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

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

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New post Updated on: 18 Feb 2014, 00:55
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C
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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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Re: If p and q are positive integers, what is the value of p/q^2  [#permalink]

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New post 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.

Answer: C.

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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New post 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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