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Worked Examples

Example-1

Description: 82011.png

Solution

Observe the numbers in the opposite sectors of the circle.

 

They are of the form n, n2 + 5.

 

30 = 52 + 5; 41 = 62 + 5. So, the missing number is 72 + 5 = 54.

 

Answer: 54
 

 

Example-2

Description: 82021.png

Solution

On analysing the pattern of numbers in the first figure, we notice that the number inside the triangle is related to the numbers at the vertices by the following formula:

 

Formula: Description: 82033.png

 

By applying the same formula, we can find the number inside the second triangle.

 

Description: 82068.png

 

Answer: 10
 

 

Example-3

Description: 82077.png

Solution

We notice that the outer square is divided into four equal smaller squares and each such smaller square contains three numbers. These three numbers are related as given below:

 

15 × 10 ÷ 2 = 75

 

14 × 17 ÷ 2 = 119

 

16 × 12 ÷ 2 = 96

 

By applying the same formula, we can find the missing number.

 

18 × 11 ÷ 2 = 99

 

Answer: 99
 

 

Example-4

Description: 82122.png

Solution

Each of the four smaller squares contains three numbers. The innermost number is half the square of the sum of the numbers that are outside.

 

5 + 11 = 16; 162 = 256 256 ÷ 2 = 128

 

9 + 5 = 14; 142 = 196 196 ÷ 2 = 98

 

11 + 7 = 18; 182 = 324 324 ÷ 2 = 162

 

8 + 4 = 12; 122 = 144 144 ÷ 2 = 72

 

Answer: 72
 

 

Example-5

Description: 82152.png

Solution

The number in the inner small square is twice the sum of the square roots of the outer numbers.

 

Description: 82176.png18 × 2 = 36

 

Description: 82183.png11 × 2 = 22

 

Description: 82190.png14 × 2 = 28

 

Description: 82199.png17 × 2 = 34

 

Answer: 34
 

 

Example-6

Description: 82215.png

Solution

Consider the numbers at the ends of each straight line segments. They are related to each other as under:

 

4 × 3 = 12

 

6 × 4 = 24

 

7 × 5 = 35

 

9 × 6 = 54

 

Answer: 54
 

 

Example-7

Description: 82243.png

Solution

Add the outer numbers in the bigger circle and multiply the sum by the number at the top to obtain the number inside the small circle.

 

(7 + 5 + 4) × 7 = 16 × 7 = 112

 

Similarly, (8 + 3 + 6) × 8 = 17 × 8 = 136

 

Answer: 136
 

 

Example-8

Description: 82255.png

Solution

The number inside the circle is the square root of the sum of all the numbers that are outside.

 

14 + 17 + 9 + 6 + 11 + 7 = 64; Description: 82263.png = 8

 

12 + 9 + 14 + 15 + 13 + 18 = 81; Description: 82272.png = 9

 

Answer: 9
 

 

Example-9

Description: 82282.png

Solution

Observe the numbers in the opposite segments of the hexagon. They follow the pattern n, n3.

3, 33 = 27 5, 53 = 125 6, 63 = 216

 

Similarly, 4, 43 = 64 7, 73 = 343 8, 83 = 512

 

Answer: 512
 

 

Example-10

Description: 82295.png

Solution

The numbers in the opposite segments of the circle follow the pattern n, n3 + 1.

 

3, 33 + 1 = 28; 5, 53 + 1 = 126

 

2, 23 + 1 = 9

 

Similarly, 4, 43 + 1 = 65; 8, 83 + 1 = 513

 

7, 73 + 1 = 344

 

Answer: 344
 





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