Ch.14 :- Number Series :- Exercise 1

✦ Directions for Q. No. 1 to 15 : In each of the following questions, one number is missing in the series. You have to understand the pattern of the series and then insert the missing number.

(1). 4, 7, 11, 18, 29, 47, ….. , 123, 199
(a) 76
(b) 70
(c) 84
(d) 102
(e) 95

Ans.(a)

3rd number is the sum of 1st and 2nd, 4th number is the sum of 2nd and 3rd, 5th number is the sum of 3rd and
4th and so on. Hence, missing number will be 29 + 47 = 76

(2). 2, 6, 12, 20 ,…., 42, 56, 72, 90
(a) 20
(b) 21
(c) 30
(d) 12
(e) 23

Ans.(c)

Series moves with the increasing difference by 2 i.e., 4, 6, 8, 10, 12 Therefore, the missing number will be 30.

(3). 17, 7, 24, 19, 9, 28, ….. , 8, 31, 27, 10, 37
(a) 20
(b) 21
(c) 18
(d) 12
(e) 23

Ans.(e)

Each 3rd number is the sum of preceding two numbers. i.e., 17 + 7 = 24, 19 + 9 = 28,23 + 8 = 31. Hence, the missing number will be 23.

(4). 6, 126, …., 9, 108, 12, 7, 133, 19, 12, 72, 6
(a) 21
(b) 23
(c) 30
(d) 35
(e) 40

Ans.(a)

Number between 1st and 3rd, 4th and 6th, 7th and 9th is the product of the adjacent numbers. Hence, the missing number will be 126/ 6 = 21.

(5).  2…., 8, 16, 32, 64, 128, 256
(a) 2
(b) 3
(c) 5
(d) 4
(e) None of these

Ans.(d)

Each number of the series is the double of the preceding number. Hence,the missing number will be 4.

(6). 45, 54, 47, …., 49, 56, 51, 57, 53
(a) 48
(b) 55
(c) 50
(d) 53
(e) None of these

Ans.(b)

There are two alternate series in the single series, one of them moves with a difference of one number starting with 45, and another. is a consecutive series starting with 54. Hence,the missing number will be 55.

(7). 3, 128,6, 64, 9, …., 12, 16, 15, 8
(a) 32
(b) 12
(c) 108
(d) 72
(e) 64

Ans.(a)

There are two alternate series- one, 3, 6, 9, 12, 15 and the other 8, 16,32,64, 128 (every number is double of
preceding number). Hence,the missing number will be 32.

(8). 5, 7, 11, 19, 35, 67, …., 259
(a) 64
(b) 131
(c) 135
(d) 32
(e) None of these

Ans.(b)

Series moves with a difference of 2, 4, 8, 16, 32, 64.
Hence,the missing number will be 67 + 64 = 131.

(9).  8, 4, 12, 6, 18, …., 27
(a) 10
(b) 12
(c) 18
(d) 24
(e) None of these

Ans.(e)

3rd, 5th and 7th numbers are the sums of preceding two numbers. Hence, the missing number is 9 as 18 + 9 = 27

(10). 16, 22, 34, 58, 106, …..,
(a) 178
(d) 170
(c) 288
(b) 175
(e) 202

Ans.(e)

Series moves with a difference of 6, 12, 24, 48, 96.
Hence,the missing number is 202.

(11). 2, 3, 5, 9, 17, 33, ….
(a) 85
(c) 63
(b) 37
(d) 64
(e) 65

Ans.(e)

Series moves with a difference of 1, 2, 4, 8, 16, 32.
Hence,the missing number is 65.

(12). 2, 9, 23, 3, 8, 25, 4, …., 27
(a) 7
(b) 29
(c) 23
(d) 14
(e) 20

Ans.(a)

There are three alternative series 2, 3, 4 …… (consecutive numbers), 9, 8, 7 …… (consecutive number in descending order), and 23, 25, 27 ……
Hence, 7 will come-in place of the missing number.

(13). 121, 112, …., 97, 91, 86
(a) 102
(b) 108
(c) 99
(d) 104
(e) 101

Ans.(d)

Series is written in descending order with a difference of 9, 8, 7, 6 and 5, respectively. Hence, the missing number will be 104.

