure-counting/squares) · [Rectangles](https://ipmatway.com/learn/non-verbal/figure-counting/rectangles)

## Paper folding / cutting (Non-verbal Reasoning, LR / DI)
Source: https://ipmatway.com/learn/non-verbal/paper-folding

Idea: A sheet is folded one or more times, a hole is punched through all the layers, and the sheet is opened out. Every fold doubles the number of layers, so every opening doubles the holes: each hole gets a twin, its reflection in the fold line. Listed in the Rohtak and JIPMAT syllabi; no paper has asked it in 2019–2026.
Exam method: 1. One punched hole gives 2^f holes after f folds (fewer only if it lies on a fold line). 2. Check where one hole's twin must lie for the first fold opened; that usually leaves one option.
Traps: Too few holes: a fold left closed. Wrong mirror line: the twin placed across the wrong line. Wrong order: open the last fold first.

Lessons: [Paper folding / cutting: start here](https://ipmatway.com/learn/non-verbal/paper-folding/start-here) · [Punch unfold](https://ipmatway.com/learn/non-verbal/paper-folding/punch-unfold)

## Age relation puzzles (Age / Quant-Reasoning puzzles, LR / DI)
Source: https://ipmatway.com/learn/age-puzzles/age-relation

Idea: Age questions are linear equations in disguise. Name the present ages, translate each time-shifted statement into one equation, and solve. The one fact that never changes is the difference between two ages.
Exam method: 1. Ratios: write the ages as ak and bk, then use one more statement to find k. 2. Averages: convert to totals; shift totals by (number of people x years). 3. Sufficiency: a statement is enough only if it gives a numeric equation; two pure differences never fix an age. 4. Test the answer options back in the stem when the algebra is long.
Traps: Subtracting the years from one person only. Using 'older than' for 'times as old as'. Calling a statement sufficient because it mentions the target person.

Lessons: [Age relation puzzles: start here](https://ipmatway.com/learn/age-puzzles/age-relation/start-here) · [Linear equation](https://ipmatway.com/learn/age-puzzles/age-relation/linear-equation) · [Ratio ages](https://ipmatway.com/learn/age-puzzles/age-relation/ratio-ages) · [Average age](https://ipmatway.com/learn/age-puzzles/age-relation/average-age) · [Age sufficiency](https://ipmatway.com/learn/age-puzzles/age-relation/age-sufficiency) · [Birth year](https://ipmatway.com/learn/age-puzzles/age-relation/birth-year)

## Money and notes (Quant-flavoured reasoning (money, bounds, shifts, counting), LR / DI)
Source: https://ipmatway.com/learn/quant-reasoning/money-notes

Idea: Money puzzles in the LR section are small linear equations in disguise: a total value, a few denominations, and a condition on the counts. JIPMAT 2024 asked one (a cashier with equal numbers of 2, 10 and 50 rupee notes).
Exam method: Group the denominations into one "set" when counts are equal (2 + 10 + 50 = 62). For ratios, find the value of one ratio unit. For "how many ways", fix the biggest note's count and list.
Traps: Total vs one kind: reread the last line of the question. Equal count vs equal value: the first gives one set, the second gives equal shares of the total.

Lessons: [Money and notes: start here](https://ipmatway.com/learn/quant-reasoning/money-notes/start-here) · [Equal notes](https://ipmatway.com/learn/quant-reasoning/money-notes/equal-notes) · [Note count](https://ipmatway.com/learn/quant-reasoning/money-notes/note-count) · [Min notes](https://ipmatway.com/learn/quant-reasoning/money-notes/min-notes) · [Ways to pay](https://ipmatway.com/learn/quant-reasoning/money-notes/ways-to-pay) · [Unreachable amount](https://ipmatway.com/learn/quant-reasoning/money-notes/unreachable-amount)

## Integer bounds (Quant-flavoured reasoning (money, bounds, shifts, counting), LR / DI)
Source: https://ipmatway.com/learn/quant-reasoning/integer-bounds

Idea: Several people's counts are linked by "more than" and "less than" statements; only one whole number survives all of them. Rohtak 2020 asked the night-shift version.
Exam method: Find the tightest lower bound and the tightest upper bound first; check the survivors against the other statements.
Traps: Strict bounds: the ends are not allowed. Wrong comparison: check who is compared with whom.

