# CAT 2018 Quant Questions

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

 −32 48 64 16
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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 ${(a - b)^2}$ $\ge$ 0

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

$\Rightarrow$ ab $\le$ 48.5

Hence, ab $\ne$ 64.

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