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Worked Examples: Type-I

In this type of problems, the numbers in each row or in each column follow a particular rule or pattern.
 

Example-1

7

6

21

8

5

20

12

4

____

a

b

c

Solution

In this problem, we observe that in each row the last number is half the product of the first two numbers.

 

Formula: Description: 76603.png

 

7 × 6 = 42; 42 ÷ 2 = 21

 

8 × 5 = 40; 40 ÷ 2 = 20

 

12 × 4 = 48; 48 ÷ 2 = 24

 

Answer: 24
 

 

Example-2

7

5

6

a

6

3

4

b

26

16

____

c

Solution

In this example, consider the numbers in each column. The last number in each vertical column is twice the sum of the first two numbers.

 

Formula: (a + b) × 2 = c

 

2 (7 + 6) = 2 (13) = 26

 

2 (5 + 3) = 2 (8) = 16

 

2 (6 + 4) = 2 (10) = 20

 

Answer: 20
 

 

Example-3

24

6

8

12

4

____

16

2

16

Solution

Divide the first number of each row by the second number and multiply the quotient by 2 to get the third number.

 

Formula: a ÷ b × 2 = c

 

24 ÷ 6 × 2 = 8

 

12 ÷ 4 × 2 = 6

 

16 ÷ 2 × 2 = 16

 

Answer: 6
 

 

Example-4

7

4

121

5

8

169

8

6

____

Solution

The third number in each row is the square of the sum of the first two numbers.

 

Formula: (a + b)2 = c

 

7 + 4 = 11; 112 = 121

 

5 + 8 = 13; 132 = 169

 

8 + 6 = 14; 142 = 196

 

Answer: 196
 

 

Example-5

25

12

49

81

13

16

36

14

____

Solution

Observe the numbers in each row. The middle number in each row is the sum of the square roots of the first number and the last number.

 

Description: 76692.png

 

The same relation can be written in the following form also.

 

Description: 76702.png

 

(12 – Description: 76715.png)2 = (12 – 5)2 = 72 = 49

 

(13 – Description: 76719.png)2 = (13 – 9)2 = 42 = 16

 

(14 – Description: 76734.png)2 = (14 – 6)2 = 82 = 64

 

Answer: 64

 

Example-6

7

6

8

9

8

4

10

4

____

Solution

In this example, the sum of the numbers in each horizontal row is 21.

 

7 + 6 + 8 = 21

 

9 + 8 + 4 = 21

 

10 + 4 + 7 = 21

 

Answer: 7
 

 

Example-7

1

2

4

6

1

4

16

36

3

5

7

8

8

24

____

63

Solution

The numbers in the second row are formed by squaring the numbers in the first row. The numbers in the fourth row are formed by squaring the numbers in the third row and subtracting 1.

 

12 = 1; 22 = 4; 42 = 16; 62 = 36 → 1st and 2nd row numbers.

 

32 – 1 = 8; 52 – 1 = 24; 72 – 1 = 48; 82 – 1 = 63 → 3rd and 4th row numbers.

 

Answer: 48
 

 

Example-8

32

35

39

13

17

22

41

46

____

Solution

In the first row, the numbers are increased by 3 and 4. In the second row, they are increased by 4 and 5.

 

Hence, in the third row they must increase by 5 and 6.

 

32

+

3

=

35;

35

+

4

=

39

13

+

4

=

17;

17

+

5

=

22

41

+

5

=

46;

46

+

6

=

52

 

Answer: 52
 

 

Example-9

4

3

50

6

5

122

7

9

____

Solution

Add the first and second number of each row, square the sum, and add 1 to it. You get the last number in the row.

 

Formula: (a + b)2 + 1 = c

 

4 + 3 = 7; 72 = 49; 49 + 1 = 50

 

6 + 5 = 11; 112 = 121; 121 + 1 = 122

 

7 + 9 = 16; 162 = 256; 256 + 1 = 257

 

Answer: 257
 

 

Example-10

5

7

74

8

4

80

6

9

____

Solution

The third number of each row is the sum of the squares of the first and second numbers.

 

Formula: a2 + b2 = c

 

52 + 72 = 25 + 49 = 74

82 + 42 = 64 + 16 = 80

62 + 92 = 36 + 81 = 117

 

Answer: 117
 

 

Example-11

6

9

135

5

7

76

8

11

____

Solution

The third number in each row is the difference between the cube of the first number and the square of the second number.

 

Formula: a3 – b2 = c

 

63 = 216; 92 = 81; 216 – 81 = 135

 

53 = 125; 72 = 49; 125 – 49 = 76

 

83 = 512; 112 = 121; 512 – 121 = 391

 

Answer: 391
 

 

Example-12

13

37

71

11

49

24

96

13

52

43

____

14

Solution

The fourth number in each row is the square root of the sum of the first three numbers.

Description: 76829.png

 

13 + 37 + 71 = 121; Description: 76843.png = 11

 

49 + 24 + 96 = 169; Description: 76864.png = 13

 

52 + 43 + x = 95 + x; Description: 76871.png = 14

 

So, 95 + x = 196 i.e., x = 196 - 95 = 101

 

Answer: 101
 





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