Mensa IQ Test Mensa IQ Numerical Reasoning and Arithmetic 3 — Questions and Answers
Question 1: What is the missing number? 7, 14, 28, 56, [?], 224
- 112 (Correct answer)
- 96
- 108
- 120
Correct answer: 112
Each term doubles; 56 × 2 = 112.
Question 2: In a 3×3 magic square, each row, column, and diagonal sums to the same magic constant. Given top row: 2, 7, 6; middle row: 9, 5, 1; what is the sum of the bottom row?
- 15 (Correct answer)
- 12
- 18
- 14
Correct answer: 15
The magic constant for this square is 15 (each row, column, diagonal); bottom row = 4, 3, 8 sums to 15.
Question 3: A sequence: 4, 9, 16, 25, 36, [?]
- 49 (Correct answer)
- 48
- 50
- 45
Correct answer: 49
These are perfect squares of consecutive integers starting at 2: 2², 3², 4², 5², 6², 7² = 49.
Question 4: A factory produces 240 units in 8 hours with 6 workers. How many units do 9 workers produce in 10 hours at the same rate?
- 450 (Correct answer)
- 360
- 480
- 400
Correct answer: 450
Rate = 240/(8×6) = 5 units per worker per hour; 9 workers × 10 hours × 5 = 450.
Question 5: What value replaces [?] in the sequence: 1, 3, 7, 15, 31, [?]?
- 63 (Correct answer)
- 57
- 61
- 67
Correct answer: 63
Each term = 2 × previous + 1; or equivalently each term = 2ⁿ − 1: 1, 3, 7, 15, 31, 63.
Question 6: Three numbers are in ratio 2:3:5. Their sum is 150. What is the largest of the three numbers?
- 75 (Correct answer)
- 45
- 30
- 90
Correct answer: 75
Total parts = 2+3+5 = 10; each part = 150/10 = 15; largest (5 parts) = 5×15 = 75.
Question 7: A number sequence alternates between adding and multiplying: 1, +3→4, ×2→8, +3→11, ×2→22, +3→[?]
- 25 (Correct answer)
- 44
- 24
- 26
Correct answer: 25
The rule alternates: add 3, multiply by 2. After 22+3 = 25.
Mensa IQ Test Mensa IQ Numerical Reasoning and Arithmetic 3
What is the missing number? 7, 14, 28, 56, [?], 224