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If px = qy, is x/y an integer?

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If px = qy, is x/y an integer? [#permalink] New post 08 May 2013, 07:13
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If px = qy, is x/y an integer?

(1) q and p are primes.
(2) Positive integer y is neither composite nor prime

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[Reveal] Spoiler: OA

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Last edited by mau5 on 19 May 2013, 06:49, edited 1 time in total.
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Re: If px = qy, is x/y an integer? [#permalink] New post 08 May 2013, 07:28
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If px = qy, is x/y an integer?

I.q and p are primes.
\(3*20=2*30\) => \(\frac{20}{30}\) no integer
\(3*1=3*1\) => \(\frac{1}{1}\) integer
Not sufficient

II. Positive integer y is neither composite nor prime
So y is \(1\), no info about x.
Not sufficient

I + II)\(px=q\), if \(p=q\) then \(x=1\) and \(\frac{x}{y}=\frac{1}{1}\) is an integer
if \(p\neq{q}\) ie: \(5*x=7, x=\frac{7}{5}\), then \(\frac{x}{y}\) is NOT an integer
Not sufficient.
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Re: If px = qy, is x/y an integer? [#permalink] New post 08 May 2013, 08:22
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vinaymimani wrote:
If px = qy, is x/y an integer?

I.q and p are primes.
II. Positive integer y is neither composite nor prime


Question: is x/y an integer?

px = qy
x/y = q/p

We need to know whether q/p is an integer.

I.q and p are primes.
This means that q has only two factors - 1 and q itself. If p = q, then p is a factor q, else it is not.
Not sufficient.

II. Positive integer y is neither composite nor prime
This means y = 1. We still cannot say whether x/y is an integer since x may or may not be an integer.
Not sufficient.

Both taken together, nothing changes. We still do not know whether x/y is an integer.
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Re: If px = qy, is x/y an integer?   [#permalink] 08 May 2013, 08:22
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