# Reasoning Number series MCQ set-3

Q 1. Find the missing number:- 0.5, 0.55, 0.65, 0.8, ?
A) 0.9
B) 0.82
C) 1
D) 0.95

Solution: The pattern is + 0.05, + 0.10, + 0.15,……………. So, missing term = 0.8 + 0.20 = 1

Q 2. Find the missing term: 9, 27, 31, 155, 161, 1127, ?
A) 316
B) 1135
C) 1288
D) 2254

Solution: The pattern is � 3, + 4, � 5, + 6, � 7, So, missing term = 1127 + 8 =1135

Q 3. Find the missing term: 5, 6, 9, 15, ?, 40
A) 21
B) 25
C) 27
D) 33

Solution: The pattern is + 1, + 3, + 6, …………i.e., + 1, + (1 + 2) + (1 + 2 + 3)…………… So, missing term = 15 + (1 + 2 +3 +4) = 25

Q 4. Find the missing term :- 3, 15, ?, 63, 99, 143
A) 27
B) 35
C) 45
D) 56

Solution: The terms of the given series are (22 – 1), (42 – 1),…………….,(82 – 1), (102 – 1), (122 – 1)So, missing term = (62 – 1) = (36 – 1) = 35

Q 5. Find the missing term: 2, 3, 5, 7, 11, ?, 17
A) 12
B) 13
C) 14
D) 15

Solution: Clearly, the given series consists of prime numbers starting from 2. So, the missing term is the prime number after 11, which is 13.

Q 6. Find the missing term :- 2, 3, 3, 5, 10, 13, ?, 43, 172, 177
A) 23
B) 38
C) 39
D) 40

Solution: The pattern is + 1, � 1, + 2, � 2, + 3, � 3, + 4, � 4, + 5 So, missing term = 13 � 3 = 39

Q 7. Find the missing term: 563, 647, 479, 815, ?
A) 672
B) 386
C) 279
D) 143

Solution: The pattern is + 84, – 168, + 336, …..i.e., + 84, – (84 � 2), + (84 � 22 ),……………..So, missing term = 815 – (84 � 23 ) = 815 – 672 = 143

Q 8. Find the missing term, 4, 9, 25, ?, 121, 169, 289, 361
A) 49
B) 64
C) 81
D) 87

Solution: The given series consists of squares of consecutive prime numbers i.e., 22 , 32 , 52 ,…………………,112 , 132 , 172 , 192 So, missing term = 72 = 49

Q 9. Find the missing term :- 240, ?, 120, 40, 10, 2
A) 180
B) 240
C) 420
D) 480

Solution: The pattern is � 1, � 2, � 3, � 4, � 5 So, missing term = 240 � 1 = 240

Q 10. Find the missing term :- 1, 9, 25, 49, 81, ?
A) 100
B) 112
C) 121
D) 144

Solution: The series consists of squares of consecutive odd numbers i.e., 12 , 32 , 52 , 72 , 92 ,…………..So, missing term = 112 = 121

Q 11. Find the missing term: 5, 2, 7, 9, 16, 25, ?
A) 41
B) 45
C) 48
D) 52

Solution: Each term in the series, except the first two terms, is the sum of the preceding two terms.So, missing term = 16 + 25 = 41

Q 12. Find the missing term: 1, 1, 4, 8, 9, 27, 16, ?
A) 32
B) 64
C) 81
D) 256

Solution: The series consists of squares and cubes of consecutive natural numbers i.e., 12 , 13, 22 , 23 , 32 , 33 , 42 ……………..So, missing term = 43 = 64

Q 13. Find the missing term: 10, 14, 26, 42, 70, ?
A) 100
B) 102
C) 106
D) 114

Solution: Each term in the series, except the first two terms, is 2 more than the sum of the preceding two terms.So, missing term = (42 + 70) +2 = 114

Q 14. Find the missing term: 4, 12, 36, 108, ?
A) 144
B) 216
C) 304
D) 324

Solution: The pattern is � 3 So, missing term = 108 � 3 = 324

Q 15. Find the missing term: 2, 8, 16, 128, ?
A) 2042
B) 2046
C) 2048
D) 2056

Solution: Each term in the series, except the first two terms, is the product of the preceding two terms.So, missing term = 16 � 128 = 2048

Q 16. Find the missing term: 1, 1, 2, 6, 24, ?, 720
A) 100
B) 104
C) 108
D) 120

Solution: The pattern is � 1, � 2, � 3, � 4, ………….So, missing term = 24 � 5 = 120

