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Number Series

Question : It contains a series of numbers and it will be in a certain pattern .
Objective: To find the missing or wrong number in that series .

5172÷2=2536

2536÷2=1268

1268÷2=634

634÷2=317

understand the procedure and try to solve , it will be easy while you are scrolling down.)

In such type of questions, we have to find the difference between consecutive numbers Difference between consecutive numbers will follow a pattern (consecutive addition/subtraction or multiplication/division).

Difference between 30 & 46 is 16

Difference between 46 & 78 is 32

Difference between 78 & 126 is 48

Difference between 126 & 190 is 64

Difference between 190 & 270 is 80

Here the differences are all multiples of 16 i.e. (16*1), (16*2), (16*3), (16*4), (16*5), so obviously the next number will be (16*6).

So in series the next number will be addition of (16*6 =) 96 therefore the answer is 270+96 = 366

Find the difference between the numbers, and the differences are

Difference between 17 & 20 = 3

Difference between 20 & 26 = 6 (3*2)

Difference between 26 & 38 = 12 (6*2)

Difference between 38 & 62 = 24 (12*2)

Difference between 62 & 110 = 48 (24*2)

1250÷2.5 = 500

500÷2.5=200

200÷2.5= 80

80÷2.5=32

32÷2.5=12.8

12.8÷2.5=5.12

23+3=26

26-2=24

24+3=27

27-2=25

25+3=28

28-2=26

If difference between consecutive numbers do not follow any patterns , try these patterns

(there is no need to by heart all this pattern , just know how the patterns can be in the series this will make easy to guess the pattern for you)

For series

difference between 3&732 = 729 i.e. 93

difference between 25 & 61 = 36 (12*3)

difference between 61 & 121 = 60 (12*5)

difference between 121 & 205 = 84 (12*7)

120÷8 =15

15*7=105

105÷6=17.5

17.5*5=87.5

87.5÷4=21.875

Difference between 3&6 is 3

Difference between 21&28 is 7

Difference between 55& 66 is 11

Difference between ? & 120 is 15 therefore the number is 105

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There will be

**5 problems from number series,**among these problems –**1 will be easy**and**3 will be moderate**and**1 will be hard**. we can**easily crack**these questions in a few second if we guess the pattern . i have made an effort to cover all the patterns , i am sure after reading this topic you will get some idea.**Difficulty level – Easy :***(By keen observation itself, you can easily find pattern.)***Prime numbers**-2, 3, 5, 7, 11

**Squares of numbers**-

1, 4, 9, 16, 25

169, 225, 289, 361, 441 – squares of odd number

(132, 152, 172, 192, 212)

so 17 + 3 = 20 is answer

Difference between successive numbers are 13 and they are in decreasing order so answer will be

169, 225, 289, 361, 441 – squares of odd number

(132, 152, 172, 192, 212)

*Addition/subtraction by a common number***Example : 11, 14, 17, ? , 23**

**Difference between successive numbers are 3.**

so 17 + 3 = 20 is answer

**Example : 975, 962, ?, 936 , 923 .**

Difference between successive numbers are 13 and they are in decreasing order so answer will be

**962 – 13 = 949.**

**Multiplication/ division**

*In this pattern, a certain number is multiplied or divided with the previous number to get next number in the series.*

**Example : 15, 30, 60, 120, 240**

15*2 = 30

30 *2= 60

60*2 = 120

120*2 = 240

30 *2= 60

60*2 = 120

120*2 = 240

**Example : 5172, 2536, 1268, 634, 317**

5172÷2=2536

2536÷2=1268

1268÷2=634

634÷2=317

*If you are not able to find the pattern by observing the question, you have to follow the below procedures*

**(From here real problems start , no need to panic for that , patiently**

*Difficulty level – moderate*understand the procedure and try to solve , it will be easy while you are scrolling down.)

In such type of questions, we have to find the difference between consecutive numbers Difference between consecutive numbers will follow a pattern (consecutive addition/subtraction or multiplication/division).

**Example 1: 30, 46, 78, 126, 190, 270, ?**

Difference between 30 & 46 is 16

Difference between 46 & 78 is 32

Difference between 78 & 126 is 48

Difference between 126 & 190 is 64

Difference between 190 & 270 is 80

Here the differences are all multiples of 16 i.e. (16*1), (16*2), (16*3), (16*4), (16*5), so obviously the next number will be (16*6).

So in series the next number will be addition of (16*6 =) 96 therefore the answer is 270+96 = 366

**Example 2: 17, 20, 26, 38, 62, 110**

Find the difference between the numbers, and the differences are

Difference between 17 & 20 = 3

Difference between 20 & 26 = 6 (3*2)

Difference between 26 & 38 = 12 (6*2)

Difference between 38 & 62 = 24 (12*2)

Difference between 62 & 110 = 48 (24*2)

**Example 3: 1250, 500, 200, 80, 32, 12.8, ?**Whenever you see a decimal number in series, your guess for the number should be a decimal digit or division process Here too a decimal number is multiplied or divided to form this series.