Lessons: [Integer bounds: start here](https://ipmatway.com/learn/quant-reasoning/integer-bounds/start-here) · [Bounded integer](https://ipmatway.com/learn/quant-reasoning/integer-bounds/bounded-integer)

## Table calculation set (DI: Tables, LR / DI)
Source: https://ipmatway.com/learn/di-tables/calculation-di

Idea: A DI table gives numbers by row and column; JIPMAT asks two to five one-step questions on it: a percentage change, a ratio, an average, a share of a total, a value built from two columns (percent of a number, runs per wicket), the highest or second highest, or the next value of a pattern. JIPMAT 2022 (company expenditure), 2023 (toll plaza), 2024 (family expenditure), 2025 (faculty by department) and 2026 (steel, bowler, businessmen) all set such tables.
Exam method: 1. Unit first. "in 100s" or "in ₹10,000" is applied once to the final answer. 2. Use printed totals. when they exist (family expenditure: 1050 of 10500 = 10% in one step). 3. Estimate before computing. for the largest percent change compare rise/base quickly; compute exactly only the close ones. 4. Approximate options. 190.4 / 1848 = 0.103; options 0.094, 0.043, 0.101, 0.085: pick 0.101 without more digits.
Traps: Wrong base: a rise of 150 from 150 to 300 is 100%, not 50%. Reversal: "2000 as a percentage of 2003" is 81.70%; 122.39% answers the reverse question. Units: a table "in 100s" gives 2440, not 24.4. Profit percent is on expenditure (cost) unless the paper's options show otherwise.

Lessons: [Table calculation set: start here](https://ipmatway.com/learn/di-tables/calculation-di/start-here) · [Percent change](https://ipmatway.com/learn/di-tables/calculation-di/percent-change) · [Ratio](https://ipmatway.com/learn/di-tables/calculation-di/ratio) · [Average](https://ipmatway.com/learn/di-tables/calculation-di/average) · [Share of total](https://ipmatway.com/learn/di-tables/calculation-di/share-of-total) · [Derived quantity](https://ipmatway.com/learn/di-tables/calculation-di/derived-quantity) · [Trend scan](https://ipmatway.com/learn/di-tables/calculation-di/trend-scan) · [Max min](https://ipmatway.com/learn/di-tables/calculation-di/max-min) · [Difference](https://ipmatway.com/learn/di-tables/calculation-di/difference)

## Table with missing values (DI: Tables, LR / DI)
Source: https://ipmatway.com/learn/di-tables/missing-data

Idea: A partial table gives a few cells and some sentence conditions (a percentage, a fraction of a group, an average). Every blank can be filled by row and column sums. JIPMAT 2022 Q4-7 gave a 3 x 4 grid of sex by grade with only three cells and three conditions; all four questions read off the completed grid.
Exam method: 1. Grand total first. girls = 40 and 50% are girls, so the total is 80. 2. Group fractions. 1/4 of the 40 boys have C = 10. 3. Chain. A or B = 40, so C total = 40, girls C = 30; boys B = 40 - 5 - 10 = 25; girls B = 30 - 25 = 5. 4. Read all the answers off the finished grid.
Traps: "Half the students have grade A and B" means A + B together = half; it does not mean each grade has half. A fraction is of the group named (boys), not of the whole class. Fill totals before inner cells; filling inner cells first leads to guesses.

