Sequence and Series Questions and Solutions : Logical Reasoning

1.

Which number would replace underline mark in the series? 
2, 5, 10, 17, ---, 37

   A.) 27
   B.) 24
   C.) 26
   D.) 28

Answer: Option 'C'

Here the difference between the consecutive terms is increase by 2 
5 - 2 = 3, 
10 - 5 = 5, 
17 - 10 = 7, 
then 17 + 9 = 26.

2.

Which number would replace underline mark in the series?
1, 6, 26,_____, 426.

   A.) 86
   B.) 76
   C.) 106
   D.) 96

Answer: Option 'C'

Here the difference between the consecutive terms is multiplied by 4. 
The difference of the two consecutive numbers is 5, 20, ..... 
5 × 4 = 20 
20 × 4 = 80 
26 + 80 = 106.

3.

Which number would replace underline mark in the series?
1, 20, 58, ____, 191.

   A.) 105
   B.) 115
   C.) 111
   D.) 116

Answer: Option 'B'

Here the difference between the two consecutive terms is 19, 38, 57, 76 
58 + 57 = 115

4.

2, 10, 40, 120,____

   A.) 240
   B.) 360
   C.) 470
   D.) 210

Answer: Option 'A'

Here the series is a multiplication series.
The order of the multiplication is ×5, ×4, ×3, ×2 
120 × 2 = 240

5.

18 21 25 18 29 33 18
What numbers should come next ?

   A.) 43 18
   B.) 41 44
   C.) 37 41
   D.) 38 41

Answer: Option 'C'

This is a simple addition series with a random number, 18, interpolated as every third number.
In the series, 4 is added to each number except 18, to arrive at the next number

6.

20 20 17 17 14 14 11 What numbers should come next ?

   A.) 8 8
   B.) 8 9
   C.) 11 8
   D.) 8 9s

Answer: Option 'C'

This is a simple subtraction with repetition series.
It begins with 20, which is repeated, then 3 is subtracted, resulting in 17, which is repeated, and so on.
Rule = (1st no) (1st no) (1st no - 3 = 2nd no) (2nd no repeat) (2nd no - 3 = 3rd no) (3rd no repeat). . .
Now (20) (20) (20 - 3 = 17) (17) (17 - 3 = 14) (14) (14 - 3 = 11) (11) (11 - 3 = 8) (8)
So the answer is e = 11 8.

7.

3 13 18 23 28 33
What number should come next?

   A.) 38 43
   B.) 37 42
   C.) 38 44
   D.) 39 44

Answer: Option 'A'

In this simple addition series, each number is 5 greater than the previous number.
Rule = (1st no) (1st no + 5 = 2nd no) (2nd no + 5 = 3rd no) . . .
Now (3) (3 + 5 = 8) (8 + 5 = 13) (13 + 5 = 18) (18 + 5 = 23) (23 + 5 = 28) (28 + 5 = 33) (33 + 5 = 38) (38 + 5 = 43)
So the answer is c = 38 43

8.

Look at this series: 1000, 200, 40, . . . 
What number should come next?

   A.) 10
   B.) 8
   C.) 9
   D.) 12

Answer: Option 'B'

This is a simple division series.
Each number is divided by 5.
Rule = (1st number / 5 = 2nd number) (2nd number / 5 = 3rd number)....
Now, (1000 / 5 = 200), (200 / 5 = 40), (40 / 5 = 8)...
So answer is a = 8.

9.

Look at this series: 7, 10, 8, 11, 9, 12, . . . 
What number should come next?

   A.) 7
   B.) 10
   C.) 15
   D.) 18

Answer: Option 'B'

This is a simple alternating addition and subtraction series.
In the first pattern, 3 is added;
In the second pattern, 2 is subtracted.
Rule =(1st number) (1st number + 3 = 2nd number) (2nd number - 2 = 3rd number) (3rd number + 3 = 4th number)
Now (7) (7 + 3 = 10) (10 - 2 = 8) (8 + 3 = 11) (11 - 2 = 9) (9 + 3 = 12) (12 - 2 = 10)...
So the answer is b = 10.

10.

1, 2, 3, 10, ____, 9802

   A.) 199
   B.) 999
   C.) 99
   D.) 298

Answer: Option 'C'

12 + 1 = 2

22 - 1 = 3

32 + 1 = 10

102 - 1 = 99.

11.

2, 10, 26, 50, ___, 122.

