reasoning-number-series-theory

 NUMBER SERIES

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

1. 120, 99, 80, 63, 48, ?

A.35

B.38

C.39

D.40

Answer: Option A

Explanation:

The pattern is - 21, - 19, - 17, - 15,.....

So, missing term = 48 - 13 = 35.

2.589654237, 89654237, 8965423, 965423, ?

A.58965

B.65423

C.89654

D.96542

Answer: Option D

Explanation:

The digits are removed one by one from the beginning and the end in order alternately

so as to obtain the subsequent terms of the series.

3. 3, 10, 101,?

A.10101

B.10201

C.10202

D.11012

Answer: Option C

Explanation:

Each term in the series is obtained by adding 1 to the square of the preceding term.

So, missing term = (101)² + 1 = 10202.

4. In the series 2, 6, 18, 54, ...... what will be the 8th term ?

A.4370

B.4374

C.7443

D.7434

Answer: Option B

Explanation:

Clearly, 2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54,.....

So, the series is a G.P. in which a = 2, r = 3.

Therefore 8th term = ar^8-1 = ar⁷ = 2 x 3⁷ = (2 x 2187) = 4374.

5. 125,80,45,20,?

A.5

B.8

C.10

D.12

Answer: Option A

Explanation:

The pattern is - 45, - 35, - 25, .....

So, missing term = 20 - 15 = 5.

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

6. 1, 1, 4, 8, 9, 27, 16, ?

A.32

B.64

C.81

D.256

Answer: Option B

Explanation:

The series consists of squares and cubes of consecutive natural numbers i.e. 1², 1³, 2², 2³, 3², 3³, 4², .....

So, missing term = 4³ = 64.

7. 1, 2, 3, 6, 9, 18, ?, 54

A.18

B.27

C.36

D.81

Answer: Option B

Explanation:

The pattern is x 2, x 3/2, x 2, x 3/2, x 2,.....

So, missing term = 18 x 3/2 = 27.

8. 6, 13, 25, 51, 101, ?

A.201

B.202

C.203

D.205

Answer: Option C

Explanation:

The pattern is x 2 + 1, x 2 - 1, x 2 + 1, x 2 - 1,.....

So, missing term = 101 x 2 + 1 = 203.

9. 0, 4, 6, 3, 7, 9, 6, ?, 12

A.8

B.10

C.11

D.14

Answer: Option B

Explanation:

The given sequence is a combination of three series :

I. 0, 3, 6 II.4,7,? III. 6, 9, 12

The pattern in each of these series is' + 3. So, missing term = 7 + 3 = 10.

10. 105, 165, 195, 255, 285, 345, ?

A.395

B.390

C.420

D.435

Answer: Option D

Explanation:

Each number of the series is 15 multiplied by a prime number i.e. 15 x 7, 15 x 11, 15 x 13,

15 x 17, 15 x 19, 15 x 23,.....

So, missing term = 15 x 29 = 435.

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

11. 5,6,9, 15, ?, 40

A.21

B.25

C.27

D.33

Answer: Option B

Explanation:

The pattern is + 1, + 3, + 6,....., i.e. + 1, + (1, + 2), + (1 + 2 + 3),.....

So, missing term = 15 + (1 + 2 + 3 + 4) = 25.

12. 1, 3, 4, 8, 15, 27, ?

A.37

B. 44

C.50

D.55

Answer: Option C

Explanation:

The sum of any three consecutive terms of the series gives the next term.

So, missing number = 8 + 15 + 27 = 50.

13.3, 4, 7, 7, 13, 13, 21, 22, 31, 34, ?

A.42

B.43

C.51

D.52

Answer: Option B

Explanation:

The given sequence is a combination of two series :

I. 3, 7, 13, 21, 31, ? and II. 4, 7, 13, 22, 34

The pattern in I is + 4, + 6, + 8, + 10,.....

The pattern in II is + 3, + 6, + 9, + 12,.....

So, missing term = 31 + 12 = 43.

14. 198, 194, 185, 169, ?

A.92

B.112

C.136

D.144

Answer: Option D

Explanation:

The pattern is - 4, - 9, - 16,.....i.e. - 2², - 3², - 4²,.....

So, missing pattern = 169 - 52 = 169 - 25 = 144.

15. 2, 3, 5,7,11,?, 17

A.12

B.13

C.14

D.15

Answer: Option B

Explanation:

Clearly, the given series consists of prime numbers starting from 2. So, the missing

term is the prime number after 11, which is 13.