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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]  08 May 2013, 07:13
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Difficulty:

55% (hard)

Question Stats:

39% (01:50) correct 61% (01:00) wrong based on 51 sessions
If px = qy, is x/y an integer?

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

Question created by me.
[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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Kudos [?]: 1455 [1] , given: 219

Re: If px = qy, is x/y an integer? [#permalink]  08 May 2013, 07:28
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KUDOS
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.
E
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Kudos [?]: 7595 [1] , given: 186

Re: If px = qy, is x/y an integer? [#permalink]  08 May 2013, 08:22
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Expert's post
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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