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# If p and q are positive integers, what is the value of p/q^2

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Intern
Joined: 13 Dec 2013
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If p and q are positive integers, what is the value of p/q^2  [#permalink]

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Updated on: 18 Feb 2014, 00:55
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11
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Difficulty:

95% (hard)

Question Stats:

46% (01:57) correct 54% (01:49) wrong based on 187 sessions

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If p and q are positive integers, what is the value of p/(q^2)?

(1) p is a multiple of q^2.

(2) q is a multiple of p.

Originally posted by civi83 on 17 Feb 2014, 23:43.
Last edited by Bunuel on 18 Feb 2014, 00:55, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 58453
Re: If p and q are positive integers, what is the value of p/q^2  [#permalink]

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18 Feb 2014, 01:08
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If p and q are positive integers, what is the value of p/(q^2)?

(1) p is a multiple of q^2 --> $$\frac{p}{q^2}=integer$$. If $$p=q=1$$, then $$\frac{p}{q^2}=1$$ but if $$p=2$$ and $$q=1$$, then $$\frac{p}{q^2}=2$$. Not sufficient.

(2) q is a multiple of p --> $$\frac{q}{p}=integer$$. If $$p=q=1$$, then $$\frac{p}{q^2}=1$$ but if $$q=2$$ and $$p=1$$, then $$\frac{p}{q^2}=\frac{1}{4}$$. Not sufficient.

(1)+(2) From (1) we have that $$\frac{p}{q^2}=integer_1$$ and $$\frac{q}{p}=integer_2$$. Multiply these two: $$\frac{p}{q^2}*\frac{q}{p}=integer_1*integer_2=integer$$ --> $$\frac{1}{q}=integer$$. Since we know that q is a positive integer, then $$q=1$$. Now, if $$q=1$$, then from $$\frac{q}{p}=integer$$ --> $$\frac{1}{p}=integer$$ --> $$p=1$$. Therefore $$\frac{p}{q^2}=1$$. Sufficient.

Hope it's clear.
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Re: If p and q are positive integers, what is the value of p/q^2  [#permalink]

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10 Oct 2018, 11:50
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Re: If p and q are positive integers, what is the value of p/q^2   [#permalink] 10 Oct 2018, 11:50
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