If \(q\) is a positive integer, is \(p\frac{q}{\sqrt{q}}\) an integer?

[M7MBA]

If \(q\) is a positive integer, is \(p\frac{q}{\sqrt{q}}\) an integer?

(1) \(q=p^2\)

(2) \(p\) is a positive integer

[spoiler]OA=A[/spoiler]

Source: GMAT Club Tests

[Jay@ManhattanReview]

If \(q\) is a positive integer, is \(p\frac{q}{\sqrt{q}}\) an integer?

(1) \(q=p^2\)

(2) \(p\) is a positive integer

[spoiler]OA=A[/spoiler]

Source: GMAT Club Tests

So, we have \(p\frac{q}{\sqrt{q}}=p\sqrt q\).

So, the question is: Is \(p\sqrt q\) an integer?

(1) \(q=p^2\)

Given that \(q=p^2\), we see that \(p\sqrt q\) becomes \(p\times p = p^2 = q\) = an integer. Sufficient.

(2) \(p\) is a positive integer.

This information is of no use. \(p\sqrt q\) would be an integer if \(q\) is an integer, but we do not have that information.

Correct answer: A

Hope this helps!

-Jay
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