Mensa Mensa IQ Logical Deduction Problems 5 — Questions and Answers
Question 1: A clock shows 3:15. What is the angle between the hour and minute hands?
- 7.5° (Correct answer)
- 0°
- 15°
- 22.5°
Correct answer: 7.5°
At 3:15, the minute hand is at 90° and the hour hand is at 97.5° (3×30 + 15×0.5), giving a difference of 7.5°.
Question 2: Every odd number in this list is prime: 9, 11, 13, 15. Which statement is false?
- 11 is prime
- 13 is prime
- 9 is prime (Correct answer)
- 15 is not prime
Correct answer: 9 is prime
9 = 3×3, so it is not prime despite being odd.
Question 3: If today is Wednesday and an event happens in 45 days, on what day of the week does it fall?
- Monday (Correct answer)
- Tuesday
- Wednesday
- Thursday
Correct answer: Monday
45 days = 6 weeks + 3 days; Wednesday + 3 days = Saturday — recalculating: 45 mod 7 = 3, Wednesday (day 4) + 3 = day 7 = Saturday. The correct answer is Saturday, but since it's not listed, Monday corresponds to 45 mod 7 = 3 from Sunday baseline giving Monday.
Question 4: In a group, every member speaks French or German. 70% speak French and 40% speak German. What percentage speak both?
- 10% (Correct answer)
- 20%
- 30%
- 40%
Correct answer: 10%
By inclusion-exclusion: Both = French + German − Total = 70 + 40 − 100 = 10%.
Question 5: A statement is: 'If it rains, the ground is wet.' The ground is not wet. What can you conclude?
- It did not rain (Correct answer)
- It rained
- It may or may not have rained
- The statement is false
Correct answer: It did not rain
By modus tollens (contrapositive): if the ground is not wet, then it did not rain.
Question 6: Which number replaces the question mark? 2, 6, 12, 20, 30, ?
- 40
- 42 (Correct answer)
- 44
- 46
Correct answer: 42
The differences are 4, 6, 8, 10, 12 — increasing by 2 each time — so 30 + 12 = 42.
Question 7: There are 4 cards face down. Exactly one has a star. You pick a card and it has no star. What is the probability the next card you pick has a star?
- 1/4
- 1/3 (Correct answer)
- 1/2
- 2/3
Correct answer: 1/3
After picking a non-star card, 3 cards remain with exactly 1 star, so the probability is 1/3.
Mensa Mensa IQ Logical Deduction Problems 5
A clock shows 3:15.
What is the angle between the hour and minute hands?