How to Solve Number Series Quickly - Short Tricks
YOU MUST LEARN SQUARES OF NUMBERS UPTO 40 AND CUBES OF NUMBERS UPTO 20.
Note: In the wrong number series, the pattern of series will always be wrong immediately before and after of the wrong number.
There are uncountable numbers of series because series is an imagination. Some of the important series pattern are discussed below:
1. Based on addition and subtraction.
4,9,14,18,24,29
the difference of two successive numbers is 5 but difference of 18 and 14 is 4, difference of 24 and 18 is 6. So, wrong number is 18. 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 wrong and correct number is 27.
3. Based on 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 prime number which is missing. In place of 83, there should be 73 i.e. 343
4. Based on mix pattern.
6,11,21,40,81,161
This series could have followed two patterns.
Pattern 1: difference is –5---10----19-----41---80. Successive difference is2 times of 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 pattern of wrong number series and have practiced them. You will not have any problem in solving the series. Now, we will discuss 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 pattern.
| 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) = 12 12x(1+.5) = 18 18x(1.5+1) = 45 45x (2.5+1.5) = 180 180x(4+2) = 1080 1080x(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 ? (SBI PO Prelims 2016)
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.
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
Common Patterns in "Number Series" Questions
(1) Prime Numbers: when numbers are a series of prime numbers (a natural number which is greater than 1 and has no positive divisors other than 1 and the number itself)
For example - 11, 13, 17, 19...
(2) Squares/ Cubes: when numbers are a series of perfect square or cube roots.
For example - 81, 100, 121, 144, 169...
(3) Patterns in differences: Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference.
For example - 2, 5, 8, 11, 14... (here the difference between the numbers is 3, hence the next number will be 17)
(4) Pattern in alternate numbers: when there is a pattern between every alternate or third number in the series
For example - 2, 9, 5, 1, 8 , 15, 11....
(5) Geometric series: when each successive number in the series is obtained by multiplying or dividing the previous number by a fixed number.
For example - 5, 45, 405, 3645
(6) Odd one out: when all but one number is part of a series
For example - 5, 10, 12, 15, 20... (Here all numbers except, 12 are multiples of 5)
(7) pattern in adjacent number: when adjacent numbers in the series changes based on a logical pattern.
For example - 2, 4, 12, 48... (Here the first number is multiplied by 2, the second number by 3 and the third number by 4)
(8) Complex series: in some patterns the differences between numbers is dynamic rather than being fixed, but there still is a clear logical rule.
For example - 3, 4, 6, 9, 13, 18.. (Here you can add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2 and after the third number you can add 3)
(9) Using two or more basic arithmetic functions: in some series more than one operation (+, -, ÷, x) is used.
For example - 5, 7, 14, 16, 32... (here you can add 2, multiply by 2, add 2, multiply by 2, and so on)
(10) Cube roots/ square roots: when the number are a series of cube roots and square roots
For example - 512, 729, 1000... (here the next number in the series will be 1331)
Some steps which may be helpful to solve number series.
Step 1: Check difference
Step 2: If step 1 does not work, then check difference of difference. If it also does not work, try to find is there any multiplication or division relationship between numbers?
Step 3: If 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 combination of above discuss steps.
Step 5: If none of the steps works, then try to use elimination method, which may help you in eliminating 2 to 3 options.
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