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

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

Then,

- Both A and B are false
- A is true but B is false
- A is false but B is true
- Both A and B are true