CAT 2018

Slot 1

QA

Question & Solution

We know that one of the 3 numbers is 37.
Let the product of the other 2 numbers be x.
It has been given that 73x-37x = 720
36x = 720
x = 20

Product of 2 real numbers is 20. 
We have to find the minimum possible value of the sum of the squares of the 2 numbers. 
Let x=a*b
It has been given that a*b=20

The least possible sum for a given product is obtained when the numbers are as close to each other as possible. 
Therefore, when a=b, the value of a and b will be $\sqrt{20}$. ($\sqrt{20}$ is irrational number, but it is a real number)

Sum of the squares of the 2 numbers = 20 + 20 = 40.

Therefore, 40 is the correct answer.