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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.