CAT 2018 [SLOT 2] Quant Question with Solution 24

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

  1. −32
  2. 48
  3. 64
  4. 16
Show Answer
Correct Answer: 3
Let a and b be the two numbers.
We know that for any two numbers $A M \geq G M$
$\Rightarrow \frac{a^{2}+b^{2}}{2} \geq a b$
$a b \leq \frac{97}{2}$
$a b \leq 48.5$
Among the options, only 64 is greater than 48.5

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