Free Mensa IQ Number Series Completion Practice Test — Questions and Answers
Question 1: What is the next number? 3, 7, 13, 21, 31, ?
- A. 41
- B. 43 (Correct answer)
- C. 45
- D. 47
Correct answer: B. 43
Differences: 4, 6, 8, 10, 12 — increasing by 2 each time. Next difference = 12, so 31 + 12 = 43.
Question 2: Complete the series: 2, 3, 5, 8, 13, 21, ?
- A. 29
- B. 33
- C. 34 (Correct answer)
- D. 36
Correct answer: C. 34
This is the Fibonacci sequence — each number is the sum of the two preceding ones: 13+21=34.
Question 3: Find the missing number: 1, 8, 27, 64, 125, ?
- A. 196
- B. 210
- C. 216 (Correct answer)
- D. 225
Correct answer: C. 216
These are perfect cubes: 1³, 2³, 3³, 4³, 5³. The next is 6³ = 216.
Question 4: What comes next? 100, 91, 83, 76, 70, ?
- A. 65 (Correct answer)
- B. 64
- C. 63
- D. 66
Correct answer: A. 65
Differences: -9, -8, -7, -6, -5. The decreasing differences reduce by 1 each time. Next difference = -5, so 70 - 5 = 65.
Question 5: Find the next number: 5, 10, 20, 40, 80, ?
- A. 120
- B. 140
- C. 160 (Correct answer)
- D. 200
Correct answer: C. 160
Each number is doubled: 5×2=10, 10×2=20, 20×2=40, 40×2=80, 80×2=160. This is a geometric sequence with ratio 2.
Question 6: Complete the sequence: 1, 4, 10, 20, 35, ?
- A. 52
- B. 56 (Correct answer)
- C. 60
- D. 63
Correct answer: B. 56
Differences: 3, 6, 10, 15 — these are triangular numbers. Next difference = 21. So 35 + 21 = 56. These are tetrahedral numbers.
Question 7: What is the missing term? 2, 6, 18, 54, ?, 486
- A. 108
- B. 144
- C. 162 (Correct answer)
- D. 216
Correct answer: C. 162
Each term is multiplied by 3: 2×3=6, 6×3=18, 18×3=54, 54×3=162, 162×3=486. The missing term is 162.
Question 8: Find the next number: 1, 1, 2, 6, 24, ?
- A. 48
- B. 100
- C. 120 (Correct answer)
- D. 144
Correct answer: C. 120
These are factorials: 0!=1, 1!=1, 2!=2, 3!=6, 4!=24, 5!=120.
Question 9: What comes next? 3, 6, 11, 18, 27, ?
- A. 36
- B. 38 (Correct answer)
- C. 40
- D. 38
Correct answer: B. 38
Differences: 3, 5, 7, 9 — odd numbers increasing by 2. Next difference = 11. So 27 + 11 = 38.
Question 10: Complete the series: 256, 128, 64, 32, ?
- A. 8
- B. 16 (Correct answer)
- C. 18
- D. 24
Correct answer: B. 16
Each number is halved: 256÷2=128, 128÷2=64, 64÷2=32, 32÷2=16.
Question 11: Find the missing number: 7, 14, 28, ?, 112, 224
- A. 42
- B. 48
- C. 56 (Correct answer)
- D. 64
Correct answer: C. 56
Each number is doubled: 7×2=14, 14×2=28, 28×2=56, 56×2=112, 112×2=224. The missing number is 56.
Question 12: What is the next term? 2, 5, 10, 17, 26, ?
- A. 35
- B. 37 (Correct answer)
- C. 39
- D. 41
Correct answer: B. 37
Pattern: n² + 1. 1²+1=2, 2²+1=5, 3²+1=10, 4²+1=17, 5²+1=26, 6²+1=37.
Question 13: Complete: 1, 3, 7, 15, 31, ?
- A. 55
- B. 57
- C. 60
- D. 63 (Correct answer)
Correct answer: D. 63
Each number = previous×2 + 1: 1×2+1=3, 3×2+1=7, 7×2+1=15, 15×2+1=31, 31×2+1=63.
Question 14: Find the next number: 10, 9, 7, 4, 0, ?
- A. -3
- B. -4
- C. -5 (Correct answer)
- D. -6
Correct answer: C. -5
Differences: -1, -2, -3, -4, -5. Each difference decreases by 1. So 0 + (-5) = -5.
Question 15: What comes next? 1, 2, 4, 7, 11, 16, ?
- A. 20
- B. 21
- C. 22 (Correct answer)
- D. 23
Correct answer: C. 22
Differences: 1, 2, 3, 4, 5, 6. Each difference increases by 1. Next = 16 + 6 = 22.
Question 16: Complete the sequence: 81, 27, 9, 3, ?
- A. 0
- B. 1 (Correct answer)
- C. 2
- D. -1
Correct answer: B. 1
Each term is divided by 3: 81÷3=27, 27÷3=9, 9÷3=3, 3÷3=1.
Question 17: Find the missing number: 3, 9, 27, 81, ?
- A. 162
- B. 210
- C. 243 (Correct answer)
- D. 270
Correct answer: C. 243
Each term is multiplied by 3 (powers of 3): 3¹, 3², 3³, 3⁴, 3⁵=243.
Question 18: What is the next term? 1, 5, 14, 30, 55, ?
