(1) \(\sqrt{x^2}\) is an integer. --> x is an integer. But we don't know whether x is positive or negative. --> Not sufficient.

Number plugging:

If \(\sqrt{3^2}= 3\) --> \(x=3\) --> Yes.

If \(\sqrt{(-3)^2}= 3\) --> \(x=-3\) --> No.

(2) \(\sqrt{x^2} = x\) --> x is positive. But we don't know whether x is integer. --> Not sufficient.

Number plugging:

If \(\sqrt{3^2}= 3\) --> \(x=3\) --> Yes.

If \(\sqrt[]{(\sqrt[]{3})^{2}} = \sqrt[]{3}\) --> \(x=\sqrt[]{3}\) --> No.

(1) + (2): x is an integer AND x is positive.--> Yes --> Sufficient.

Answer C.

Harshgmat wrote:

If \(x^2\) is a positive integer, is \(x\) a positive integer?

(1) \(\sqrt{x^2}\) is an integer.

(2) \(\sqrt{x^2} = x\)

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