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Which of the following numbers is wrong in the series?

1. 3, 6, 10, 16, 21, 28

16

10

15

28

Answer (a). The series should be 3, 6, 10, 15, 21, 28. The difference between the consecutive numbers increases progressively. The difference between 3 and 6 is 3, 6 and 10 is 4, 10 and 15 is 5, 15 and 21 is 6 and 21 and 28 is 7.

2. 126, 98, 70, 41, 14

98

70

126

41

Answer (d). The difference between the consecutive numbers is 28. Replacing 41 with 42 would satisfy the condition. 126 - 28 = 98; 98 - 70 = 28; 70 - 42 = 28; 42 - 14 = 28.

3. 1, 9, 25, 50, 81

1

25

50

81

Answer (c). The correct sequence is 1, 9, 25, 49, 81. The series is made up of squares of all the odd numbers starting from 1.

4. 6, 12, 21, 32, 45, 60

6

12

21

32

Answer (a). The difference between the consecutive numbers is 21 - 12 = 9; 32 - 21 = 11; 45 - 32 = 13; 60-45 = 15. The correct series would be 5, 12, 21, 32, 45 and 60.

5. 6, 9, 15, 22, 51, 99

99

51

22

15

Answer (c). The difference between the numbers doubles progressively. Thus replacing 22 with 27 would give the consecutive differences 3, 6, 12, 24, 48.

6. 7, 28, 63, 124, 215, 344

28

63

124

342

Answer (c). The correct series is 2³-1, 3³+1, 4³-1, 5³+1, 6³-1, 7³+1. Hence 126 should replace 124.

7. 3, 9, 27, 81, 243, 730

27

81

243

730

Answer (d). The correct sequence should be 3, 9, 27, 81, 243, 729. 3 x 3 = 9 x 3 = 27 x 3 = 81 x 3 = 243 x 3 = 729.

8. 2, 10, 30, 68, 120, 222

68

120

30

222

Answer (b). The sequence is 1³ + 1 = 2, 2³ + 2 = 10, 3³ + 3 = 30, 4³ + 4 = 68, 5³ + 5 = 130, and 6³ + 6 = 222. Therefore in the place of 120 the number should have been 130.

9. 462, 422, 380, 342, 306

422

380

342

306

Answer (a). The correct series would be 462 - 420 = 42; 420 - 380 = 40; 380 - 342 = 38; 342 - 306 - 36. Changing 422 to 420 would make the series as required.

Answer (c). 9, 9 x 2 = 18 + 1 = 19, 19 x 2 = 38 + 2 = 40, 40 x 2 = 80 + 3 = 83, 83 x 2 = 166 + 4 = 170 and 170 x 2 = 340 + 5 = 345. 340 should have been 345.

12. 21, 28, 33, 35, 37, 36

21

36

33

35

Answer (d). The sequence in the differences of the numbers is 7, 5, 3, 1, -1. Substituting 35 with 36 satisfies the sequence.

13. 5, 13, 29, 61, 120, 253

120

253

61

29

Answer (a). The difference between two consecutive numbers increases by 8, 16, 32, 64, 128. Thus 5 + 8 = 13 + 16 = 29 + 32 = 61 + 64 = 125 + 128 = 253.

14. 7, 28, 63, 124, 215

28

215

7

63

Answer (a). The sequence here should be 2³ - 1, 3³ - 1, 4³ - 1, 5³ - 1 and 6³ - 1. Therefore 26 should replace 28 to safisfy the condition.

15. 17, 36, 53, 68, 83, 92

53

68

83

92

Answer (c). The difference between the numbers is an odd number in decreasing order starting from 19. Change 83 to 81 to compelete the sequence properly.

16. 8, 16, 34, 64, 128

16

34

64

128

Answer (b). A simple sequence where each number is double of the preceding number. The sequence should be 8, 16, 32, 64, 128.

17. 8, 15, 29, 50, 77, 113

77

29

50

15

Answer (a). The sequence here is formed by the differences equal to the multiples of 7. 8 + 7 = 15 + 14 = 29 + 21 = 50 + 28 = 78 + 35 = 113. So replace 77 by 78.

18. 225, 196, 166, 144, 121, 100

196

121

166

144

Answer (c). The correct sequence here would be 15², 14², 13², 12², 11², and 10². Therefore 166 should be replaced by 169.

19. 5, 21, 38, 53, 69, 85

21

69

53

38

Answer (d). The difference between consecutive numbers here should be 16. Therefore change 38 to 37 to satisfy the condition. 5 + 16 = 21 + 16 = 37 + 16 = 53 + 16 = 69 + 16 = 85.

20. 121, 144, 225, 289, 361, 441

121

225

144

361

Answer (c). The sequence has been formed by squares of all odd numbers starting from 11. 144 is the square of 12 and hence should be replaced with 169.

21. 13, 19, 29, 44, 64, 89

13

19

29

44

Answer (a). The sequence here should be formed by adding a multiple of 5 in increasing order. So changing 13 to 14 would give the sequence as 14 + 5 = 19 + 10 = 29 + 15 = 44 + 20 = 64 + 25 = 89.

22. 56, 90, 124, 158, 193, 226

90

124

158

193

Answer (d). The difference between each consecutive number in the correct series is 34. 56 + 34 = 90 + 34 = 120 + 34 = 158 + 34 = 192 + 34 = 226.