Start here · the first lesson of Day of the week / odd days
Day of the week / odd days
Clocks and Calendars · for IPMAT Indore, IPMAT Rohtak and JIPMAT
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The 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.
Textbook vs exam method
Textbook method
Odd days up to the date = odd days in complete centuries + complete years + complete months + days of the month; 0 = Sunday, 1 = Monday, …, 6 = Saturday.
Exam method
- 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).
- Same date, later year. add 1 per year, plus 1 for each 29 February crossed.
- Same calendar. both ordinary or both leap, and the odd days in between total a multiple of 7 (2009 → 2015; 2023 → 2034).
- Overlapping clues. intersect the date ranges first, then test the weekday (JIPMAT 2023: Wednesday between the 16th and 19th → 18th).