Lessons: [Table with missing values: start here](https://ipmatway.com/learn/di-tables/missing-data/start-here) · [Complete the table](https://ipmatway.com/learn/di-tables/missing-data/complete-the-table) · [Back calculation](https://ipmatway.com/learn/di-tables/missing-data/back-calculation)

## Simple / grouped bar (DI: Bar Graphs, LR / DI)
Source: https://ipmatway.com/learn/di-bar/simple-bar

Idea: A simple or grouped bar chart shows one or several series side by side for each category (months, schools, cities). Questions read one or two bars and do one operation: ratio, average, difference, percent change, share. JIPMAT PYQ bar sets of this kind exist: students appeared vs qualified by city (2025), gross traffic receipts vs expenditure 2015-2019 (2024) and percent growth in GDP by region (2024); they are banked as PYQs in this chapter.
Exam method: 1. Derive once. if one series is a percentage of another, write the counts for every category before the questions. 2. Totals, not averages. compare sums when the divisor is the same. 3. Cancel early. reduce ratios (480 : 590 = 48 : 59) before multiplying. 4. Back-solve given ratios. "December : April = 6 : 11" with December = 1800 gives April = 3300 in one step.
Traps: Wrong base in percent questions (28% vs 21.39% in the subscriber set). Direction word: 16.67% less, not more. Mixed units in one chart: a bar counting people next to bars of percentages.

Lessons: [Simple / grouped bar: start here](https://ipmatway.com/learn/di-bar/simple-bar/start-here) · [Ratio](https://ipmatway.com/learn/di-bar/simple-bar/ratio) · [Average](https://ipmatway.com/learn/di-bar/simple-bar/average) · [Difference](https://ipmatway.com/learn/di-bar/simple-bar/difference) · [Share of total](https://ipmatway.com/learn/di-bar/simple-bar/share-of-total) · [Percent change](https://ipmatway.com/learn/di-bar/simple-bar/percent-change) · [Growth rate](https://ipmatway.com/learn/di-bar/simple-bar/growth-rate) · [Max min](https://ipmatway.com/learn/di-bar/simple-bar/max-min)

## Stacked bar (DI: Bar Graphs, LR / DI)
Source: https://ipmatway.com/learn/di-bar/stacked-bar

Idea: A stacked bar splits each bar into parts (sugar, milk, other ingredients). In a 100% stacked bar each segment is a percentage of that bar's total; questions give the total (production cost) and ask for amounts, ratios or comparisons of segments.
Exam method: 1. Combine segments before multiplying. 32% + 10% of 1200 = 42% of 1200 = 504. 2. Equal totals. compare percentages directly (average sugar share 35.4%). 3. Unequal totals. amounts only (37% of 230 vs 50% of 410).
Traps: Different totals: a bigger percentage of a smaller total can be the smaller amount; always convert. Wrong segment read from a similar colour. Average direction: "average more than the company's value" counts companies below the average.

Lessons: [Stacked bar: start here](https://ipmatway.com/learn/di-bar/stacked-bar/start-here) · [Segment ratio](https://ipmatway.com/learn/di-bar/stacked-bar/segment-ratio) · [Component share](https://ipmatway.com/learn/di-bar/stacked-bar/component-share) · [Total average](https://ipmatway.com/learn/di-bar/stacked-bar/total-average) · [Segment compare](https://ipmatway.com/learn/di-bar/stacked-bar/segment-compare)

## Line graph trend (DI: Line Graphs, LR / DI)
Source: https://ipmatway.com/learn/di-line/trend-line

Idea: A line graph joins values of one or more series over time or over categories. Questions read points, gaps between lines and changes from one point to the next. No JIPMAT PYQ so far is a line graph (its DI sets are tables, bars and pies), so the sets here come from the PW pack at JIPMAT level. Several mix a line with bars, a table or ratios given under the chart.
Exam method: 1. One row per line. write the values once; most questions reuse them. 2. Derived row. profit = income - expenditure, girls = students - boys; build it before the questions. 3. Growth-rate questions. shortlist the visibly rising segments and compare rise/start for those only. 4. Percent lines. turn them into counts with the given total, then answer as a table.
Traps: Growth rate vs rise: divide by the starting value. Percent line: the other group is 100 minus the line. Left and right axes: read each line on its own scale.

