Mensa Numerical Reasoning 5 — Questions and Answers
Question 1: A number leaves a remainder of 3 when divided by 5 and a remainder of 4 when divided by 7. What is the smallest such positive integer?
- 18 (Correct answer)
- 28
- 32
- 53
Correct answer: 18
18 ÷ 5 = 3 remainder 3 ✓ and 18 ÷ 7 = 2 remainder 4 ✓, making 18 the smallest such integer.
Question 2: In a geometric progression, the 3rd term is 18 and the 6th term is 486. What is the common ratio?
- 2
- 3 (Correct answer)
- 4
- 5
Correct answer: 3
The 6th term divided by the 3rd term equals r³ = 486/18 = 27, so r = ∛27 = 3.
Question 3: A shop sells items at a 25% profit on cost. If the cost price rises by 20% but the selling price stays the same, what is the new profit percentage?
- 4.17% (Correct answer)
- 5%
- 6.25%
- 8.33%
Correct answer: 4.17%
With original cost = 100, selling price = 125; new cost = 120; new profit = 5; profit % = 5/120 × 100 ≈ 4.17%.
Question 4: What value of x satisfies the equation 2^(x+3) = 4^(x−1)?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
Rewriting 4^(x−1) as 2^(2x−2) gives x+3 = 2x−2, so x = 5.
Question 5: The ratio of boys to girls in a class is 3:4. If 6 more boys join and 2 girls leave, the ratio becomes 1:1. How many students were in the class originally?
- 42
- 49
- 56 (Correct answer)
- 63
Correct answer: 56
Let boys = 3k and girls = 4k; setting 3k+6 = 4k−2 gives k = 8, so original total = 7k = 56.
Question 6: A clock shows 3:15. What is the angle between the minute and hour hands?
- 0°
- 7.5° (Correct answer)
- 10°
- 15°
Correct answer: 7.5°
The minute hand is at 90°; the hour hand is at 90° + 15×0.5° = 97.5°; the angle between them is 7.5°.
Question 7: The sum of the first n consecutive positive integers equals 210. What is n?
- 18
- 19
- 20 (Correct answer)
- 21
Correct answer: 20
Using n(n+1)/2 = 210 gives n(n+1) = 420, and since 20×21 = 420, n = 20.
Mensa Numerical Reasoning 5
A number leaves a remainder of 3 when divided by 5 and a remainder of 4 when divided by 7.
What is the smallest such positive integer?