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NUMBER SERIES

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

Posted Date : 03-03-2021

 

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