Question

Find the missing number in each of the following question:

4	6	7
5	7	8
41	85	?

A.113
B.114
C.115
D.116

Answer 1

Hint: Here, we will find the missing term in the box. We will find the relation between the numbers in each of the boxes and continue the same relation to find the missing number in the given box. Thus we are using the concept of number analogy to find the missing number.

Complete step-by-step answer:
We are given with a series of numbers in the box.

4	6	7
5	7	8
41	85	?

First, we will consider the relation between the numbers in the columns.
The first term in the first column of the first row is multiplied with the second term in the first column of the second row and the resulting number is multiplied by a number 2 and then the resulting number is added to 1. Thus we will get the third term in the first column of the third row.
\[ \Rightarrow \left( 4 \right) \times \left( 5 \right) = 20 \times \left( 2 \right) = 40 + 1 = 41\]
The first term in the second column of the first row is multiplied with the second term in the second column of the second row and the resulting number is multiplied by a number 2 and then the resulting number is added to 1. Thus we will get the third term in the second column of the third row.
\[ \Rightarrow \left( 6 \right) \times \left( 7 \right) = 42 \times \left( 2 \right) = 84 + 1 = 85\]
Now, we will use the same relation to find the third term in the third column of the third row.
The first term in the third column of the first row is multiplied with the second term in the third column of the second row and the resulting number is multiplied by a number 2 and then the resulting number is added to 1. Thus we will get the third term in the third column of the third row.
\[ \Rightarrow \left( 7 \right) \times \left( 8 \right) = 56 \times \left( 2 \right) = 112 + 1 = 113\]
Therefore, the missing term in the box is 113.
Option (A) is the correct answer.

Note: We should always remember that the relation between the numbers is always the arithmetic operations like addition, subtraction, multiplication and division. When the missing term is in the form of a box, then the relation can be horizontal, vertical or diagonal. The missing term varies if the relation is made in the horizontal and the relation is in the vertical manner and it is not necessary to be the same in all the ways.