Start here · the first lesson of 3-set counting / max-min region values
3-set counting / max-min region values
Venn-based Reasoning · for IPMAT Indore, IPMAT Rohtak and JIPMAT
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The 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.
Textbook vs exam method
Textbook method
- Draw the circles; put the all-three number in the middle.
- Turn every "A and B" total into "A and B only" by subtracting the middle.
- Turn every circle total into "only A" by subtracting its overlaps.
- "None" = total − everyone inside the circles. Check that every stated total is reproduced.
Exam method
- Two sets. car 40%, scooter 55%, both 30 families, neither 40 → 0.95N + 10 = N → N = 200.
- 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.
- Region fill. seminar gadgets: laptop & I-pod 25 includes the 10 with all three → 15 only; then only-laptop = 75 − 15.
- Maximum. detergents 328 + 88 + 60 = 476 = 400 + E2 + 2E3 → E3 ≤ 38.