(14). 6, 9, 15, 27, …., 99.
(a) 51
(b) 34
(c) 37
(d) 84
(e) None of these

Ans.(a)

Series proceeds with a difference of 3, 6, 12, 24, 48. respectively.Hence,the missing number will be 51.

(15). 4, 7, 12, …. , 28, 39
(a) 19
(b) 24
(c) 14
(d) 16
(e) None of these

Ans.(a)

Series proceeds with a difference of 3, 5, 7, 9, 11. respectively.
Hence,the missing number will be 19.

✦ Directions for Q. No. 16 to 22 : Find the missing number in the following series :

(16). 83, 82, 81, …., 69, 60, 33
(a) 73
(b) 80
(c) 75
(d) 77
(e) None of these

Ans.(d)

Series has been written in reverse order with a
difference of (1)2,(1)2, (2)2, (2)2, (3)2, (3)2 i.e., 1, 1,4, 8,9,27.

(17). 77, 78, 77, 81, 73, …, 55
(a) 69
(b) 71
(c) 82
(d) 89
(e) None of these

Ans.(c)

Series increases and decreases alternatively with a difference of +(1)2, -(1)2, +(2)2,-(2)3, +(3)2, -(3)3 i.e., + 1,-1, + 4, -8, +9, -27.

(18). 6, 7, 9, 13, 21, …..
(a) 25
(b) 29
(c) 37
(d) 32
(e) None of these

Ans.(c)

Series moves with a difference of 1, 2, 4, 8, 16. Hence, the missing number will be 37.

(19). 5, 7, …., 9, 7, 11, 8, 13,
(a) 8
(b) 6
(c) 19
(d) 7
(e) None of these

Ans.(b)

There are two alternate series 5, 6, 7, 8 and 7, 9, 11, 13.
Hence,the missing number will be 6.

(20). 4, 8, 12, 24,36, 72, ….
(a) 108
(b)98
(c) 92
(d) 96
(e) None of these

Ans.(a)

Series proceeds with a difference of 4, 4, 12, 12, 36, 36.
Hence,the missing number will be 108.

(21). 1, 2, 3, 5, 7, ….
(a)8
(b) 9
(c)10
(d) 13
(e) None of these

Ans.(c)

Series moves with a difference of 1, 1,2,2,3,3 and so on.
Hence,the missing number will be 10.

(22). 3, 6, 6, 12, 9, …., 12
(a) 15
(b) 18
(c) 11
(d) 13
(e) None of these

Ans.(b)

There are two alternate series 3, 6, 9, 12 and 6, 12, 18…….
Hence,the missing number will be 18.

✦ Directions for Q. No. 23 to 31 : In each of the following questions, one number is wrong in the series. Find out the wrong number.

(23). 3, 5, 12, 39, 154, 772, 4634
(a) 5
(b) 3
(c) 39
(d) 154
(e) None of these

Ans.(c)

Series follows the pattern -3 x 1 + 2 = 5, 5 x 2 + 2 = 12, 12 x 3 + 2 = 38, 38 x 4 + 2 = 154 and so on.
Hence, number 39 should be replaced with 38.

(24). 376, 188, 88, 40, 16, 4, -2
(a)4
(b) 16
(c) 40
(d) 188
(e) None of these

Ans.(d)

Series has been written in descending order with a differences of 192,96,48,24, 12, 6 respectively.
Hence, the number 188 should be replaced by number 184.

(25). 444, 300, 200, 136, 87, 84, 80
(a) 200
(b) 136
(c) 87
(d) 80
(e) None of these

Ans.(c)

Series has been written in descending order with a difference of 144 , 100, 64, 36, 16 and 4 i.e.,squares of even natural numbers.
Hence,the number 87 should be replaced by number 100.

(26). 2, 3, 12, 37, 86, 166, 288
(a) 2
(b) 3
(c) 166
(d) 86
(e) 37

Ans.(c)

Series moves with a difference of squares of odd natural numbers i.e., 1, 9, 25, 49, 81, 121.
Hence, the number 166 should be replaced by number 167.

