Patwari Exam · Reasoning
Mathematical Reasoning & Puzzles
This note explains transitive relations, clock angle, and calendar questions in mathematical reasoning.
- Reasoning & Numerical Ability
- 5 min read
Verified 6 October 2026
Key Formulas & Methods
- Transitive relation
- If A>B>C and C>D then A>D — this is a transitive relation.
- Matrix questions
- Matrix questions: find the rule in a 3×3 grid and fill in the blank.
- Clock hand speed
- Clock-related: the minute hand moves 36° in 6 minutes = 6°/minute; the hour hand moves 0.5°/minute.
- Clock hands meeting
- The hands meet at 12 o'clock, then every 65.45 minutes after that.
- Calendar basics
- Calendar: a normal year has 365 days = 52 weeks + 1 day; a leap year = 52 weeks + 2 days.
- Leap year rule
- Leap year: a multiple of 4, not of 100 (unless also a multiple of 400).
- Clock angle formula
- Exam tip: the angle on a clock = |30H – 5.5M| where H = hour, M = minutes.
Frequently Asked Questions
What is a transitive relation?+
If A>B>C and C>D, then it is certain that A>D will also hold — this is called a transitive relation.
What is the formula for finding the angle between clock hands?+
The clock angle is found using the formula |30H – 5.5M|, where H is the hour and M is the minutes; the minute hand moves at 6°/minute and the hour hand at 0.5°/minute.
How do you identify a leap year?+
A year that is a multiple of 4 but not of 100 (unless also a multiple of 400) is a leap year; a normal year has 365 days (52 weeks + 1 day) while a leap year has 52 weeks + 2 days.