   A.) 82
   B.) 90
   C.) 80
   D.) 62

Answer: Option 'A'

Here the series of the form (12 + 1), (32 + 1), (52 + 1), .......

12.

Look at this series: 14, 28, 20, 40, 32, 64, . . .
What number should come next ?

   A.) 52
   B.) 56
   C.) 86
   D.) 98

Answer: Option 'B'

This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
Rule = (1st no.) (1st x 2 = 2nd no.) (2nd - 8 = 3rd no.) (3rd x 2 = 4th no.)....
Now (14) (14 x 2 = 28) (28 - 8 = 20) (20 x 2 = 40) (40 - 8 = 32) (32 x 2 = 64) (64 - 8 = 56)...
So the answer is b = 56.

13.

Look at this series: 5.2, 4.8, 4.4, 4, . . . 
What number should come next?

   A.) 3
   B.) 3.6
   C.) 3.5
   D.) 3.3

Answer: Option 'B'

In this simple subtraction series, each number decreases by 0.4.
Rule = (1st no.) (1st no. - 0.4 = 2nd no.) (2nd no. - 0.4 = 3rd number)...
Now (5.2) (5.2 - 0.4 = 4.8) (4.8 - 0.4 = 4.4) (4.4 - 0.4 = 4) (4 - 0.4 = 3.6) ...
So the answer is d = 3.6

14.

84 78 72 66 60 54 48
What number should come next ?

   A.) 44 34
   B.) 42 36
   C.) 42 32
   D.) 40 34

Answer: Option 'B'

In this simple subtraction series, each number is 6 less than the previous number.
Rule = (1st number) (1st no - 6 = 2nd no.) (2nd no - 6 = 3rd no). . .
Now (84) (84 - 6 = 78) (78 - 6 = 72) (72 - 6 = 66) (66 - 6 = 60) (60 - 6 = 54) (54 - 6 = 48) (48 - 6 = 42) (42 - 6 = 36).
So the answer is b = 42 36

15.

Look at this series: 3, 4, 7, 8, 11, 12, . . . 
What number should come next ?

   A.) 7
   B.) 10
   C.) 15
   D.) 20

Answer: Option 'C'

This alternating addition series begins with 3;
then 1 is added to give 4;
then 3 is added to give 7;
then 1 is added, and so on.
Rule = (first number + 1) (second number + 3) (third number + 1) (fourth number + 3)...
Now The series is 3, 4, 7, 8, 11, 12...
(3 + 1 = 4), (4 + 3 = 7), (7 + 1 = 8), (8 + 3 = 11), (11 + 1 = 12) (12 + 3 = 15)...
So the answer is d = 15.

16.

Look at this series: 31, 29, 24, 22, 17, . . . 
What number should come next?

   A.) 15
   B.) 14
   C.) 13
   D.) 12

Answer: Option 'A'

This is a simple alternating subtraction series, which subtracts 2, then 5.
Rule = (first number - 2) (second number - 5) (third number - 2) (fourth number - 5)...
Now The series is 31, 29, 24, 22, 17, . . . 
(31 - 2 = 29), (29 - 5 = 24), (24 - 2 = 22), (22 - 5 = 17), (17 - 2 = 15)...
So the answer is a = 15.

17.

Find the wrong number in the series. 
1, 2, 6, 15, 31, 56, 91

   A.) 31
   B.) 71
   C.) 81
   D.) 91

Answer: Option 'D'

The difference odd the two consecutive numbers are
1, 4, 9, 16, 25, 35.
+12, +22, +32,+42,+52,+62
Here 35 is is wrong. wrong answer 91

18.

Find the wrong number in the series. 
2, 5, 10, 17, 26, 37, 50, 64

   A.) 5
   B.) 26
   C.) 64
   D.) 17

Answer: Option 'C'

12 + 1, 22 + 1, 32 + 1 ..........82 + 1 = 65

But 64 has been given here. So our wrong number is 64

19.

Find the missing number in the following series. 
512, 256, 64, 32, ?

   A.) 16
   B.) 4
   C.) 8
   D.) 10

Answer: Option 'C'

512/2 = 256 
256/4 = 64 
64/2 = 32 
32/4 = 8.

20.

Find the missing number in the following series. 
2, 3, 6, 15, 45, ?

   A.) 95
   B.) 105.5
   C.) 147
   D.) 157.5

Answer: Option 'D'

2 × 1.5 = 3 
3 × 2 = 6 
6 × 2.5 = 15 
15 × 3 = 45 
45 × 3.5 = 157.5


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