Mensa IQ Test Mensa IQ Clocks and Calendars

Question 1

What is the angle between the hour and minute hands of a clock at 3:30?

Accepted Answer

75°

Answer

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?

Accepted Answer

100°

Answer

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?

Accepted Answer

Monday

Answer

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?

Accepted Answer

11

Answer

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?

Accepted Answer

Friday

Answer

100 days after Wednesday: 100 ÷ 7 = 14 weeks remainder 2. Wednesday + 2 days = Friday. (The 100th school day falls on a Friday.)

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Mensa IQ Test Mensa IQ Clocks and Calendars