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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If x, y are positive integers, is xy=1? [#permalink]

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10 Aug 2017, 00:13
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15% (low)

Question Stats:

71% (00:37) correct 29% (00:20) wrong based on 58 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Kudos [?]: 3313 [0], given: 0

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

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10 Aug 2017, 06:17
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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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Kudos [?]: 6421 [0], given: 122

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4683

Kudos [?]: 3313 [0], given: 0

GPA: 3.82
Re: If x, y are positive integers, is xy=1? [#permalink]

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13 Aug 2017, 17:15
==> 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).

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Re: If x, y are positive integers, is xy=1?   [#permalink] 13 Aug 2017, 17:15
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