Loading....
Coupon Accepted Successfully!

 

Worked Examples: Type-II

In this type of problems, the numbers in each row or in each column do not follow any pattern. But the given numbers on a whole follow some pattern or rule. This type of problems can be solved by arranging the given numbers in the ascending order and taking the difference between these numbers, or observing the format, pattern and the rule involved.
 

Example-1

12

47

____

30

3

17

5

38

8

Solution

First, arrange the numbers in the ascending order and then take the difference.

 

Description: 76893.png

 

You can observe that the differences are 2, 3, 4, 5, 13, 8 and 9.

 

If the difference 13 is split into 2 parts as 6 and 7, then you observe that the differences are 2, 3, 4, 5, 6, 7, 8 and 9, which are in arithmetic progression with common difference 1.

 

So, the missing number is 17 + 6 = 23.

 

Answer: 23
 

 

Example-2

2

19

13

7

11

3

23

5

____

Solution

In this example, the numbers are consecutive prime numbers in a jumbled order. The missing prime number in the series is 17.

 

Answer: 17
 

 

Example-3

0

80

24

____

48

35

15

63

3

Solution

Arrange the given numbers in the ascending order.

 

Description: 76932.png

 

You can notice that the differences are 3, 12, 9, 11, 13, 15 and 17. However, between the second and third numbers, the difference is 12. Split this as 5 + 7. The missing number is 3 + 5 = 8 (Verification: 8 + 7 = 15 which is the next number).

 

Answer: 8
 

You can also solve the above problem by applying the algebraic formula, n2 – 1.

 

12 – 1 = 0; 22 – 1 = 3

 

42 – 1 = 15; 52 – 1 = 24

 

62 – 1 = 35; 72 – 1 = 48

 

82 – 1 = 63; 92 – 1 = 80

The missing number is 32 – 1 = 8

 

Answer: 8
 

 

Example-4

2

9

1

3

4

____

1

27

1

Solution

Arrange the numbers in the ascending order.

 

1 1 1 2 3 4 9 27

 

On careful observation, you notice that the formula followed by the numbers is n, n2, n3.

 

That is, 1 12 13 2 22 3 32 33

 

The missing number is 23 = 8.

 

Answer: 8
 


Example-5

10

8

12

9

7

11

8

6

____

Solution

Arrange the numbers in the ascending order.

 

6 7 8 8 9 10 11 12

 

Observe that the first three numbers 6, 7 and 8 are consecutive natural numbers. The next three numbers 8, 9 and 10 are also consecutive natural numbers. Further, 8 has appeared in both these sets of three numbers. By following the same pattern, the next three numbers should be 10, 11, 12. So, the missing number is 10.

 

Answer: 10
 

 

Example-6

20

12

42

6

30

2

____

90

72

Solution

Arrange the numbers in the ascending order.

 

2

6

12

20

30

42

72

90

12 + 1

22 + 2

32 + 3

42 + 4

52 + 5

62 + 6

82 + 8

92 + 9

22 – 2

32 – 3

42 – 4

52 – 5

62 – 6

72 – 7

92 – 9

102 – 10

 

Formula: n2 + n (or) n2 – n

 

The missing number is 72 + 7 (or 82 – 8) = 56

 

Answer: 56
 





Test Your Skills Now!
Take a Quiz now
Reviewer Name