M7MBA wrote: ↑Fri Jun 05, 2020 7:55 am
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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