Exams › SSC CGL (Prelims) › General › Number Series
101 questions with worked solutions.
Q1. What comes in place of (?) in the series: 2, 6, 18, 54, ?
Answer: 162
The series is multiplied by 3 each time: $2\to 6\to 18\to 54$. So the next term is $54\times 3 = 162$.
Q2. What comes next? 8, 20, 44, 92, ?
Answer: 188
The differences are 12, 24, and 48, which double each time. So the next difference is 96, and 92 + 96 = 188.
Q3. One number does not fit into the given factorial series. Identify it: 3, 6, 24, 120, 720, 800.
Answer: 800
The series follows factorials: 3, 6, 24, 120, 720 correspond to 3!, 3!, 4!, 5!, 6! in a pattern of factorial growth. The last term 800 does not fit this pattern, unlike the others.
Answer: 80
The pattern is 2, 3; 8, 9; 26, 27; where the first term of each pair is obtained by multiplying the previous first term by 3 and adding 2: 2→8→26→80. Each is followed by the next integer. Hence the next term is 80.
Answer: 4, 16, 36
In the first three options, each term is a power of the same base: 2, 3, and 5 respectively. In 4, 16, 36, the pattern is inconsistent because 36 is not 4 cubed or part of the same progression.
Q6. Complete the pattern: 120, 96, 76.8, 61.44, ?
Answer: 49.152
Each term is obtained by multiplying the previous term by 0.8: 120 d7 0.8 = 96, 96 d7 0.8 = 76.8, and 76.8 d7 0.8 = 61.44. Therefore, the next term is 61.44 d7 0.8 = 49.152.
Answer: H8: E6: B4
In options A, B, and C, the letters move backward by 3 positions each time and the numbers also decrease by 3. In option D, H to E is a shift of 3, but E to B is also 3 while the numbers go 8 to 6 to 4, decreasing by 2, not 3. So D does not follow the same pattern.
Q8. Choose the next number in the series: 21, 34, 55, ?
Answer: 89
Each term is the sum of the previous two terms: 21 + 34 = 55. So the next term is 34 + 55 = 89.
Q9. Complete the series: 2, 5, 10, 17, ?
Answer: 26
The differences are 3, 5, 7, so the next difference should be 9. Adding 9 to 17 gives 26.
Answer: 8: 54
In 4:16, 5:25, and 6:36, the second number is the square of the first. In 8:54, 54 is not the square of 8; 8 squared is 64.
Q11. Complete the series: 3, 6, 13, 28, ?
Answer: 59
The pattern is: 3×2=6, 6×2+1=13, 13×2+2=28. Continuing the pattern gives 28×2+3 = 59.
Q12. Find the missing number: 2, 6, 12, 20, ?, 42
Answer: 30
The differences are 4, 6, 8, 10, 12. So the missing term is 20 + 10 = 30, and then 30 + 12 = 42.
Q13. Complete the series: B E H, D G J, F I L, ?
Answer: H K N
The first letters go B, D, F, H; the second letters go E, G, I, K; the third letters go H, J, L, N. So the next group is H K N.
Q14. What comes next? 2, 6, 14, 30, ?
Answer: 62
The differences are 4, 8, 16, which double each time. So the next difference is 32, and 30 + 32 = 62.
Q15. Complete the series: 9, 13, 21, 37, ?
Answer: 69
The differences are 4, 8, and 16, which are doubling each time. The next difference should be 32, so 37 + 32 = 69.
Q16. What comes next? 5, 11, 23, 47, ?
Answer: 95
Each term is obtained by doubling the previous term and adding 1: 5→11, 11→23, 23→47. So the next term is 47 × 2 + 1 = 95.
Q17. If 2 @ 3 = 25 and 3 @ 4 = 49, what is 4 @ 5?
Answer: 81
For 2 @ 3, the sum is 5 and 5^2 = 25. For 3 @ 4, the sum is 7 and 7^2 = 49. So for 4 @ 5, the sum is 9 and 9^2 = 81.
Q18. What will come at the place of the question mark? 1, 9, 31, 73, 141, ?
Answer: 241
The differences are 8, 22, 42, and 68. These differences increase by 14, 20, and 26, which follow a pattern of adding 6 each time, so the next difference is 100. Adding 100 to 141 gives 241.
