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CAT 2018 Question Paper (Slot 2) - QUANT Question 18
Question 18

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

Solution

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 $$\neq$$ 64. Therefore, option D is the correct answer.


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