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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
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82
If x, y are positive integers, is xy=1? [#permalink]

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10 Aug 2017, 01:13
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Difficulty:

15% (low)

Question Stats:

71% (00:39) correct 29% (00:26) wrong based on 63 sessions

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

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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 5928 Re: If x, y are positive integers, is xy=1? [#permalink] ### Show Tags 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 _________________ 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 GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5600 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If x, y are positive integers, is xy=1? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If x, y are positive integers, is xy=1?   [#permalink] 13 Aug 2017, 18:15
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