Numbers in Geometrical Figure

Overview:

Numbers are given in different segments of a geometrical figure. One segment is left blank. We are required to analyze the pattern or rule followed by the numbers and find out the number that fits into the blank segment. Some of the problems contain two or more similar geometrical figures, instead of one. In such problems, a blank space is left only in one figure. We are required to analyze and identify the pattern of numbers in the figures where all the segments are filled and apply the same rule to the last figure to find the missing number.

Example with Analysis:

Example 1:

Example 1

Solution:

Observe the numbers in the opposite sector 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

Ans. 54

Example 2: 

Example 2

Solution:10

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

(7 + 5 + 4) x 7 = 16 x 7 = 112
Similarly, (8 + 3 + 6) x 8 = 136

Ans. 136

Example 3: 

Example 3

Solution:

On analyzing 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 : (√25 + √49 + √16) / 2 = 8

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

(√64 + √9 + √81) / 2 = 10

Ans. 10