Number Series Tricks & Tips

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What is Number Series?

Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in that series, we need to observe and find the accurate number to the series of numbers.

Tips For Number Series

1 ) Try to observe if there are any familiar numbers in the given series.
2 ) Familiar numbers are the numbers which which are easy to identify like primes numbers, perfect squares, cubes.
3 ) If you are unable to find familiar number, Calculate the differences between the numbers and observe the pattern in the differences.
4)  If the differences are growing slowly it might be an addition or subtraction series or If the differences are growing rapidly it might be a square series, cube series, or multiplicative series.
5) If the differences also are not having any pattern then observe every alternate number (ie every 3rd number form a series) for any pattern.
6) The possible cases may be like sum or the average of two consecutive numbers gives 3rd number.
7 )If still you do not find any pattern, it signifies that the series follows a complex pattern. Check for cases like multiplying the number and adding/subtracting a constant number from it to reach the pattern.

THE BEST WAY TO SOLVE NUMBER SERIES

There is one approach, which helped me a lot to solve these type of questions. Use this extremely useful tool to crack number series questions: RECOGNIZING THE NUMBERS. The trick is to recognize the numbers in the series and proceed accordingly. However, for this to work, you will need to remember some of the very crucial numbers in maths like:-

1.SQUARES OF NUMBERS
2.SQUARE ROOTS OF NUMBERS
3.CUBES OF NUMBERS
4.CUBE ROOTS OF NUMBERS
5.PRIME NUMBERS
6.NUMBERS WITH A LOT OF DIVISORS (E.g. numbers like 24 or 72)
7.ARITHMETIC TABLES

See the numbers of the given series very carefully. If all the numbers are near some perfect squares or cubes, you need to think on lines of squares or cubes of numbers. If you are not able to find any common factors between the numbers, think along the lines of prime numbers. If you see numbers with a lot of common divisors, think about multiplication or division with common factors. Solving this way would surely reduce the permutations you will need to think before getting the right answer. It is also extremely helpful and surely better than randomly guessing the logic.

But remember – start with the logical answer first and then slowly proceed to a difficult level. So, with this trick, there is a very less probability that you actually miss out on something.

Let me discuss one more important thing that you need to know. There is also a chance that the series is not uniform and continuous. Sometimes, two completely different series are mixed in an alternating fashion. The answer might be easy if you solve questions considering only alternate numbers. There is no way of predicting what the person thought about a question. So, keep your mind open to alternate possibilities. You never know which thought might come handy.

Also, don’t hesitate to leave this type of question if you just seem to figure it out. It’s better to focus on the remaining paper as one question might not affect your score a lot.

Just keep practising a lot. The more you practice such questions, the better you get at solving them and recognizing the logic behind the series quickly.

Different types of Number Series

There are some format of series which are given in Exams.

Perfect Square Series:

This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.

Example 1: 441, 484, 529, 576?

Answer: 441 = 21², 484 = 22², 529 = 23², 576 = 24² , 625 = 25².

 

Perfect Cube Series: 

This Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series

Example 2: 1331, 1728, 2197, ?

Answer : 11³ ,  12³ ,  13³ ,  14³

 

Geometric Series:

This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.

Example 3: 5, 45, 405, 3645,?

Answer: 5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.

 

Mixed Series:

This type of series are more than one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule. This mixed series Examples are describes in separately.

 

Examples 5:  11, 24, 50, 102, 206, ?

Answer: 

11 x 2 = 22 +2 = 24,

24 x 2 = 48 + 2 = 50,

50 x 2 = 100 + 2 = 102,

102 x 2 = 204 + 2 = 206,

206 x 2 = 412 + 2 = 414.

So the missing number is 414.

 

Example:- 2, 3, 5, 7,11, 13, _ , 19

Solution:-Here the terms of the series are the prime numbers in order.
The prime number after 13 is 17. So the answer to this question is 17.

 

Example:-  2, 5, 11, 17, 23, _, 41

Solution:- Here the series is framed by taking the alternative prime numbers. After 23, the prime numbers are 29 and 31. So the answer is 31.

