# Number Series

This is one of the most important topic for SSC, Railways and as well as for banking examinations. Here, mostly questions will be asked on some standard logic.

* Square, Square root

Cube, Cube root

* Sum, Difference

* Product, Division

* Double difference

* Fractions

* Binomial series

* Decreasing / Increasing series

1. 10, 12, 18, 42, 162, ?

A) 216   B) 416    C) 325    D) 882

Sol: Here, in the given series, all the numbers are some what close to each other. whenever all the numbers are close, the first logic we should check is difference. If we observe the differences

they are like 2! = 2, 3! = 6, 4! = 24 and 5! = 120, so the next difference must be,

6 factorial = 6! = 720

next number = 162 + 720 = 882

Ans: D

2. 2, 8, 28, 102, 432, ?

A) 600    B) 1820     C) 2190    D) 2560

Sol: If we observe, here the first and last numbers are somewhere far away, so more chance is there for multiplication logic. 432 × 5 + 30 = 2190

Ans: C

3. 0, 1, 8, 54, 384, ?

A) 620    B) 2560     C) 3000     D) 3200

Sol: Here the logic is

0! × 0 2 = 0

1! × 1 2 = 1

2! × 2 2 = 8

3! × 3 2 = 54

4! × 4 2 = 384

the next number is 5! × 5 2 = 3000

Ans: C

4. 8, 3, 0, −1, 0, ?

A) 0    B) 1   C) 2    D) 3

Sol: Here, as the numbers are close to each other, we can go with the difference logic. Required number = 3 − 0 = 3

Ans: D

5. 26, 34, ?, 50, −6, 66

A) 25    B) 10    C) 16    D) 15

Sol: It is like increasing, decreasing series and all the numbers are close to each other, so addition and subtraction logic.

26 + (+ 8) = 34

34 + (− 24) = 10

10 + (+ 40) = 50

Odd multiple of 8

50 + (− 56) = − 6

− 6 + (+ 72) = 66

Ans: B

6. 196, 194, 198, 190, ?

A) 196    B) 200   C) 204    D) 206

Sol: It is also increasing / decreasing series ⇒ 190 + 16 = 206

Ans: D

7. 32, ?, 1024, 2048, 2048

A) 128   B) 256   C) 512    D) 24

Sol: Here, the first number and last numbers are some where for away. so, it must be based on multiplication logic.

32 × 8 = 256

256 × 4 = 1024

1024 × 2 = 2048

2048 × 1 = 2048

Ans: B

8. 8, 4, 4, 8, 32, ?

A) 16    B) 64    C) 128    D) 256

Sol: It is a kind of decreasing and there after continuously increasing series. so, first number must be multiplied by a number which is less then one.

8 × 0.5 = 4

4 × 1 = 4

4 × 2 = 8

8 × 4 = 32

32 × 8 = 256

Ans: D

9. 15, 5, 4.5, 5.8, 7.9, ?

A) 9.25    B) 10.74    C) 6.25    D) 8.56

Sol: If we observe, this series is in decreasing manner in the starting and there after increasing.

15 × 0.2 + 2 = 5

5 × 0.3 + 3 =4.5

4.5 × 0.4 + 4 = 5.8

5.8 × 0.5 + 5 = 7.9

7.9 × 0.6 + 0.6 = 10.74

Ans: B

10. 96, 320, 800, 1600, ?

A) 1000   B) 1200    C) 2666.7   D) 3201.6

Sol: Here the logic is Ans: C

11. 110, ?, 42, 20, 6

A) 72    B) 80    C) 65    D) 50

Sol: If we observe the series, all the numbers are close to square numbers

112 − 11 = 110

92 − 9 = 72

72 − 7 = 42

52 − 5 = 20

32 − 3 = 6

Ans: A Sol: This series is having mixed fractions and numbers are close to each other. First convent the mixed fractions into improper fractions. Ans: C

13. 9, 15, 24, 39, 63, ?

A) 85    B) 91    C) 99    D) 105

Sol: Here as all the numbers are close to each other, we can go with the difference logic. next number = 63 + 36 = 99

Ans: C

14. 18900, 4200, 1200, 480, ?

A) 360   B) 320    C) 240    D) 120

Sol: Here, after observing the first and last terms, it is clear that the series is based on division logic Ans: B

15. 17, 19, 28, 92, ?

A) 126    B) 257    C) 625     D) 717

Sol: Here, as all the numbers are close to each other.

We can go with the differce logic. ⇒ next number = 92 + 625 = 717

Ans: D

16. 71, 88, 113, 150, 203, ?

A) 300   B) 276    C) 216   D) 285

Sol: If we observe this series, all the numbers are close ti each other. So, the series must be based on difference logic ⇒ Next number = 203 + 73 = 276

Ans: B

17. 3, 5, 17, 97, 769, ?

A) 7681    B) 3691    C) 5721    D) 4326

Sol: Here, if we observe the starting and last numbers, they have a big difference between them, so the series is based on difference logic.

3 × 2 − 1 = 5

5 × 4 − 3 = 17

17 × 6 − 5 = 97

97 × 8 − 7 = 769

⇒ 769 × 10 − 9 = 7681

Ans: A

18. 2, 1, 1, 2, 8, ?

A) 4    B) 16    C) 64    D) 18

Sol: Here, the series in the starting decreased and there after it keeps on increasing. So, initially it should be multiplied by a number which is less than one.

2 × 0.5 = 1

1 × 1 = 1

1 × 2 = 2

2 × 4 = 8

8 × 8 = 64

Ans: C

19. 2, 1, 1, 2, 4, ?

A) 4   B) 6    C) 8    D) 7

Sol: This is also same as above series almost, but here the previous logic fails. So, as the numbers are close to each other, we can go with the difference logic ⇒ Next number = 4 + 3 = 7

Ans: D

20. 33, 165, 825, ?, 20625

A) 3605   B) 4125   C) 5625   D) 3160

Sol: Here, the difference between the starting and ending numbers is more, so, we can go with the product logic. 33 × 5 = 165;        165 × 5 = 825

825 × 5 = 4125;        4125 × 5 = 20625

Ans: B

21. 1716, 990, 504, 210, 60, ?

A) 12    B) 8    C) 6    D) 10

Sol: Here, if we observe clearly all the numbers are close to cubes.

​​​​​​​123 − 12 = 1716;     103 − 10 = 990

8 3 − 8 = 504;          63 − 6 = 210

4 3 − 4 = 60

2 3 − 2 = 6

Ans: C

Posted Date : 02-03-2023

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