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Re: If q is a positive integer, is p*q/q^(1/2) an integer? [#permalink]

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16 Nov 2014, 22:20

1) q=p^2 take the square root on both sides p=(sqroot)q

so p*(q/(sqroot)q) = (sqroot)q * q/(sqroot)q = q and from definition we know that q is a positive integer. sufficient

2)p is an integer let p=2 and q=3 then the equation becomes 2 * 3 / (sqroot)3 which is not an integer let p=2 and q=4 then the equations becomes 2 * 4 / (sqroot)4 = 4 which is an integer insufficient

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

(1) \(q = p^2\). Take the square root from botth sides: \(p=\sqrt{q}\). Substitute \(p\): \(p\frac{q}{\sqrt{q}}=\sqrt{q}*\frac{q}{\sqrt{q}} = q = \text{integer}\). Sufficient.

(2) \(p\) is a positive integer. So, we have that \(p\frac{q}{\sqrt{q}}=\text{integer}*\sqrt{q}\). This product may or may not be an integer depending on \(q\). Not sufficient.

Re: If q is a positive integer, is p*q/q^(1/2) an integer? [#permalink]

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17 Nov 2014, 04:25

1

This post received KUDOS

Expression given pq/q^1/2

this can be further simplified as (pq/q^1/2)*(q^1/2)/q^1/2

this will reduced to pq^1/2

1)q=p^2 since q is positive integer the main expression will be =p^2. is an integer. Sufficient 2)p is positive integer. this does not provide any solution. Insufficient

Re: If q is a positive integer, is p*q/q^(1/2) an integer? [#permalink]

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17 Nov 2014, 11:29

statement 1: sufficient If q=p^2 and q is a positive integer, then p must also be an integer. After plugging in p^2 for Q in the question , then after reducing you see that it is equal to p^2.

statement 2: insufficient If q=9 and p=2 then plug into the equation to get 6 as your answer. However, if you plug in q=6 and p=2, the equation does not equal an integer. not enough info.

Re: If q is a positive integer, is p*q/q^(1/2) an integer? [#permalink]

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29 May 2016, 09:30

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