Seeing some recent exams, it has been found that the latest pattern of number series is to identify wrong numbers given in the series. So, we will discuss this latest pattern.

This latest pattern is nothing but an advanced pattern of missing numbers. If you know the basics of number series, then it will be easier for you.

**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: 2^{3}=8, 3^{3}=27, 5^{3}=125, 8^{3}=512,11^{3}=1331,13^{3}=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 8^{3}, there should be 7^{3} 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

6×2-1 = 11

11×2-1 = 21

21×2 -1 = 41

41×2 – 1 = 81

81×2 -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 |

12×1 = 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 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

7×1 – 2 = 5

5×2 – 3 = 7

7×3 – 4 = 17

17×4 – 5 = 63

63×5 – 6 = 309

**Example 3:** 50…… 61 89 154 280 (SBI PO Prelims 2016)

**Answer :** 52

50+(1^{3}+1) = 52

52+(2^{3}+1) = 61

61+(3^{3}+1) = 89

89+(4^{3}+1) = 154

154+(5^{3}+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:** 9×7=63, 9×8=72,8×6=48

So, 70 is wrong in this series

**Example 8:** 1,4,11,34,102,304,911

**Answer:** 102

Pattern of Series is

1

1×3+1 = 4

4×3-1 = 11

11×3+1 = 34

34×3-1 = 101

101×3+1 = 304

304×3-1 = 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

1^{3}-2^{0} = 1-1 =0

2^{3}-2^{1 }= 8-2 =6

3^{3}-2^{2 }= 27-4 = 23

4^{3}-2^{3}= 64-8 = 56

5^{3}-2^{4}= 125-16 = 109

6^{3}-2^{5}= 216-32 = 184

7^{3}-2^{6}= 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

1^{3}-1^{2}=0

2^{3}-2^{2 }= 4

3^{3}-3^{2 }= 18

4^{3}-4^{2}= 48

5^{3}-5^{2}=100

6^{3}-6^{2}= 180

7^{3}-7^{2}=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

2×2+5 = 9

9×2+6 = 24

24×2+7 = 55

55×2+8 = 118

118×2+9 = 245

**Example 15:** 109,131,209,271,341,419

**Answer**: 131

11^{2}-12 = 109

13^{2}-14 = 155

15^{2}-16 = 209

17^{2}-18 = 271

19^{2}-20 = 341

21^{2}-22 = 419

**Example 16:** 6, 7,27, 115,513,3069

**Answer **: 115

6×2-5 = 7

7×3+6 = 27

27×4-7 = 101

101×5+8 = 513

513×6-9 = 3069

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.