 

Example:-  3, 5, 8, 13, 21
Solution:- Here starting from third number
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
So, the answer is 13 + 21=34

 

Example:- 1, 2, 2, 4, 8, 32. _
Solution:- Here starting from the third number
1 X 2 = 2
2 X 2 = 4
2 X 4 = 8
4 X 8 = 32
So, the answer is 8 X 32 = 256

 

Example:- 4, 7, 10, 13, 16, 19, _, 25
Solution:-Here the difference of any term from its succeding term is 3.
7 – 4 = 3
10 – 7 = 3
So, the answer is 19 +3 =22

 

Example:-  2, 10, 26, 50, 82, _
Solution:-Here, The difference between two consecutive terms are
10 – 2 = 8
26 – 10 = 16
50 – 26 = 24
82 – 50 = 32
Here, the difference is increased by 8 (or you can say the multiples of 8). So the next difference will be 40 (32 + 8). So, the answer is 82 + 40 =122

 

Example:-  6, 17, 38, 79, _
Solution:- 6 x 2 + 5 = 17
17 x 2 + 4 = 38
38 x 2 + 3 = 79
So, the answer is 79 x 2 + 2 = 160

 

Example:- 3, 7, 23, 95, _
Solution:- 
3 x 2 + 1 = 7
7 x 3 + 2 = 23
23 x 4 + 3 = 95
So, the answer will be 95 x 5 + 4 = 479

Practice Set On Number Series

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Directions(1-5): Find the missing number in the following number series.

1. 20     24     33    49     74     ?
   A) 115
   B) 88
   C) 96
   D) 110
   E) 123
    

   Answer

     Option D
   Solution:
   20 + 2^2 = 24
   24 + 3^2 = 24
   33 + 4^2 = 49
   49 + 5^2 = 74
   74 + 6^2 = 110

    
2. 1     ?     27    64     125
   A) 8
   B) 11
   C) 12
   D) 16
   E) None of these
    

   Answer

     Option A
   Solution:
   1  = 1^3
   ? = 2^3 = 8
   3 = 3^3
   4 = 4^3
   5 = 5^3

    
3. 12   14    17    13   ?   14   21    13
   A) 11
   B) 8
   C) 10
   D) 12
   E) None of these
    

    Answer

     Option B
   Solution:
   12…..(+2)……14….(+3)…..17…..
   (-4)……13……(-5)……8……(+6)……14……(+7)…..21…..(-8)…..13
   +2, +3, -4, -5, +6, +7, -8

    
4. 5    11     ?      55      117
   A) 22
   B) 25
   C) 33
   D) 30
   E) None of these
    

     Option B
   Solution:
   5  * 2 + 1 = 11
   11 * 2 + 3 = 25
   25 * 2 + 5 = 55
   55 * 2 + 7 = 117

    
5. 85     43    44    67.5     ?     345
   A) 125
   B) 140
   C) 137
   D) 112
   E) None of these
    
     Option C
   Solution:
   85 * 0.5 + 0.5 = 43
   43 * 1 + 1 = 44
   44 * 1.5 + 1.5 = 67.5
   ? = 67.5 * 2  + 2 = 137
   137 * 2.5 + 2.5 = 345

Directions(6-10): In each of the following questions number series, there is a wrong number that does not follow the pattern of the series. Find the wrong number.

6. 62    87    187    420    812    1437
   A) 87
   B) 187
   C) 420
   D) 812
   E) None of these
    
     Option C
   Solution:
   62 + 5^2 = 62 + 25 = 87
   87 + 10^2 = 87 + 100 = 187
   187 + 15^2 = 187 + 225 = 412
   412 + 20^2 = 412 + 400 = 812
   812 + 25^2 = 812 + 625 = 1437

    
7. 120    137    170    222    290   375
   A) 137
   B) 170
   C) 222
   D) 290
   E) 375
    

     Option B
   Solution:
   120 + 1 * 17 = 137
   137 + 2 *17 = 171
   171 + 3 * 17 = 222
   222 + 4 * 17 = 290
   290 + 5 * 17 = 375

