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m02 #20

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Re: m02 #20 [#permalink]

07 Dec 2012, 06:14

ConkergMat wrote:

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

1. q = p^2
2. p is a positive integer

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note: I was not aware how to post the mathematical expression but basically
its a mixed fraction which I translated to math equation.

I believe either the question or explanation might have a typo.

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

(1) q = p^2 --> p=\sqrt{q} --> p\frac{q}{\sqrt{q}}=\sqrt{q}*\frac{q}{\sqrt{q}}=q=integer. Sufficient.

(2) p is a positive integer --> p\frac{q}{\sqrt{q}}=integer*\sqrt{q}. This product may or may not be an integer depending on q. Not sufficient.

Answer: A.
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Re: m02 #20 [#permalink]

07 Dec 2012, 06:32

Yep. Got it.

I guess the funda here is hidden in the Q stem.
Does not matter if the answer is a negative or positive as long as it is an integer.

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Re: m02 #20 [#permalink]

20 Dec 2012, 15:19

the question boils down to P*sqrt(q) is an integer only when p is an integer and q is a perfect sq

Statement 1 - both are satisfied so sufficient
statemnt 2 not sufficient

Answer A

Re: m02 #20 [#permalink] 20 Dec 2012, 15:19

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m02 #20

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