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

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If m and n are positive integers, and if p and q are differe [#permalink] New post 22 Mar 2012, 19:52
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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?

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

(2) m is not dvisible by q.
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Re: If m and n are positive integers, and if p and q are differe [#permalink] New post 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.

Answer: B.
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Re: If m and n are positive integers, and if p and q are differe   [#permalink] 23 Mar 2012, 00:52
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