How to Solve Number Series Quickly - Short Tricks to Solve Wrong Number Series Questions

Number Series Concepts

YOU MUST LEARN SQUARES OF NUMBERS UP TO 40 AND CUBES OF NUMBERS UP TO 20.
Note: In the wrong number series, the pattern of the series will always be wrong immediately before and after the wrong number.

There are uncountable numbers of series because the series is an imagination. Some of the important series patterns are discussed below:

1. Based on addition and subtraction.
4,9,14,18,24,29
the difference between the two successive numbers is 5 but the difference between 18 and 14 is 4, the difference between 24 and 18 is 6. So, the wrong number is 18. The correct answer is 19.

2. Based on multiplication and division.
18,28,40.5,60.75,91.125,136.6875
Solution: The problem with this type of series is how to identify these types of series. Check the difference between successive numbers.
----10----12.5----20.25----30.375----45.5625
we can see that the difference is half of the previous number. 10 is not the half of 18 and 12.5 is not the half of 28. So, 28 is wrong and the correct number is 27.

3. Based on the square and cube.
8 27 125 512 1331 2197
Solution: 2³=8, 3³=27, 5³=125, 8³=512,11³=1331,13³=2197
In this, all are cubes of numbers 2,3,5,8,11,13. These numbers are prime numbers except 8 and from 2 to 11, 7 is also a prime number that is missing. In place of 8³, there should be 7³ i.e. 343

4. Based on the mixed pattern.
6,11,21,40,81,161
This series could have followed two patterns.
Pattern 1: The difference is –5---10----19-----41---80. Successive difference is2 times of the previous one. But 19 and 41 are not following the pattern. We can guess that something is wrong in this term if we want 20 and 40, we have to replace 40 with 41. Hence 40 is wrong.
Pattern 2:   6                                      
  6x2-1 = 11
11x2-1 = 21
21x2 -1 = 41
41x2 – 1 = 81
81x2 -1 = 161 Hence, 40 is wrong
If you go through various types of a pattern of wrong number series and have practiced them. You will not have any problem solving the series. Now, we will discuss the previous year's questions based on the number series.

Example 1:  12 12 18 45 180 1080 12285
In this series also there can be two patterns.

So, If it follows pattern1, the wrong number in the series is 1080 and if it follows pattern2, the wrong number in the series is 12285. It depends on the options given in exams.

Example 2: 7 5 7 17 63 ? 
Answer: 309
7x1 – 2 = 5
5x2 – 3 = 7
7x3 – 4 = 17
17x4 – 5 = 63
63x5 – 6 = 309

Example 3: 50…… 61 89 154 280 (SBI PO Prelims 2016)
Answer : 52
50+(1³+1) = 52
52+(2³+1) = 61
61+(3³+1) = 89
89+(4³+1) = 154
154+(5³+1) = 280

Example 4: 17, 19, 25, 37, ......,87 (SBI PO Prelims 2016)
Answer: 57
17 + 1 x 2 = 19
19 + 2 x 3 = 25
25 + 3 x 4 = 37
37 + 4 x 5 = 57
57 + 5 x 6 = 87

Example 5: 11, 14, 19, 28, 43, ? (SBI PO Prelims 2016)
Answer:  66
3...5...9...15...23 
2...4....6.......8
Answer 43+23= 66

Example 6: 26 144 590 1164 ? (SBI PO Prelims 2016)
Answer: 1182
26 x 6 – 12 = 144
144 x 4 + 14 = 590 
590 x 2 – 16 = 1164
1164 x 1 + 18 = 1182 

Example 7: 6 48 8 70 9 63 7 Find the wrong number?
Answer: 9x7=63, 9x8=72,8x6=48
So, 70 is wrong in this series

Example 8: 1,4,11,34,102,304,911
Answer: 102
Pattern of Series is
1
1x3+1 = 4
4x3-1 = 11
11x3+1 = 34
34x3-1 = 101
101x3+1 = 304
304x3-1 = 911

Example 9: 1,2,12,146,2880,86400,3628800
Answer: 146
1
1x1x2=2
2x2x3=12
12x3x4=144
144x4x5=2880
2880x5x6=86400
86400x6x7= 3628800

Example 10: 0,6,23,56,108,184,279
Answer: 108
1³-2⁰ = 1-1 =0
2³-2¹ = 8-2 =6
3³-2² = 27-4 = 23
4³-2³= 64-8 = 56
5³-2⁴= 125-16 = 109
6³-2⁵= 216-32 = 184
7³-2⁶= 343-64 =279

Example 11: 813,724,635,546,457,564,279
Answer : 564
Hundred place digit is decreasing by 1, tens place is increasing by 1, and unit place digit is also increasing by 1. But this pattern is not followed in 564. 368 should be there in place of 564.

Example 12: 0,4,19,48,100,180,294
Answer: 19
1³-1²=0
2³-2² = 4
3³-3² = 18
4³-4²= 48
5³-5²=100
6³-6²= 180
7³-7²=294

Example 13: 3.2, 4.8, 2.4, 3.6, 1.6, 2.7
Answer : 1.6
3.2 x 1.5 = 4.8
4.8 ÷ 2 = 2.4
2.4 × 1.5 = 3.6
3.6 ÷ 2 = 1.8
1.8 x 1.5 = 2.4

Example 14: 2, 9,24,55,117,245
Answer : 117
2x2+5 = 9
9x2+6 = 24
24x2+7 = 55
55x2+8 = 118
118x2+9 = 245

Example 15: 109,131,209,271,341,419
Answer: 131
11²-12 = 109
13²-14 = 155
15²-16 = 209
17²-18 = 271
19²-20 = 341
21²-22 = 419

Example 16: 6, 7,27, 115,513,3069
Answer : 115
6x2-5 = 7
7x3+6 = 27
27x4-7 = 101
101x5+8 = 513
513x6-9 = 3069

Some steps which may be helpful to solve number series.

Step 1: Check the difference
Step 2: If step 1 does not work, then check the difference of difference. If it also does not work, try to find is there any multiplication or division relationship between numbers?
Step 3: If a difference is sharply increasing or decreasing, then you can guess that it may be due to the multiplication or division pattern of series.
Step 4: If there is more irregularity indifference, then it may be the combination of the above-discussed steps.
Step 5: If none of the steps works, then try to use the elimination method, which may help you in eliminating 2 to 3 options