Mensa Mensa IQ Logical Deduction Problems 5

Question 1

A clock shows 3:15. What is the angle between the hour and minute hands?

Accepted Answer

7.5°

Answer

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?

Accepted Answer

9 is prime

Answer

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?

Accepted Answer

Monday

Answer

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?

Accepted Answer

10%

Answer

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?

Accepted Answer

It did not rain

Answer

By modus tollens (contrapositive): if the ground is not wet, then it did not rain.

Mensa Practice Test

Mensa Practice Test

Mensa Mensa IQ Logical Deduction Problems 5