Lessons: [Line graph trend: start here](https://ipmatway.com/learn/di-line/trend-line/start-here) · [Ratio](https://ipmatway.com/learn/di-line/trend-line/ratio) · [Average](https://ipmatway.com/learn/di-line/trend-line/average) · [Share of total](https://ipmatway.com/learn/di-line/trend-line/share-of-total) · [Difference](https://ipmatway.com/learn/di-line/trend-line/difference) · [Gap between lines](https://ipmatway.com/learn/di-line/trend-line/gap-between-lines) · [Percent change](https://ipmatway.com/learn/di-line/trend-line/percent-change) · [Growth rate](https://ipmatway.com/learn/di-line/trend-line/growth-rate)

## Single pie (percent/degree) (DI: Pie Charts, LR / DI)
Source: https://ipmatway.com/learn/di-pie/single-pie

Idea: A pie chart splits one total into sectors, given in percent or in degrees (360 degrees = 100%). Every question reads one or two sectors and turns them into an amount, a ratio, a difference or a change. JIPMAT asks a pie set almost every year: cost of production (2021), balls by colour and students by activity (2022), brand sales (2023), book production expenses (2024) and a family budget in degrees (2025). All of them are banked as PYQs in this chapter.
Exam method: 1. One conversion. 1% = total/100, or 1 degree = total/360. Write it at the top. 2. Stay in shares. for ratios, "what percent of" and "how many times": the total cancels. 3. Anchor on a given sector. when the total is missing. 4. Changes on several sectors. add the changes in share points (A +50% of 45 = +22.5; E +10% of 22 = +2.2; total +24.7%).
Traps: Points vs percent: a 45-degree gap is 12.5 percentage points, whatever the sizes of the two sectors. Degrees as percent: convert with 3.6 before you compare with a percentage option. Base of a change: "B is what percent more than A" divides by A's share.

Lessons: [Single pie (percent/degree): start here](https://ipmatway.com/learn/di-pie/single-pie/start-here) · [Amount from share](https://ipmatway.com/learn/di-pie/single-pie/amount-from-share) · [Degree to percent](https://ipmatway.com/learn/di-pie/single-pie/degree-to-percent) · [Share of total](https://ipmatway.com/learn/di-pie/single-pie/share-of-total) · [Ratio](https://ipmatway.com/learn/di-pie/single-pie/ratio) · [Difference](https://ipmatway.com/learn/di-pie/single-pie/difference) · [Percent change](https://ipmatway.com/learn/di-pie/single-pie/percent-change) · [Max min](https://ipmatway.com/learn/di-pie/single-pie/max-min)

## Two pies / pie + table (DI: Pie Charts, LR / DI)
Source: https://ipmatway.com/learn/di-pie/double-pie

Idea: Two pies, side by side or one inside the other, show two totals (two years, all students and female students, appeared and qualified, all sales and chocolate sales). Questions compare a sector across the pies, so each share has to be turned into an amount with its own total first. No JIPMAT PYQ so far uses two pies; the sets here come from the PW pack and are JIPMAT-level practice.
Exam method: 1. Table first. one row per sector you need, one column per pie, values as amounts. 2. Same total, skip the multiplication. if both pies split the same number, compare the shares directly. 3. Share of a share. chocolates are 24% of daily-need sales and one brand 15% of chocolates, so that brand = 0.24 x 0.15 = 3.6% of all sales. 4. Changes. new amount = old share x old total x (1 + rate); never apply the rate to the share alone.
Traps: Shares across pies are not comparable until multiplied by their totals. Sub-pie base: a share inside a sub-pie is a share of that sector, not of the grand total. Largest share is not largest amount when the totals differ.

