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
Show Answer
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Correct Answer: 3

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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CAT 2018 Quant Questions
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