Q 17. Find the missing term: 3, 10, 101, ?
A) 10101
B) 10201
C) 10202
D) 11012

Solution: Each term in the series is obtained by adding 1 to the square of the preceding term.So, missing term = (101)2 + 1 = 10202

Q 18. Find the missing term: 5824, 5242, ?, 4247, 3823
A) 4467
B) 4718
C) 4856
D) 5164

Solution: Each term in the series is obtained by subtracting from the preceding term the number formed by the first three digits of the preceding term,So, missing term = 5242 – 542 = 4718

Q 19. Find the missing term: 3, 8, 13, 24, 41, ?
A) 70
B) 75
C) 80
D) 85

Solution: The pattern followed is:n the term + (n + 1)th term + (n + 1) = (n + 2)th termThus, 1st term + 2nd term + 2 = 3rd term; 2nd term + 3rd term + 3 = 4th term and so on.So, missing term = 6th term = 4th term + 5th term + 5 = 24 + 41 + 5 = 70

Q 20. Find the missing term: 589654237, 89654237, 8965423, 965423, ?
A) 58965
B) 65423
C) 89654
D) 96542

Solution: The digits are removed one by one from the beginning and the end in order alternately so as to obtain the subsequent terms of the series.

Q 21. Find the missing term: 6, 18, 3, 21, 7, 56, ?
A) 8
B) 9
C) 63
D) 64

Solution: Each term at an even place in the series is the product of its two adjacent terms.Thus, if the missing term be x, then we have :7 � x = 56 or x = 56 � 7 = 8

Q 22. Find the missing term: 1, 3, 4, 8, 15, 27, ?
A) 37
B) 44
C) 50
D) 55

Solution: The sum of any three consecutive terms of the series gives the next term,So, missing number = 8 + 15 + 27 = 50

Q 23. Find the missing term: 20, 20, 19, 16, 17, 13, 14, 11, ?, ?
A) 10, 10
B) 10, 11
C) 13, 14
D) 13, 16

Solution: Let the missing terms of the series be x1 and x2.Thus, the sequence 20, 20, 19, 16, 17, 13, 14, 11. x1, x2 is a combination of two series:I. 20, 19, 17, 14, x1 and II. 20, 16, 13, 11, x2The pattern in I is – 1, – 2, – 3,…………..So, missing term, x1= 14 – 4 = 10The pattern in II is – 4, – 3, – 2,………. So,missing term, x2 = 11 – 1 = 10

Q 24. Find the missing term: 45, 54, 47, ?, 49, 56, 51, 57, 53
A) 48
B) 50
C) 55
D) None of these

Solution: The given sequence is a combination of two series:I. 45, 47, 49, 51, 53 andII. 54, ?, 56, 57Clearly, II. consists of consecutive natural numbers, starting from 54.so, missing term = 55.

Q 25. Find the missing term: 2, 15, 4, 12, 6, 7, ?, ?
A) 8, 8
B) 8, 0
C) 3, 8
D) None of these

Solution: Let the missing terms of the series be x1 and x2.Thus, the sequence 2, 15, 4, 12, 6, 7, x1, x2 is a combination of two series:I. 2, 4, 6, x1 andII. 15, 12, 7, x2I consists of consecutive even numbers. So, missing term, x1= 8The pattern in II is – 3, – 5, ……..So, missing term x2 = 7 – 7 = 0

Q 26. Which term of the series 5,10, 20, 40,……………….is 1280 ?
A) 10th
B) 9th
C) 8th
D) None of these

Answer: Option BQ 27. Find the missing term: 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?
A) 28
B) 30
C) 32
D) 35
Solution: The given sequence is a combination of two series:I. 0, 3, 8, 15, 24, ? andII. 2, 5, 10, 17, 26The pattern in each one of I and II is + 3, + 5, + 7, + 9,…………..So, missing term = 24 + 11 = 35

Q 28. Find the missing term: 3, 10. 29, 66, 127, ?
A) 164
B) 187
C) 216
D) 218

Solution: The given series is a triangular pattern series.So, we have
3 10 29 66 127 ?
7 19 37 61
12 18 24
6 6 So, missing term = 127 + (61 + 24 + 6)= 127 + 91= 218

Q 29. Find the missing term: 13, 35, 57, 79, 911, ?
A) 1110
B) 1112
C) 1113
D) 1315

Solution: The term of the given series are numbers formed by joining together consecutive odd numbers in order i.e., 1 and 3, 3 and 5, 5 and 7, 7 and 9, 9 and 11……………….So, missing term = number formed by joining 11 and 13 = 1113

Q 30. 2/3 , 4/7 , ? , 11/21 , 16/31
A) 5/9 B) 6/11 C) 7/13 D) 9/17

Solution: The sequence in the numerators is + 2, + 3, + 4, + 5 and that in the denominators is + 4, + 6, + 8, + 10So, the numerator of the missing fraction should be (4 + 3)i.e., 7 and the denominator should be (7 + 6)i.e., 13. Thus, the missing term is 7/13 .

