Number series tests present numerical sequences that follow a logical rule which is based on elementary arithmetic. An initial sequence is given from which the rule is to be deduced. You are then asked to predict the next number or missing number that obeys the rule. Sometimes you need to find out the wrong number in that series which doesn’t follow that rule
Tips to find the rules..
* Try to identify numbers
They may be even numbers, odd numbers, prime numbers, squares, cubes etc or sometimes they may be more/less than them.
Ex: 11, 18, 27, 38, 51, .......
Here the numbers in the series are
32 + 2, 42 + 2, 52 + 2, 62 + 2 and 72 + 2. The next number will be 82 + 2 = 66
* Check the difference between adjacent numbers:
The difference between two consecutive numbers may be constant, continuously increasing/ decreasing, prime numbers, squares, or cubes etc.
Ex: 19, 24, 29, 34, 39, ...
Here difference between the adjacent numbers is 5. The next number is 39 + 5 = 44
Ex: 32, 35, 40, 47, 58, 71 ...
Here the differences between the adjacent numbers are 3, 5, 7, 11, and 13 which are prime numbers. The next number will be 71 + 17 = 88
* Observe whether there is a multiplication or division pattern between two adjacent numbers.
Ex: 4, 8, 24, 96, 480, ........
Here the relation between the adjacent numbers is × 2, × 3, × 4 and × 5. The next number will be 480 × 6 = 2880
* Observe if you can find a rule that involves using two or more basic arithmetic functions (+, −, ÷, ×). In the below series, the functions alternate in an orderly fashion.
Ex: 6, 18, 23, 69, 74, 222 .....
Here the relation between the adjacent numbers is × 3, + 5, × 3, + 5 and × 3. The next number will be 222 + 5 = 227
* Alternate Series
Sometimes two number series are given in a single sequence. In odd places one series and even places another series.
Ex: 11, 5, 13, 15, 16, 45, 20, 135, ....
Here, Odd places numbers are 11, 13, 16, 20, ......
Differences between the numbers are 2, 3 and 4.
The next number will be 20 + 5 = 25
Even places numbers are 5, 15, 45, and 135
The relation between the numbers is × 3
EXERCISE
Directions (Q.No.1-5): What should come in place of question mark (?) in the following number series questions?
1. 320 80 160 40 80 ? 40
1) 60 2) 30 3) 20 4) 40 5) None of these
2. 156 119 90 67 48 ?
1) 27 2) 31 3) 24 4) 16 5) None of these
3. 20 29 54 103 184 ?
1) 305 2) 224 3) 382 4) 296 5) None of these
4. 24 36.2 30.4 33.6 32 ?
1) 32.8 2) 36.2 3) 34.6 4) 38.8 5) None of these
5. 6 9 13.5 20.25 30.375 ?
1) 45.7585 2) 46.7520 3) 28.7345 4) 45.5625 5) 49.7525
Directions (Q.No.6-10): In each of the following questions, a number is wrong. You have to identify that number.
6. 36 144 18 212 13.5 270
1) 196 2) 204 3) 236 4) 212 5) 224
7. 328 340 360 412 508 700
1) 360 2) 700 3) 412 4) 328 5) 340
8. 12 18 45 156.5 708.75 3898.125
1) 708.75 2) 45 3) 12 4) 156.5 5) 18
9. 0.7 1.1 1.9 3.1 4.7 6.9
1) 6.9 2) 1.9 3) 3.1 4) 0.7 5) None of these
10. 3399 1131 375 125 39 11
1) 39 2) 11 3) 375 4) 125 5) 3399
Directions (Q.No. 11-15): In each of the following number series questions, a number is wrong. You have to identify that number.
11. 19 21 45 137 561 2811
1) 19 2) 2811 3) 45 4) 137 5) None of these
12. 4 18 48 100 190 294
1) 294 2) 18 3) 190 4) 100 5) 148
13. 32 57 106 187 308 479
1) 479 2) 187 3) 32 4) 57 5) None of these
14. 2.5 4.7 0.3 9.3 -8.5 26.7
1) 26.7 2) 9.3 3) 4.7 4) -8.5 5) 26.7
15. 12 66 326 1626 8126 40626
1) 326 2) 1626 3) 8126 4) 12 5) 66
Directions (Q.No.16-20): In each of the following questions, a number series is given. One number is missing. What is that missing number?
16. 1 244 163 190 181 ?
1) 188 2) 184 3) 172 4) 196 5) None of these
17. 14 8 9 14.5 30 ?
1) 44 2) 76 3) 68 4) 52 5) None of these
18. 124 213 338 ? 720 989
1) 445 2) 585 3) 505 4) 372 5) None of these
19. 54 35 ? 3 -10 -21 -30
1) 18 2) 24 3) 28 4) 12 5) None of these
20. 11 12 20 43 ? 339.5 1194.25
1) 136 2) 124 3) 111.5 4) 225 5) None of these
Directions (Q.No.21-25): In each of the following number series questions a number is wrong. You have to identify that number.