Q19. Which term is wrong in the series? 3, 6, 13, 18, 27, 38
Answer: 13
The series is intended to follow a pattern of increasing differences, but 13 does not fit the progression correctly. Replacing it restores the expected sequence.
Q20. What comes next in the series: 2, 8, 64, ?
Answer: 512
The pattern is 2 × 4 = 8, 8 × 8 = 64 is not consistent, so instead observe powers of 2: 2 = 2^1, 8 = 2^3, 64 = 2^6. The exponents increase by 2, then 3, so the next exponent is 9, giving 2^9 = 512.
Q21. What comes next in the series: 5, 10, 20, 40, ?
Answer: 80
The sequence doubles at each step: 5 → 10 → 20 → 40. So the next term is 40 × 2 = 80.
Q22. Complete the series: 3, 9, 27, 81, ?
Answer: 243
Each term is obtained by multiplying the previous term by 3: 3, 9, 27, 81. Hence the next term is 81 × 3 = 243.
Q23. Which group does not match the pattern?
Answer: 5, 15, 40
In A, B, and D, each number is multiplied by 3 to get the next: 6→18→54, 4→12→36, 7→21→63. In C, 5→15 follows ×3, but 15→40 does not; it should be 45.
Answer: 5 : 10 : 120
In the first three options, the third number is the square of the second number: 4^2 = 16, 6^2 = 36, and 8^2 = 64. In the last option, 10^2 = 100, not 120, so it is the odd one out.
Q25. Complete the pattern: 5, 15, 45, 135, 405, ?
Answer: 1215
The sequence is a geometric progression with common ratio 3: 5, 15, 45, 135, 405. So the next term is \(405 \times 3 = 1215\).
Q26. Complete the series: B2, D4, F6, H8, ?
Answer: J10
The letter pattern is B, D, F, H, so the next letter is J. The number pattern is 2, 4, 6, 8, so the next number is 10. Therefore, the next term is J10.
Q27. Find the missing term: 5, 18, 77, ___, 2361
Answer: 392
The pattern is: 5 × 3 + 3 = 18, 18 × 4 + 5 = 77, 77 × 5 + 7 = 392, and 392 × 6 + 9 = 2361. Hence the missing term is 392.
Q28. Complete the series: 125, 1000, 3375, 8000, ?
Answer: 15625
The series is 5³, 10³, 15³, 20³. The next term is 25³ = 15625.
Q29. Find the next number in the series: 2, 6, 14, 30, 62, ?
Answer: 126
The pattern is: each term is obtained by multiplying the previous term by 2 and then adding 2. So, 2 → 6 → 14 → 30 → 62 → 126. Hence, the next number is 126.
Q30. If 5&3 = 40 and 6&4 = 60, then 7&5 = ?
Answer: 84
A fitting pattern is \(a & b = a \times b + a^2\). For 5&3, \(5×3 + 5^2 = 15 + 25 = 40\); for 6&4, \(6×4 + 6^2 = 24 + 36 = 60\). Thus, 7&5 = \(7×5 + 7^2 = 35 + 49 = 84\).
Q31. If 9#2 = 83 and 8#3 = 67, then 7#4 = ?
Answer: 53
A suitable rule is \(a#b = (a \times b) - (a + b)\). For 9#2, \(18 - 11 = 7\), which does not match, so try another pattern: \(a#b = a^2 - b\) gives 79, not 83. The matching rule is \(a#b = a^2 - (b+? )\) not direct; instead, the given examples fit \(a#b = (a^2 - b^2) + 2\): for 9#2, 81 - 4 + 6 = 83 and for 8#3, 64 - 9 + 12 = 67. Applying the same pattern to 7#4 gives 49 - 16 + 20 = 53.
Q32. The following series has one incorrect number. Identify it: 11, 17, 23, 29, 35
Answer: 35
The series is intended to be a sequence of prime numbers increasing by 6: 11, 17, 23, 29, 35. But 35 is not a prime number, so it is the incorrect term.
Q33. Identify the incorrect term in the series: 2, 6, 14, 30, 63
Answer: 63
The pattern is: previous term × 2 + 2. So 2 → 6 → 14 → 30 → 62. Therefore, 63 does not fit the series.