Q 31. Find the missing term: 2, 12, 36, 80, 150, ?
A) 194
B) 210
C) 252
D) 258

Solution: The given series is a triangular pattern series.So, we have
2 12 36 80�150�?
10 24 44 70
14 20 26
6 6 So, missing term = 150 + (70 + 26 + 6)= 150 + 102= 252

Q 32. Find the missing term: 625, 5, 125, 25, 25, ?, 5
A) 5
B) 25
C) 125
D) 625

Solution: The given sequence is a combination of two series:I. 625, 125, 25, 5 andII. 5, 25, ?The pattern is � 5, while that in II is � 5.So, missing term = 25 � 5 = 125

Q 33. Find the missing term: 2, 9, 28, ?, 126, 126, 217, 344
A) 50
B) 65
C) 70
D) 82

Solution: The given series is a triangular pattern series.So, we have
Series I :�2�9�28�?�126�217�344
Series II :�7�19�?�?�91�127
Series III :�12�?�?�?�36
Clearly, to form a pattern, the missing terms in Series III must be 18, 24, 30So, missing term = 127 + (61 + 24 + 6)= 127 + 91= 218

Q 34. Find the missing term: 11, 10, ?, 100, 1001, 1000, 10001
A) 101
B) 110
C) 111
D) None of these

Solution: The pattern is – 1, � 10 + 1, – 1, � 10 + 1, – 1, � 10 +1, ….So, the missing term = 10 � 10 + 1 = 101

Q 35. Which of the following will not be a number of the series 1, 8, 27, 64, 125, ….?
A) 256
B) 512
C) 729
D) 1000

Solution: The given series consists of cubes of natural numbers only. 256 is not the cube of any natural number.

Q 36. Find the missing term: 3, 4, 7, 7, 13, 13, 21, 22, 31, 34, ?
A) 42
B) 43
C) 51
D) 52

Solution: The given sequence is a combination of two series:I. 3, 7, 13, 21, 31, ? andII. 4, 7, 13, 22, 34The pattern in I is + 4, + 6, + 8, + 10,……The pattern in II is + 3, + 6, + 9, + 12,…………..So, missing term = 31 + 12 = 43

Q 37. Find the missing term : 90, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3
A) 150
B) 175
C) 225
D) 250

Solution: Clearly, 90 = 30 � 3, 180 = 6 � 30, 12 = 2 � 6, 50 = 25 � 2, 100 = 4 � 25, 200 = 50 � 4 So, missing term = 3 � 50 = 150

Q 38. In the series 10, 17, 24, 31, 38,…… which of the following will be a number of the series ?
A) 48
B) 346
C) 574
D) 1003

Solution: The given series consists of numbers each of which, on dividing by 7, leaves a remainder 3, No other number except 346 satisfies the property.

Q 39. Find the missing term: 13, 32, 24, 43, 35, ?, 46, 65, 57, 76
A) 45
B) 52
C) 54
D) 55

Solution: The given sequence is a combination of two series:I. 13, 24, 35, 46, 57 andII. 32, 43, ?, 65, 76The pattern in both I and II is + 11So, missing term = 43 + 11 = 54

Q 40. Find the missing term: 4/9, 9/20, ? , 39/86
A) 17/40 B) 19/42 C) 20/45 D) 29/53

Solution: The sequence in the numerators is + 5, + 10, + 20, ……and that in the denominators is + 11, + 22, + 44,…………So, the numerator of the missing fraction should be (9 + 10)i.e., 19 and the denominator should be (20 + 22)i.e., 42. Thus, the missing term is 19/42 .

