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# If m and n are positive integers, and if p and q are differe

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Manager
Joined: 31 Oct 2011
Posts: 235
If m and n are positive integers, and if p and q are differe  [#permalink]

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22 Mar 2012, 19:52
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6
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Difficulty:

65% (hard)

Question Stats:

58% (01:38) correct 42% (01:58) wrong based on 155 sessions

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If m and n are positive integers, and if p and q are different prime numbers, do p/q and n/m represent different numbers?

(1) Neither n nor m is a prime number.

(2) m is not dvisible by q.
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Joined: 02 Sep 2009
Posts: 51121
Re: If m and n are positive integers, and if p and q are differe  [#permalink]

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23 Mar 2012, 00:52
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If m and n are positive integers, and if p and q are different prime numbers, do p/q and n/m represent different numbers?

Given: $$n$$ and $$m$$ are integers $$p$$ and $$q$$ are different prime numbers.

Question: is $$\frac{n}{m}=\frac{p}{q}$$?

Notice that, since $$n$$ and $$m$$ are integers then this equation will hold true if $$n$$ and $$m$$ are multiples of prime numbers $$p$$ and $$q$$ respectively. For example: $$\frac{n}{m}=\frac{2}{3}=\frac{4}{6}=\frac{6}{9}=\frac{p}{q}=\frac{2}{3}$$. If we were not told that $$p$$ and $$q$$ are different then this won't be necessary, for example following case would be possible: $$\frac{n}{m}=\frac{8}{8}=1=\frac{3}{3}=\frac{p}{q}$$

(1) Neither n nor m is a prime number. If $$n=px$$ and $$m=qx$$ (for some integer x more than 1) then the answer ill be YES, if not then the answer will be No. For example: if $$p=2$$, $$q=3$$ and $$n=2*4=8$$, $$m=3*4=12$$ then $$\frac{n}{m}=\frac{p}{q}=\frac{2}{3}$$. Not sufficient.

(2) m is not dvisible by q. As discussed above, if $$m$$ is not a multiple of $$q$$ then $$\frac{n}{m}\neq{\frac{p}{q}}$$. Sufficient.

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Re: If m and n are positive integers, and if p and q are differe  [#permalink]

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29 Nov 2018, 17:45
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Re: If m and n are positive integers, and if p and q are differe &nbs [#permalink] 29 Nov 2018, 17:45
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