1250÷2.5 = 500

500÷2.5=200

200÷2.5= 80

80÷2.5=32

32÷2.5=12.8

12.8÷2.5=5.12

**Example 4: 23, 26, 24, 27, 25, 28, ?**In this problem, numbers are increasing and decreasing and the variations are also small, therefore both addition and subtraction operations can take place.

23+3=26

26-2=24

24+3=27

27-2=25

25+3=28

28-2=26

**Difficulty level : hard**

If difference between consecutive numbers do not follow any patterns , try these patterns

(there is no need to by heart all this pattern , just know how the patterns can be in the series this will make easy to guess the pattern for you)

For series

**a, b, c, d, e, f,**the pattern will be any one of these following patterns.

TIPS:To find the pattern try this technique.

Multiply the number before last number with 2 and compare the resultant number with the last number

- a) If the resultant number is greater than the last number then it will be the addition or subtraction of square/cube of number i.e. pattern(I).
- b) If the resultant number is less than the last number and difference is large, then the pattern will be any of these (II) or (III) or (IV) or (V)
- c) If the resultant number is less than the last number but difference is small it belongs to (VI).

Solving these problems will make you understand better.

**Example 1: 3, 732, 1244, 1587, 1803, 1928, ?**

**Step 1:**1803*2 = 3606 >1928 therefore it will be pattern (I)

**Step 2:**Now find the difference between the two numbers consecutively

difference between 3&732 = 729 i.e. 93

difference between 732&1244 = 512 i.e.83

difference between 1244&1587 = 343 i.e. 73

difference between 1587&1803 = 216 i.e. 63

difference between 1803&1928 = 125 i.e. 53

obviously next will be addition of 43+ 1928 = 1992

**Example 2: 13, 25, 61, 121, 205, ?**

**Step 1:**121*2>205 and variation is small , so it will follow pattern (I)

**Step 2:**Difference between 13 & 25 = 12

difference between 25 & 61 = 36 (12*3)

difference between 61 & 121 = 60 (12*5)

difference between 121 & 205 = 84 (12*7)

Obviously next number in series will be addition of 108(12*9) with 205 = 313

1*2 + 2*2 = 6

6*4+3*4=36

36*6+4*6=240

240*8 +5*8 =1960 so 1960*10+6*10=19660

376*5=1880 adding 5 we get correct number 1885

So pattern is 376*5+5=1885

13*1+1=14

14*2+2=30

Answer will be 1885*6+6=11316

173*2+11=357

12*2+11=35

Answer will be 357*2+11=725

Number series is a vast topic , there always an exception cases .)

If the numbers in the series are increasing and decreasing and a decimal numbers are in the series then you can guess decimal numbers playing in this series

7*0.5 + 0.5 = 4

4*1+1=5

5*1.5+1.5 = 9

9*2+2 = 20

20*2.5+2.5 =52.5

**Example 3: 1, 6, 36, 240, 1960, ?**

**Step 1:**240*2<1960 and the variation is large too, so the pattern will be either (II) or (III) or (IV) or (V)

**Step 2:**Now use the trial and error method but don’t apply it to whole series use it in any of the two numbers.

1*2 + 2*2 = 6

6*4+3*4=36

36*6+4*6=240

240*8 +5*8 =1960 so 1960*10+6*10=19660

__Example 4:__13, 14, 30, 93, 376, 1885, ?**Step 1.**376*2<1885 and the variation is also large, so the pattern will be (II) or (III) or (IV) or (V)

**Step 2.**Use the trial and error method and find the pattern, it is wise to check in last two numbers.

376*5=1880 adding 5 we get correct number 1885

So pattern is 376*5+5=1885

13*1+1=14

14*2+2=30

Answer will be 1885*6+6=11316

**Example 5: 12, 35, 81, 173, 357, ?**

**Step 1.**173*2<357 and the variation is small so it will follow pattern (VI).

**Step 2.**173*2=346 to get 357 add 11 .

**Pattern is**

173*2+11=357

12*2+11=35

Answer will be 357*2+11=725

**Miscellaneous**

**Example : 7, 4, 5, 9, ? , 52.5, 160.5**If the numbers in the series are increasing and decreasing and a decimal numbers are in the series then you can guess decimal numbers playing in this series

7*0.5 + 0.5 = 4

4*1+1=5

5*1.5+1.5 = 9

9*2+2 = 20

20*2.5+2.5 =52.5

**Example: 120 15 105 17.5 87.5 ?**

120÷8 =15

15*7=105

105÷6=17.5

17.5*5=87.5

87.5÷4=21.875

**Example: 3 6 21 28 55 66 ? 120**

Difference between 3&6 is 3

Difference between 21&28 is 7

Difference between 55& 66 is 11

Difference between ? & 120 is 15 therefore the number is 105

**That’s all about number series hope you have get some idea, practice some more number series problem it will increase your speed in guessing the pattern .**

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**IBTS**

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**Call :- ****9316488822 / 88821**

India's Leading Institution for Competitive Exams in Chandigarh

**Call :-**

**9316488822 / 88821**

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