    
8. 550   542   537   521    496   460
   A) 496
   B) 521
   C) 537
   D) 542
   E) 460
    

     Option D
   Solution:
   550 – 2^2 = 546
   546 – 3^2 = 537
   537 – 4^2 = 521
   521 – 5^2 = 496
   496 – 6^2 = 460

    
9. 12      48     168     500    1260   2520
   A) 500
   B) 168
   C) 48
   D) 1260
   E) 2520
    

     Option A
   Solution:
   12 * 4 = 48
   48 * 3.5 = 168
   168 * 3 = 504
   504 * 2.5 = 1260
   1260 * 2 = 2520

    
10. 24   536   487    703     670    742
    A) 536
    B) 487
    C) 670
    D) 703
    E)742
     

    Option C
    Solution:
    24 + 8^3 = 536
    536  – 7^2 = 487
    487 + 6^3 = 703
    703 – 5^2 = 678
    678 + 4^3 = 742
     

Directions(1-5): In the following number series only one number is wrong. Find out the wrong number.

1. 484   240      118       57        5      11.25     3.625
   A) 26.5
   B) 57
   C) 5
   D) 3.625
   E) 240
    

     Option  C
   Solution:
   (484 / 2) – 2 = 240
   (240/2) – 2 = 118
   (118/2) – 2 = 57
   (57/2) – 2 = 26.5
2. 5    7     16     57    244     1245     7506
   A) 7506
   B) 5
   C)244
   D) 7
   E) 16
    

     Option D
   Solution:
   5*1 + 1^2 = 6
   6*2 + 2^2 = 16
   16*3 + 3^2 = 57
   57*4 + 4^2 = 244
   244*5 + 5^2 = 1245
3. 4     2.5     3.5     6.5     15.5      41.25       126.75
   A) 41.25
   B) 6.5
   C) 126.75
   D) 4
   E) 2.5
    

     Option B
   Solution:
   4*0.5 + 0.5 = 2.5
   2.5*1 + 1 = 3.5
   3.5*1.5 +1.5 = 6.75
   6.75*2 + 2 = 15.5
   15.5*2.5 + 2.5  = 41.25
   41.25*3 + 3 = 126.75
4. 210    209    211    186    202     77
   A) 209
   B) 77
   C) 211
   D) 186
   E) 202
    

     Option C
   Solution:
   210 – 1^3 = 209
   209 + 2^3 = 213
   213 – 3^3 = 186
   186 + 4^3 = 202
   202 – 5^3 = 77
5. 33       321       465       537        575      591     600
   A) 465
   B) 33
   C) 600
   D) 575
   E) 591
    

     Option D
   Solution:
   33 + 288 = 321
   321 + 144 = 465
   465 + 72 = 537
   537 + 36 = 573
   573 +18 = 591
   591 + 9 = 600

   Directions(6-10): What should  come in place of question mark in the following series.

6. 3    7     18    26    ?    53   64   96
   A) 37
   B) 30
   C) 40
   D) 35
   E) 32
    

     Option A
   Solution:
   3 + 4  * 2^0 = 7
   7 + 11  = 18
   18 + 4*(2)^1 = 26
   26+ 11 = 37
   37 + 4*(2)^2 = 53
   53 + 11 = 64
   64+ 4 *(2)^3 = 96
7. 1.7     3.2      2.7     4.2     3.7     ?     4.7      6.2
   A) 3.8
   B) 5.2
   C) 4.4
   D) 4.8
   E) 5.5
    

     Option B
   Solution:
   1.7    + 1.5 = 3.2
   3.2  – 0.5 = 2.7
   2.7 + 1.5 = 4.2
   4.2 – 0.5 = 3.7
   3.7 + 1.5 = 5.2
   5.2 – 0.5 = 4.7
   4.7 + 1.5 = 6.2
8. 6        8      10     42       ?       770     4578
   A) 110
   B) 150
   C) 132
   D) 148
   E) 115
    

     Option D
   Solution:
   6 * 1 + 1*2 = 8
   8*2  – 2*3 = 10
   10 * 3 + 3*4 = 42
   42*4 – 4*5 = 148
   148*5 + 5*6 = 770
   770*6 – 6*7 = 4578
9. 7    13     31     85      247     ?
   A) 733
   B) 680
   C)700
   D) 650
   E) 666
    