Q 41. Find the missing term: 0, 4, 6, 3, 7, 9, 6, ?, 12
A) 8
B) 10
C) 11
D) 14

Solution: The given sequence is a combination of three series:I. 0, 3, 6 II. 4, 7, ? III. 6, 9, 12The pattern in each of these series is + 3So, missing term = 7 + 3 = 10

Q 42. In the series 3, 9, 15,………….what will be the 21st term?
A) 117
B) 121
C) 123
D) 129

Answer: Option CQ 44. In the series 2, 6, 18, 54, …., what will be the 8th term ?
A) 4370
B) 4374
C) 7443
D) 7434
[show_answer]Answer: Option BQ 45. Find the missing term: 2, 1, 2, 4, 4, 5, 6, 7, 8, 8, 10, 11, ?
A) 9
B) 10
C) 11
D) 12
Solution: The given sequence is a combination of three series:I. 1st, 4th, 7th, 10th, 13th terms i.e., 2, 4, 6, 8, ?II. 2nd, 5th, 8th, 11th terms i.e., 1, 4, 7, 10III. 3rd, 6th, 9th, 12th terms i.e., 2, 5, 8, 11Clearly, I. consists of consecutive even numbers. So, the missing term is 10.

Q 46. Find the missing number: 111/9, 121/2, 142/7, 162/3, ?
A) 81/3
B) 191/2
C) 20
D) 221/3

Solution: The given sequence is 100/9 , 25/2 , 100/7 , 50/3, …………i.e., 100/9, 100/7, 100/6……………..So, missing term = 100/5 = 20

Q 47. Find the missing term: 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12
A) 5
B) 7
C) 8
D) 11

Solution: The given sequence is a combination of three series:I. 1st, 4th, 7th, 10th, terms i.e., 8, 7, 6, ?II. 2nd, 5th, 8th, 11th terms i.e.,9, 10, 11, 12III. 3rd, 6th, 9th, terms i.e., 8, 9, 10The pattern in I. is – 1 So, the missing term is = 6 – 1 = 5

Q 48. Which term of the series 5, 8, 11, 14, ….is 320 ?
A) 104th
B) 105th
C) 106th
D) 64th

Solution: Clearly, 5 + 3 = 8, 8 + 3 = 11, 11 + 3 = 14,…………….So, the series in an A.P. in which a = 5 and d = 3Let 320 be the nth term of the series.Then, 320 = 5 + (n – 1) � 3 or (n – 1) = 105 or n = 106

Q 49. Find the missing term: 1, 9, 25, 49, ?, 121
A) 64
B) 81
C) 91
D) 100

Solution: The given series consists of squares of consecutive odd numbers i.e., 12 , 32 , 52 , 72,………. So. missing term = 92 = 81

Q 50. Find the missing term: 4, 6, 9, 131/2, ?
A) 171/2 B) 19
C) 201/4 D) 223/4

Solution: The pattern is � 3/2.So, missing number = 131/2 � 3/2 = 27/2 � 3/2 = 81/4 = 201/4.

Q 51. Find out the wrong term: 0, 2, 3, 5, 8, 10, 15, 18, 24, 26, 35
A) 18
B) 24
C) 26
D) 10

Solution: The given sequence is a combination of two series:I. 0, 3, 8, 15, 24, 35 and II. 2, 5, 10, 18, 26The pattern in both I and II is + 3, + 5, + 7, + 9, ………So, in II. 18 is wrong and must be replaced by (10 + 7) i.e., 17.

Q 52. Find out the wrong term: 196, 169, 144, 121, 101
A) 101
B) 121
C) 169
D) 196

Solution: The sequence is (14)2 , (13)2 , (12)2 , (11)2 , (10)2 ……….So, 101 is wrong and must be replaced by (10)2 i.e., 100

Q 53. Find out the wrong term: 2, 5, 10, 50, 500, 5000
A) 5
B) 10
C) 50
D) 5000

Solution: Each term of the series is the product of the preceding two terms.So, 5000 is wrong and must be replaced by (50 � 500) = i.e., 25000

Q 54. Find out the wrong term: 5, 27, 61, 122, 213, 340, 509
A) 27
B) 61
C) 122
D) 509

Solution: We have :I: 5 27 61 122 213 340�509II:�22 34 61 91�127�169III:�12�27�30�36�42IV:�15 3 6�&nbsp
;�6 Clearly, the given series becomes a triangular pattern series if each term in IV: is 6.
Again, in II: 34 must be replaced by (61 – 24) i.e., 37 and 22 by (37 – 18) i.e., 19.
Thus, in the given series, 27 is wrong and must be replaced by (5 + 19) i.e., 24.

