Right angles in a day — Aptitude Question
Right angles in a day: How many times in 24 hours are the hands of a clock at right angles? Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 90 seconds
Question
How many times in 24 hours are the hands of a clock at right angles?
Options
- 22
- 24
- 44
- 48
Show the answer and the worked solution
Correct answer: C. 44
Worked solution
- In 12 hours the hands form a right angle 22 times.
- Over 24 hours that is 2 × 22 = 44.
Answer: 44.
The idea
The pattern to remember: in 12 hours the hands coincide 11 times, oppose 11 times and form right angles 22 times.
Shortcut. In 24 hours the minute hand gains 24 × 11/12 = 22 full laps on the hour hand, and each lap passes through 90° and 270° once: 2 × 22 = 44.
Common trap. "48" — allowing two right angles every hour; around 3 and 9 o'clock one right angle is shared by two hours, so 2 are lost every 12 hours.