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CAT 2003 | Question: 2-61

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Let $n (>1)$ be a composite integer such that $\sqrt{n}$ is not an integer. Consider the following statements

  1. $n$ has a perfect integer–valued divisor which is greater than $1$ and less than $\sqrt{n}$.
  2. $n$ has a perfect integer–valued divisor which is greater than $\sqrt{n}$ but less than $n.$

Then,

  1. Both A and B are false
  2. A is true but B is false
  3. A is false but B is true
  4. Both A and B are true
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