Lessons: [Two pies / pie + table: start here](https://ipmatway.com/learn/di-pie/double-pie/start-here) · [Cross pie ratio](https://ipmatway.com/learn/di-pie/double-pie/cross-pie-ratio) · [Amount from share](https://ipmatway.com/learn/di-pie/double-pie/amount-from-share) · [Ratio](https://ipmatway.com/learn/di-pie/double-pie/ratio) · [Change between pies](https://ipmatway.com/learn/di-pie/double-pie/change-between-pies)

## Combination charts (DI: Mixed / Combination, LR / DI)
Source: https://ipmatway.com/learn/di-mixed/combo

Idea: A mixed (combo) DI set gives two linked displays: a pie with a bar, a bar with a ratio table, a pie with a line. One display gives shares or totals, the other splits them further. The key step is the cross-reference: carry a number from one display into the other.
Exam method: 1. Fix the base once. the clue that is a single number (prose gap 27, revenue 15180, total 90000) usually fixes every count. 2. Build one row per category. only for the categories asked. 3. Let totals cancel. in ratio questions.
Traps: Wrong base: a % in the table is of the city, not of the state. False 'cannot be determined': BIPS boys : St. Xavior girls = 85 : 64 even with the total unknown. Revenue vs count: divide a revenue ratio by the unit tolls before counting vehicles.

Lessons: [Combination charts: start here](https://ipmatway.com/learn/di-mixed/combo/start-here) · [Cross reference](https://ipmatway.com/learn/di-mixed/combo/cross-reference) · [Ratio](https://ipmatway.com/learn/di-mixed/combo/ratio) · [Derived amount](https://ipmatway.com/learn/di-mixed/combo/derived-amount) · [Average](https://ipmatway.com/learn/di-mixed/combo/average) · [Percent change](https://ipmatway.com/learn/di-mixed/combo/percent-change) · [Share of total](https://ipmatway.com/learn/di-mixed/combo/share-of-total) · [Max min](https://ipmatway.com/learn/di-mixed/combo/max-min)

## Paragraph data caselet (DI: Caselets, LR / DI)
Source: https://ipmatway.com/learn/di-caselet/text-caselet

Idea: A caselet is a data set written as a paragraph instead of a table. Behind the sentences there is a small grid (companies x products, months x items, campuses x boys/girls). Once you fill that grid, every question is a one-line calculation: a ratio, a percentage change, an average or a difference. The skill being tested is converting the text into the table without slips. The arithmetic itself is easy.
Exam method: 1. Grid first, questions later. Fill the whole grid once. It costs a minute and saves re-reading for every question. 2. Anchor clue. Find the clue with a plain number (for example "128 girls in East, 40% of all girls"). It usually gives a total: 320 girls, 800 students. 3. One unknown. If no anchor exists, let x be the cell that most clues refer to (here, PNBE in May) and write the others as ax + b. Questions that add "if... = 42500" just fix x. 4. Remainders last. The cell that "takes the rest" (Goa's female athletes, Assam's male athletes) is total minus the others. It is also your check. 5. Read the base. For "what percent more/less than" questions, underline the word after "than": that quantity is the base.
Traps: Wrong base: "16% of the female athletes" means 16% of 3500, not of 8400. Reversed ratio: 15 : 13 and 13 : 15 are both in the options; check the order the question asks for. Non-integer warning: if a cell comes out as a fraction, you have misread a clue. Step costs: a second cook, worker or bus is needed past a capacity limit, so the cost jumps. Equal-days condition: "every day has the same demand" forces a monthly total that is a multiple of 30.

Lessons: [Paragraph data caselet: start here](https://ipmatway.com/learn/di-caselet/text-caselet/start-here) · [Tabulate first](https://ipmatway.com/learn/di-caselet/text-caselet/tabulate-first) · [Percent change](https://ipmatway.com/learn/di-caselet/text-caselet/percent-change) · [Average](https://ipmatway.com/learn/di-caselet/text-caselet/average) · [Ratio](https://ipmatway.com/learn/di-caselet/text-caselet/ratio) · [Share](https://ipmatway.com/learn/di-caselet/text-caselet/share) · [Max min](https://ipmatway.com/learn/di-caselet/text-caselet/max-min) · [Difference](https://ipmatway.com/learn/di-caselet/text-caselet/difference) · [Derived amount](https://ipmatway.com/learn/di-caselet/text-caselet/derived-amount)