- A. 80
- B. 85
- C. 91 (Correct answer)
- D. 95
Correct answer: C. 91
These are square pyramidal numbers: sum of 1², 2², 3²... Differences: 4, 9, 16, 25, 36. Next = 55 + 36 = 91.
Question 19: Complete: 0, 1, 3, 6, 10, 15, ?
- A. 19
- B. 20
- C. 21 (Correct answer)
- D. 22
Correct answer: C. 21
Triangular numbers: differences are 1, 2, 3, 4, 5, 6. Next = 15 + 6 = 21.
Question 20: What comes next? 4, 9, 25, 49, 121, ?
- A. 144
- B. 169 (Correct answer)
- C. 196
- D. 225
Correct answer: B. 169
These are squares of prime numbers: 2²=4, 3²=9, 5²=25, 7²=49, 11²=121, 13²=169.
Question 21: Find the next number: 1, 2, 6, 24, 120, ?
- A. 360
- B. 600
- C. 720 (Correct answer)
- D. 840
Correct answer: C. 720
Factorials: 1!, 2!, 3!, 4!, 5!, 6!=720.
Question 22: Complete the sequence: 5, 8, 13, 21, 34, ?
- A. 50
- B. 55 (Correct answer)
- C. 58
- D. 60
Correct answer: B. 55
Fibonacci-like: each term = sum of two before. 21+34=55.
Question 23: What is missing? 50, 44, 38, 32, ?, 20
- A. 24
- B. 25
- C. 26 (Correct answer)
- D. 27
Correct answer: C. 26
Arithmetic sequence decreasing by 6 each time: 50, 44, 38, 32, 26, 20.
Question 24: Find the next number: 2, 12, 36, 80, 150, ?
- A. 196
- B. 210
- C. 252 (Correct answer)
- D. 286
Correct answer: C. 252
Pattern: n²(n+1). 1²×2=2, 2²×3=12, 3²×4=36, 4²×5=80, 5²×6=150, 6²×7=252.
Question 25: Complete: 17, 15, 12, 8, ?
- A. 2
- B. 3 (Correct answer)
- C. 4
- D. 5
Correct answer: B. 3
Differences: -2, -3, -4, -5. Each difference decreases by 1 more. Next = 8 + (-5) = 3.
Question 26: What comes next? 2, 3, 5, 7, 11, 13, 17, ?
- A. 18
- B. 19 (Correct answer)
- C. 21
- D. 23
Correct answer: B. 19
These are prime numbers: 2, 3, 5, 7, 11, 13, 17, 19 is the next prime.
Question 27: Find the missing term: 1, 6, 15, 28, ?
- A. 40
- B. 42
- C. 44
- D. 45 (Correct answer)
Correct answer: D. 45
Differences: 5, 9, 13 — increasing by 4. Next difference = 17. So 28 + 17 = 45. (Hexagonal numbers: n(2n-1))
Question 28: What is the next number? 4, 8, 14, 22, 32, ?
- A. 40
- B. 42
- C. 44 (Correct answer)
- D. 46
Correct answer: C. 44
Differences: 4, 6, 8, 10, 12. Each increases by 2. Next = 32 + 12 = 44.
Question 29: Complete: 1000, 500, 250, 125, ?
- A. 62
- B. 62.5 (Correct answer)
- C. 63
- D. 75
Correct answer: B. 62.5
Each term is halved: 1000÷2=500, 500÷2=250, 250÷2=125, 125÷2=62.5.
Question 30: Find the next term: 3, 4, 6, 9, 13, 18, ?
- A. 22
- B. 24 (Correct answer)
- C. 26
- D. 28
Correct answer: B. 24
Differences: 1, 2, 3, 4, 5, 6. Increasing by 1. Next = 18 + 6 = 24.
Question 31: What comes next? 729, 243, 81, 27, 9, ?
- A. 1
- B. 2
- C. 3 (Correct answer)
- D. 4
Correct answer: C. 3
Powers of 3 in descending order: 3⁶, 3⁵, 3⁴, 3³, 3², 3¹=3.
Question 32: Complete: 11, 22, 33, 44, 55, ?
- A. 64
- B. 65
- C. 66 (Correct answer)
- D. 67
Correct answer: C. 66
Multiples of 11: 11×6=66.
Question 33: Find the next term: 2, 8, 18, 32, 50, ?
- A. 68
- B. 70
- C. 72 (Correct answer)
- D. 74
Correct answer: C. 72
Pattern: 2n². 2×1²=2, 2×2²=8, 2×3²=18, 2×4²=32, 2×5²=50, 2×6²=72.
Question 34: What is missing? 1, 4, 9, 16, 25, ?, 49
- A. 30
- B. 34
- C. 36 (Correct answer)
- D. 38
Correct answer: C. 36
Perfect squares: 1², 2², 3², 4², 5², 6², 7². The missing term is 6²=36.
Question 35: What comes next? 0, 3, 8, 15, 24, ?
- A. 33
- B. 34
- C. 35 (Correct answer)
- D. 36
Correct answer: C. 35
Pattern: n²-1. 1²-1=0, 2²-1=3, 3²-1=8, 4²-1=15, 5²-1=24, 6²-1=35.
Free Mensa IQ Number Series Completion Practice Test
What is the next number? 3, 7, 13, 21, 31, ?