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If x, y are positive integers, is xy=1?

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Math Revolution GMAT Instructor
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If x, y are positive integers, is xy=1? [#permalink]

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New post 10 Aug 2017, 01:13
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If x, y are positive integers, is \(xy=1\)?

1) \(x^2y^2=xy\)
2) \(\frac{1}{y}=x.\)
[Reveal] Spoiler: OA

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Re: If x, y are positive integers, is xy=1? [#permalink]

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New post 10 Aug 2017, 07:17
MathRevolution wrote:
If x, y are positive integers, is \(xy=1\)?

1) \(x^2y^2=xy\)
2) \(\frac{1}{y}=x.\)



Hi..
Statement I
\(x^2y^2=xy.......(xy)^2-xy=0....Xy(xy-1)=0\)
Therefore either xy=0, or xy=1 ...
But x and y are POSITIVE integers, so xy =1
Sufficient

Statement II
\(x=\frac{1}{y}\)....
Since y is positive, we can cross multiply
Xy=1
Sufficient

D
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Re: If x, y are positive integers, is xy=1? [#permalink]

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New post 13 Aug 2017, 18:15
==> In the original condition, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), for con 2), you get xy=1, hence it is unique and sufficient. For con 1), from (xy)^2-xy=0, xy(xy-1)=0, you get xy=0,1, but since x and y are positive, you get xy=1, and thus con 1) = con 2).

The answer is D.
Answer: D
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Re: If x, y are positive integers, is xy=1?   [#permalink] 13 Aug 2017, 18:15
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