(27). 4, 9, 19, 43, 90. 185, 375
(a) 9
(b) 19
(c) 90
(d) 185
(e) None of these

Ans.(b)

Series follows the pattern : 4 x 2 + 1 = 9, 9 x 2 + 2 = 20, 20 x 2 + 3 = 43, 43 x 2 + 4 = 90 and so on.
Hence, the number 19 should be replaced by 20.

(28). 572, 284, 140, 72, 32, 14, 5
(a) 14
(b) 32
(c) 72
(d) 5
(e) 140

Ans.(c)

Series moves from the end following the pattern 5 x 2 + 4 = 14, 14 x 2 + 4 = 32, 32 x 2 + 4 = 68 and so on.
Hence, the number 72 should be replaced by 68

(29). 4, 10, 23, 50, 104, 216, 239
(a) 4
(b) 10
(c) 23
(d) 104
(e) 216

Ans.(d)

Series follows the pattern 4 x 2 + 2 = 10, 10 x 2 + 3 = 23, 23 x 2 + 4 = 50, 50 x 2 + 5 = 105, 105 x 2 + 6 = 216 and so on.
Hence, the number 104 should be replaced by 105.

(30). 701, 348, 173, 85, 41, 19, 8
(a)173
(b) 41
(c) 19
(d) 8
(e) 348

Ans.(e)

Series follows the pattern from the right end as 8 x 2 + 3 = 19, 19 x 2 + 3 = 41, 41 x 2 + 3 = 85, 85 x 2 + 3 = 173, 173 x 2 + 3 = 349, 349 x 2 +3 = 701.
Hence, the number 348 should be replaced by 349.

(31). 2, 3, 9, 27, 112, 565, 3396
(a) 565
(b) 9
(c) 112
(d) 27
(e) 3396

Ans.(b)

Series follows the pattern: 2 x 1 + 1 = 3, 3 x 2 + 2 = 8, 8 x 3 + 3 = 27, 27 x 4 + 4 = 112 and so on.
Hence, the number 9 should be replaced by 8.

✦ Directions for Q. No. 32 to 36 : In each of the following number series, two terms have been put within brackets. Mark in the answer sheet:

(32). 3, 10, 29, (66), (127), 218
(a) if the terms in both the brackets are right.
(b) if the term in the first bracket is right but the term in the second bracket is wrong.
(c) if the term in the first bracket is wrong but the term in the second bracket is right.
(d) if the terms in both the brackets are wrong.

Ans.(a)

Both the bracket numbers are right. Each term of the series is two more than the cubes of natural numbers i.e., (1)3 + 2, (2)3 + 2, (3)3 + 2, (4)3 + 2, (5)3 + i, (6)3 + 2.

(33). (2) 5, (12), 25, 41, 61
(a) if the terms in both the brackets are right.
(b) if the term in the first bracket is right but the term in the second bracket is wrong.
(c) if the term in the first bracket is wrong but the term in the second bracket is right.
(d) if the terms in both the brackets are wrong.

Ans.(d)

Both the bracket terms are wrong. Numbers 2 and 12 should be replaced by number 1 and 13 respectively, so that the series successively moves with differences of 4, 8, 12, 16, 20.

(34). 4, 7, (9), 10, 13, 15, (16), 19
(a) if the terms in both the brackets are right.
(b) if the term in the first bracket is right but the term in the second bracket is wrong.
(c) if the term in the first bracket is wrong but the term in the second bracket is right.
(d) if the terms in both the brackets are wrong.

Ans.(a)

The terms in both the brackets are right and numbers moves with difference of 3, 2, 1, respectively.

(35). 2, 3, (6), 11, 18, (30), 38
(a) if the terms in both the brackets are right.
(b) if the term in the first bracket is right but the term in the second bracket is wrong.
(c) if the term in the first bracket is wrong but the term in the second bracket is right.
(d) if the terms in both the brackets are wrong.

Ans.(b)

The number in the 2nd bracket, 30 is wrong and should be replaced by 27 so that series moves with differences of odd natural numbers 1, 3, 5, 7, 9, 11.

(36). 4, 6, 10, (12), 16, (14), 22
(a) if the terms in both the brackets are right.
(b) if the term in the first bracket is right but the term in the second bracket is wrong.
(c) if the term in the first bracket is wrong but the term in the second bracket is right.
(d) if the terms in both the brackets are wrong.