# How To Solve Number Series for UGC NET Exam, Check Out The Study Notes!

By Mohit Choudhary|Updated : May 27th, 2022

Number Series is an important topic which is asked in UGC NET Exams. In this article, we will discuss the basics of number series, then it will be easier for you.

## Number Series Concepts

YOU MUST LEARN SQUARES OF NUMBERS UPTO 40 AND CUBES OF NUMBERS UPTO 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 of two successive numbers is 5 but the difference of 18 and 14 is 4, a difference of  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: 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 the wrong and 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 number 2,3,5,8,11,13. These numbers are prime numbers except 8 and from 2 to 11, 7 is also a prime number which 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 is 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 by 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 the pattern of wrong number series and have practised them. You will not have any problem in solving the series. Now, we will discuss the previous year asked questions based on number series.

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

 Pattern 1 Pattern 2 12x1 = 12                      12x(1.5) = 18            18x(1.5 +1) = 45       45x(2.5+1.5) = 180  180x(4+2.5)= 1170   1170x(6.5+4) = 12285 12x(1+0) = 1212x(1+.5) = 1818x(1.5+1) = 4545x (2.5+1.5) = 180180x(4+2) = 10801080x(6+2.5) = 9180

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

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

Example 3: 50…… 61 89 154 280
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
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, ?
3...5...9...15...23
2...4....6.......8

Example 6: 26 144 590 1164 ?
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?
So, 70 is wrong in this series

Example 8: 1,4,11,34,102,304,911
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
1
1x1x2=2
2x2x3=12
12x3x4=144
144x4x5=2880
2880x5x6=86400
86400x6x7= 3628800

Example 10: 0,6,23,56,108,184,279
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
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
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
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
2x2+5 = 9
9x2+6 = 24
24x2+7 = 55
55x2+8 = 118
118x2+9 = 245

Example 15: 109,131,209,271,341,419
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
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 in 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 multiplication or division pattern of series.
Step 4: If there is more irregularity in difference, then it may be the combination of 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.

All the Best for Exams.

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