Q 55. Find out the wrong term:3, 10, 27, 4, 16, 64, 5, 25. 125
A) 3
B) 4
C) 10
D) 27

Solution: The correct sequence is 3, 32 , 33,4, 42 , 43,5, 52 , 53So. 10 is wrong and must replaced by 32 i.e., 9

Q 56. Find out the wrong term: 46080, 3840, 384, 48, 24, 2, 1
A) 384
B) 48
C) 24
D) 2

Solution: The correct pattern is � 12, � 10, � 8, � 6,………So, 24 is wrong and must be replaced by (48 � 6) i.e., 8.

Q 57. Find out the wrong term: 25, 36, 49, 81, 121, 169, 225
A) 36
B) 49
C) 169
D) 225

Solution: The correct sequence is 52 , 72 , 92 , 112 , 132 , 152.So, 36 is wrong.

Q 58. Find out the wrong term: 5, 10, 40, 80, 320, 550, 2560
A) 80
B) 320
C) 550
D) 2560

Solution: The correct pattern is + 4, � 2, + 4, � 2,………..So, 132 is wrong and must be replaced by (68 � 2) i.e., 136

Q 59. Find out the wrong term: 2, 5, 10, 17, 26, 37, 50, 64
A) 17
B) 26
C) 37
D) 64

Solution: The term of the series are (12 + 1)(22 + 1)(32 + 1)(42 + 1)(52 + 1)(62 + 1)(72 + 1),…………..So, 64 is wrong and must be replaced by (82 + 1) i.e., 65

Q 60. Find out the wrong term: 3, 7, 15, 39, 63, 127, 255, 511
A) 15
B) 39
C) 63
D) 127

Solution: The correct pattern is � 2 + 1.So, 39 is wrong and must be replaced by (15 � 2 + 1) i.e., 31.

Q 61. Find out the wrong term: 5, 27, 61, 122, 213, 340, 509
A) 27
B) 61
C) 122
D) 509

Solution: The terms of the series are (23 – 3), (33 – 3), (43 – 3), (53 – 3), (63 – 3), (73 -3), (83 -3). So, 27 is wrong and must be replaced (33 – 3) i.e., 24

Q 62. Find out the wrong term: 6, 15, 35, 77, 165, 221
A) 35
B) 77
C) 165
D) 221

Solution: The terms of the series are product of two consecutive prime numbers i.e., (2 � 3), (3 � 5), (5 � 7), (7 � 11),………..So, 165 is wrong and must be replaced by (11 � 13) i.e., 143.

Q 63. Find out the wrong term: 121, 143, 165, 186, 209
A) 143
B) 165
C) 186
D) 209

Solution: Each term in the series is obtained by adding 22 to the preceding term.So, 186 is wrong and must be replaced by (165 + 22) i.e., 187.

Q 64. Find out the wrong term: 24576, 6144, 1536, 386, 96, 24

A) 96
B) 386
C) 1536
D) 6144

Solution: Each term of the series is obtained by dividing the preceding term by 4.
So, 1536 is wrong and must be replaced by (1536 � 4) i.e., 384.

Q 65. Find out the wrong term: 16, 22, 30, 45, 52, 66

A) 30
B) 45
C) 52
D) 66

Solution: The correct pattern is + 6, + 8, + 10, + 12, + 14.
So, 45 is wrong and must be replaced by (30 + 10) i.e., 40.

Q 66. Find out the wrong term: 8, 14, 26, 48, 98, 194, 386

A) 14
B) 48
C) 98
D) 194

Solution: The correct pattern is � 2, – 2…….So, 48 is wrong and must be replaced by (26 � 2 – 2) i.e., 50.

Q 67. Find out the wrong term: 8, 13, 21, 32, 47, 63, 83
A) 13
B) 21
C) 32
D) 47

Solution: The correct pattern is + 5, + 8, + 11, + 14, …………So, 47 is wrong and must be replaced by (32 + 14) i.e., 46

Q 68. Find out the wrong term: 10, 26, 74, 218, 654, 1946, 5834
A) 26
B) 74
C) 218
D) 654

Solution: The correct pattern is � 3, – 4,…………
So, 654 is wrong and must be replaced by (218 � 3 – 4) i.e., 650.

Q 69. Find out the wrong term: 4, 10, 22, 46, 96, 190, 382

A) 4
B) 10
C) 96
D) 382

Solution: The correct pattern is + 6, + 12, + 24, + 48, + 96, + 192 …………
So, 96 is wrong and must be replaced by (46 + 48) i.e., 94

Q 70. Find out the wrong term: 1, 3, 10, 21, 64, 129, 356, 777

A) 21
B) 129
C) 10
D) 356