     Option A
   Solution:
   7 + 6 = 13
   13 + 3 *6 = 31
   31 + 3 *18 = 85
   85 + 3 * 54 = 247
   247 + 3 * 162 = 733
10. 949   189.8     ?     22.776    11.388    6.8328
    A) 39.98
    B) 40.15
    C) 48.53
    D) 56.94
    E) 55.55
     

    Option D
    Solution:
    949  * 0.2 = 189.5
    189.5 * 0.3 = 56.94
    56.94 * 0.4 = 22.778
    22.778 * 0.5 = 11.388
    11.388 * 0.6 = 6.8328
     

Directions(1-5): What will come in place of question mark in the given number series.

1. 17 9      15     40      5       ?
   A) 620
   B) 650.25
   C) 550.5
   D) 688
   E) 540.15
    

     Option  B
   Solution:
   17 * 0.5 + 0.5 = 9
   9 * 1.5 + 1.5 = 15
   15 * 2.5 + 2.5 = 40
   40 * 3.5 + 3.5 = 143.5
   143.5 * 4.5 + 4.5 = 650.25
2. 2     9     25      82      335      ?
   A) 1456
   B) 1246
   C) 1682
   D) 1560
   E) 1550
    

     Option C
   Solution:
   2 * 1 + 7 = 9
   9 * 2 + 7 = 25
   25 * 3 + 7 = 82
   82 * 4 + 7 = 335
   335 * 5 + 7 = 1682
3. 1548      516     129     43     ?
   A) 9.82
   B) 11.11
   C)13.25
   D)10.75
   E) 11.25
    

     Option D
   Solution:
   1548/ 3   = 516
   516/4 = 129
   129/3 = 43
   43/4 = 10.75
4. 41      164       2624       ?        6045696
   A)94464
   B) 84500
   C)94502
   D) 78542
   E) 82456
    

     Option B
   Solution:
   41  *   2^2 = 164
   164  *  4^2 = 2624
   2624  *  6^2 = 94464
   94464  *  7^2 = 6045696
5. 4       9       29       119       599        ?
   A) 2998
   B) 4578
   C) 3245
   D) 2000
   E) 3599
    

     Option E
   Solution:
   4 * 2 + 1 = 9
   9*3  + 2 = 29
   29 * 4 + 3 = 119
   119* 5 + 4 = 599
   599*6 +5=3599

   Directions(6-10): In the  following number series only one number is wrong. Find the wrong number.

6. 133     183     241      307     381      463     480
   A) 307
   B) 133
   C) 480
   D) 241
   E) 381
    

     Option  C
   Solution:
   133 + 50 = 183
   183 + 58 = 241
   241 + 66 = 307
   307 + 74 = 381
   381 + 82 = 463
   463 + 90 = 553
7. 31     15      21    50    155.3      767.25
   A) 767.25
   B) 155.3
   C) 15
   D) 31
   E) 50
    

     Option B
   Solution:
   31 * 0.5 – 0.5 = 15
   15 * 1.5 – 1.5 = 21
   21 * 2.5 – 2.5 = 50
   50 * 3.5 – 3.5 = 171.5
   171.5  *  4.5 – 4.5 = 767.25
8. 18       119      708       3530       14136      42405
   A) 14136
   B) 708
   C) 119
   D) 3530
   E) 42405
    

     Option D
   Solution:
   18 * 7 – 7 = 119
   119* 6 – 6 = 708
   708 * 5 – 5 = 3540
   3540 * 4 – 4 = 14136
   14136 * 3 – 3 = 42405
9. 500     484     451      384      260      80
   A) 80
   B) 260
   C) 451
   D) 484
   E) 500
    

     Option B
   Solution:
   500 – 16 = 484
   484 – 33(= 16 + 17) = 451
   451 – 67(= 33 + 2 * 17) = 384
   384 – 118(= 67 + 3 * 17)= 266
   266 – 186(= 118 + 4 * 17)= 80
10. 9    10.8    18     21.6     36      64.8
    A) 21.6
    B) 10.8
    C) 36
    D) 18
    E) 9
     

    Option D
    Solution:
    9 + 1.8 = 10.8
    10.8 + 2* 1.8 = 14.4
    14.4 + 2 *3.6 = 21.6
    21.6 + 2*7.2 = 36
    36+ 2 * 14.4 = 64.8
     

 

 

 

 

 

S6. Ans.(a)
Sol.
The pattern of the series is:
×1.2,×1.25,×1.3,×1.35,×1.4,×1.45……….