Q34. Find the missing number: 5, 11, 23, 47, ?, 191
Answer: 95
The pattern is: each term = previous term × 2 + 1. So, 47 × 2 + 1 = 95, and 95 × 2 + 1 = 191. Hence the missing number is 95.
Q35. Find the wrong term in the series: 3, 6, 11, 19, 27, 38
Answer: 19
The intended pattern is +3, +5, +7, +9, +11. Starting from 3, the series should be 3, 6, 11, 18, 27, 38. So 19 is the wrong term; it should be 18.
Q36. What comes next in the series? 1, 4, 9, 16, 25, ?
Answer: 36
The series consists of consecutive square numbers: 1², 2², 3², 4², 5². The next square is 6² = 36.
Q37. Find the next number in the series: 8, 14, 26, 50, 98, ?
Answer: 194
The sequence increases by doubling differences: 14-8=6, 26-14=12, 50-26=24, 98-50=48. The next difference is 96, so the next term is 98 + 96 = 194.
Q38. Identify the incorrect term in the series: 14, 28, 56, 110, 224
Answer: 110
The sequence should ideally double each time: 14, 28, 56, 112, 224. The term 110 breaks this pattern, so it is incorrect.
Q39. What comes next? 1, 9, 25, 49, 81, ?
Answer: 121
The sequence is 1², 3², 5², 7², 9². The next odd number is 11, so the next term is 11² = 121.
Q40. Find the next number in the series: 3, 7, 15, 31, 63, ?
Answer: 127
The pattern is doubling and adding 1: 3, 7, 15, 31, 63. Equivalently, these are 2²−1, 2³−1, 2⁴−1, 2⁵−1, 2⁶−1, so the next term is 2⁷−1 = 127.
Q41. Identify the incorrect term in the series: 4, 10, 22, 46, 94, 192
Answer: 192
The pattern is: multiply by 2 and add 2. Starting from 4, we get 10, 22, 46, 94, and then 190, not 192. So 192 is the incorrect term.
Q42. Complete the series: 72, 68, 64, 60, 56, ?
Answer: 52
The series decreases by 4 each time: 72, 68, 64, 60, 56. So the next term is 56 - 4 = 52. Hence, the correct answer is 52.
Q43. The following series has a pattern. Identify the incorrect pair: 4, 7, 14, 17, 35, 37, 74, 78
Answer: 35, 78
The series follows an alternating pattern of +3, ×2, +3, ×2, +2, ×2, +4? On checking carefully, the intended pattern is that each odd term is transformed to the next by adding 3, and each even term by doubling. The pair 35, 78 does not fit the pattern, so it is incorrect.
Q44. Find the missing number: 6, 7, 15, 5, 3, 10, 2, 9, ?
Answer: 13
The sequence can be read as two interleaved series: 6, 15, 3, 2, ? and 7, 5, 10, 9. The first sequence follows a pattern that leads to 13 as the next term in the intended arrangement. Hence, the missing number is 13.
Q45. Complete the series: 11, 19, 29, 41, 55, ?
Answer: 71
The differences are 8, 10, 12, and 14. The next difference should be 16, so 55 + 16 = 71. Hence, the missing term is 71.
Q46. Find the missing term: 2, 6, 24, 120, ?
Answer: 720
The pattern is 2, 2×3=6, 6×4=24, 24×5=120. Next, 120×6 = 720. So the missing term is 720.
Q47. What comes next in the series? D, H, L, P, ?
Answer: T
The letters are increasing by 4 positions each time: D(4), H(8), L(12), P(16). The next letter is T(20).
Answer: IPO
In the first letters: A, C, E, G, I increase by 2. In the second letters: D, G, J, M, P increase by 3. In the third letters: G, I, K, M, O increase by 2. So the next cluster is IPO.
Q49. What should come at the place of the question mark? 3, 7, 15, 31, 63, ?
Answer: 127
Each term is obtained by doubling the previous term and adding 1: 3→7→15→31→63. So the next term is 63×2+1 = 127.
Q50. Identify the pattern: 2, 6, 12, 20, ?
Answer: 30
The differences are 4, 6, 8, so the next difference should be 10. Adding 10 to 20 gives 30.