21. 5 8 15 31 55 90
1) 55 2) 31 3) 8 4) 5 5) 15
22. 11 13 30 99 412 2085
1) 11 2) 30 3) 99 4) 2085 5) 13
23. 1 3 9 31 129 652
1) 3 2) 652 3) 129 4) 9 5) 31
24. 208 214 232 262 302 358
1) 358 2) 302 3) 262 4) 208 5) 232
25. 156 170 192 226 280 364
1) 280 2) 156 3) 192 4) 226 5) 364
KEY: 1-3; 2-2; 3-1; 4-1; 5-4; 6-4; 7-1; 8-4; 9-1; 10-4; 11-4; 12-3; 13-1; 14-2; 15-4; 16-2; 17-2; 18-3; 19-1; 20-3; 21-5; 22-1; 23-2; 24-2; 25-5.
EXPLANATIONS
1. 320 ÷ 4 = 80
80 × 2 = 160
160 ÷ 4 = 40
40 × 2 = 80
80 ÷ 4 = 20
20 × 2 = 40
Other method: Alternatively numbers will become half
2. 156 - 119 = 37
119 - 90 = 29
90 - 67 = 23
67 - 48 = 19
48 - 31 = 17
3. 20 + 32 = 29
29 + 52 = 54
54 + 72 = 103
103 + 92 = 184
184 + 112 = 305
4. 24 + 12.8 = 36.8
36.8 - 6.4 = 30.4
30.4 + 3.2 = 33.6
33.6 - 1.6 = 32
32 + 0.8 = 32.8
5. 6 × 3 ÷ 2 = 9
9 × 3 ÷ 2 = 13.5
13.5 × 3 ÷ 2 = 20.25
20.25 × 3 ÷ 2 = 30.375
30.375 × 3 ÷ 2 = 45.5625
6. 36 × 4 = 144
144 ÷ 8 = 18
18 × 12 = 216
216 ÷ 16 = 13.5
13.5 × 20 = 270
7. 328 + 12 = 340
340 + 24 = 364
364 + 48 = 412
412 + 96 = 508
508 + 192 = 700
8. 12 × 1.5 = 18
18 × 2.5 = 45
45 × 3.5 = 157.5
157.5 × 4.5 = 708.75
708.75 × 5.5 = 3898.125
9. 0.7 + 0.4 = 1.1
1.1 + 0.8 = 1.9
1.9 + 1.2 = 3.1
3.1 + 1.6 = 4.7
4.7 + 2 = 6.7
10. 3399 ÷ 3 - 2 = 1131
1131 ÷ 3 - 2 = 375
375 ÷ 3 - 2 = 123
123 ÷ 3 - 2 = 39
39 ÷ 3 - 2 = 11
11. 19 × 1 + 2 = 21
21 × 2 + 3 = 45
45 × 3 + 4 = 139
139 × 4 + 5 = 561
561 × 5 + 6 = 2811
12. 23 - 22, 33 - 32, 43 - 42, 53 - 52, 63 - 62, 73 - 72
13. 32 + 52 = 57
57 + 72 = 106
106 + 92 = 187
187 + 112 = 308
308 + 132 = 477
14. 2.5 + 2.2 = 4.7
4.7 - 4.4 = 0.3
0.3 + 8.8 = 9.1
9.1 − 17.6 = - 8.5
- 8.5 + 35.2 = 26.7
15. 14 × 5 - 4 = 66
66 × 5 - 4 = 326
326 × 5 - 4 = 1626
1626 × 5 - 4 = 8126
8126 × 5 - 4 = 40626
16. 1 + 243 = 244
244 − 81 = 163
163 + 27 = 190
190 - 9 = 181
181 + 3 = 184
17. 14 × 0.5 + 1 = 8
8 × 1 + 1 = 9
9 × 1.5 + 1 = 14.5
14.5 × 2 + 1 = 30
30 × 2.5 + 1 = 76
18. 53 - 1 = 124
63 - 3 = 213
73 - 5 = 338
83 - 7 = 505
93 - 9 = 720
103 - 11 = 989
19. 54 - 19 = 35
35 - 17 = 18
18 - 15 = 3
3 - 13 = -10
- 10 - 11 = - 21
- 21 - 9 = - 30
20. 11 × 1 + 1 = 12
12 × 1.5 + 2 = 20
20 × 2 + 3 = 43
43 × 2.5 + 4 = 111.5
111.5 × 3 + 5 = 339.5
339.5 × 3.5 + 6 = 1194.25
21. 5 + 22 - 1 = 8
8 + 32 - 1 =16
16 + 42 - 1 = 31
31 + 52 - 1 = 55
55 + 62 - 1 = 90
22. 12 × 1 + 1 = 13
13 × 2 + 4 = 30
30 × 3 + 9 = 99
99 × 4 + 16 = 412
412 × 5 + 25 = 2085
23. 1 × 1 + 2 = 3
3 × 2 + 3 = 9
9 × 3 + 4 = 31
31 × 4 + 5 = 129
129 × 5 + 6 = 651
24. 208 + 6 = 214
214 + 18 = 232
232 + 30 = 262
262 + 42 = 304
304 + 54 = 358
25. 156 + 14 = 170
170 + 14 + 8 = 192
192 + 22 + 12 = 226
226 + 34 + 20 = 280
280 + 54 + 32 = 366