CAT 2018

Slot 2

QA

Question & SolutionQues & Sol

If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

Let 'a' and 'b' are those two numbers. 

$\Rightarrow$ $a^2+b^2 = 97$

$\Rightarrow$ $a^2+b^2-2ab = 97-2ab$

$\Rightarrow$ $(a-b)^2 = 97-2ab$

We know that $(a-b)^2$ $\geq$ 0

$\Rightarrow$ 97-2ab $\geq$ 0

$\Rightarrow$ ab $\leq$ 48.5

Hence, ab $ eq$ 64. Therefore, option D is the correct answer.