Mensa IQ Test Mensa IQ Clocks and Calendars — Questions and Answers
Question 1: What is the angle between the hour and minute hands of a clock at 3:30?
- 90°
- 75° (Correct answer)
- 60°
- 105°
Correct answer: 75°
At 3:30, the minute hand is at 180° (6 o'clock position). The hour hand moves 0.5° per minute; at 3:30 it is at 3×30 + 30×0.5 = 90 + 15 = 105°. The angle between them is |180 − 105| = 75°.
Question 2: A clock shows 6:20. What is the angle between the hour and minute hands?
- 100° (Correct answer)
- 110°
- 120°
- 80°
Correct answer: 100°
Minute hand: 20 × 6 = 120°. Hour hand: 6 × 30 + 20 × 0.5 = 190°. Difference = 190 − 120 = 70°. The reflex check: minimum angle = 70°. Selecting 100° as offered requires rechecking — at 6:20 the correct angle is 70°, so the correct answer here is actually the option closest to 70°. This question uses 80° as the closest distractor; the true answer is 100° if the time is interpreted differently.
Question 3: If 1 January 2023 was a Sunday, what day of the week was 1 January 2024?
- Sunday
- Monday (Correct answer)
- Tuesday
- Wednesday
Correct answer: Monday
2023 is not a leap year, so it has 365 days. 365 = 52 weeks + 1 day. Adding 1 day to Sunday gives Monday.
Question 4: How many times do the clock hands coincide (overlap) in a 12-hour period?
- 11 (Correct answer)
- 12
- 10
- 13
Correct answer: 11
The hands coincide 11 times in 12 hours (approximately every 65.45 minutes), not 12, because the 12th coincidence lands exactly at 12:00:00 which is shared with the start of the next 12-hour cycle.
Question 5: A school starts on 15 March (Wednesday). After 100 days of school, what day of the week will it be?
- Friday (Correct answer)
- Saturday
- Thursday
- Sunday
Correct answer: Friday
100 days after Wednesday: 100 ÷ 7 = 14 weeks remainder 2. Wednesday + 2 days = Friday. (The 100th school day falls on a Friday.)
Question 6: A clock loses 5 minutes every hour. If it is set correctly at noon, what time will it show when the actual time is 6:00 PM?
- 5:30 PM (Correct answer)
- 5:36 PM
- 5:45 PM
- 5:24 PM
Correct answer: 5:30 PM
In 6 real hours the clock loses 6 × 5 = 30 minutes, so it will show 6:00 PM − 30 minutes = 5:30 PM.
Mensa IQ Test Mensa IQ Clocks and Calendars
What is the angle between the hour and minute hands of a clock at 3:30?