S7. Ans.(a)
Sol.
The pattern of series is:
+12,+16,+20,+24,+28

S8. Ans.(d)
Sol.
The series is:
÷5+5,÷5+5,÷5+5,÷5+5…….

S9. Ans.(d)
Sol.
The pattern of series is:
×3+1,×3-3,×3+5,×3-7,×3+9……

 

 

• 4, 5, 6, 14, ?, 100.5
  1. 32.5
  2. 47.5
  3. 67.5
  4. 37.5
  5. 27.5
   

  Answer – 1. 32.5
  Explanation :
  4 * 1 + 1 = 5
  5 * 1.5 – 1.5= 6
  6 * 2 + 2 = 14
  14 * 2.5 – 2.5 = 32.5
  32.5 * 3 + 3 = 100.5
• 8 4 4 8 32 ?
  1.354
  2.384
  3.294
  4.234
  5.256
   

  Answer – 5.256
  Explanation :
  8 * 0.5 = 4
  4 * 1 = 4
  4 * 2 = 8
  8 * 4 = 32
  32 * 8 = 256
• 2, 2, 7, ?, 87, 342
  1.21
  2.26
  3.23
  4.24
  5.22
   

  Answer – 5.22
  Explanation :
  2 + 1² – 1 = 2
  2 + 2² + 1= 7
  7 + 4² – 1= 22
• 6, 8, 8, 22, ?, 151
  1.43
  2.42
  3.44
  4.47
  5.48
   

  Answer – 4.47
  Explanation :
  6 * 1 + 2 = 8
  8 * 1.5 – 4 = 8
  8 * 2 + 6 = 22
  22 * 2.5 – 8 = 47
  47 * 3 + 10 = 151
• 4, ?, 14, 40, 88, 170
  1.9
  2.5
  3.6
  4.7
  5.2
   

  Answer – 3.6
  Explanation :
  4 + 1² + 1= 6
  6 + 3² – 1= 14
  14 + 5² + 1= 40……..
• 6, 6, 7, ?, 91, 463
  1.33
  2.43
  3.38
  4.25
  5.44
   

  Answer – 4.25
  Explanation :
  6*1 – 1 + 1 = 6
  6*2 – 2 – 3 = 7
  7*3 – 1 + 5 = 25
• 2, 5, 17, 50, 122, ?
  1.252
  2.258
  3.257
  4.225
  5.242
   

  Answer – 3.257
  Explanation :
  2 + 1³ + 2 = 5
  5 + 2³ + 4 = 17
  17 + 3³ + 6 = 50
  50 + 4³ + 8 = 122
• 2, 9, 39, 161, ?, 2613
  1.675
  2.670
  3.665
  4.651
  5.655
   

  Answer – 4.651
  Explanation :
  2 * 4 + 1 = 9
  9 * 4 + 3 = 39
  39 * 4 + 5 = 161
  161 * 4 + 7 = 651
  651 * 4 + 9 = 2613
• 5, ?, 20, 34, 76, 142
  1.4
  2.5
  3.7
  4.8
  5.9
   

  Answer – 4.8
  Explanation :
  5*2 – 2 = 8
  8*2 + 4 = 20
  20*2 – 6 = 34
• 5, 6, 8, 30, 136, ?
  1.645
  2.680
  3.650
  4.690
  5.620
   

  Answer – 1.645
  Explanation :
  5 * 1 + 1 = 6
  6 * 2 – 2 = 10
  10 * 3 + 3 = 33
  33 * 4 – 4 = 128
  128 * 5 + 5 = 645