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# If x and y are integers such that (xy)^2 + x^2 – 2xy – 2x + 2 = 0, wha

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6526
GMAT 1: 760 Q51 V42
GPA: 3.82
If x and y are integers such that (xy)^2 + x^2 – 2xy – 2x + 2 = 0, wha  [#permalink]

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25 Jul 2018, 00:12
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:07) correct 38% (02:44) wrong based on 40 sessions

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[Math Revolution GMAT math practice question]

If $$x$$ and $$y$$ are integers such that $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$, what is the value of $$y$$?

A. $$-2$$
B. $$-1$$
C. $$0$$
D. $$1$$
E. $$2$$

_________________

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" ##### Most Helpful Expert Reply MBA Section Director Affiliations: GMATClub Joined: 22 May 2017 Posts: 1005 Concentration: Nonprofit GPA: 4 WE: Engineering (Computer Software) If x and y are integers such that (xy)^2 + x^2 – 2xy – 2x + 2 = 0, wha [#permalink] ### Show Tags 25 Jul 2018, 00:23 3 3 $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$ => $$(xy)^2 + x^2 – 2xy – 2x + 1 + 1 = 0$$ => $$(xy)^2 – 2(xy) + 1 + x^2 – 2x + 1 = 0$$ => $$(xy-1)^2 + (x-1)^2 = 0$$ => (xy - 1) = 0 and (x - 1) = 0 => y = $$\frac{1}{x}$$ and x = 1 => y = 1 and x = 1 Hence option D _________________ ##### General Discussion Senior Manager Joined: 04 Aug 2010 Posts: 307 Schools: Dartmouth College Re: If x and y are integers such that (xy)^2 + x^2 – 2xy – 2x + 2 = 0, wha [#permalink] ### Show Tags 25 Jul 2018, 02:41 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x$$ and $$y$$ are integers such that $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$, what is the value of $$y$$? A. $$-2$$ B. $$-1$$ C. $$0$$ D. $$1$$ E. $$2$$ We can PLUG IN THE ANSWERS, which represent the value of y. B: y=-1 Substituting y=-1 into $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$, we get: $$x^2 + x^2 + 2x – 2x + 2 = 0$$ $$2x^2 + 2 = 0$$ $$x^2 + 1 = 0$$ $$x^2 = -1$$ Since the square of a value cannot be negative, eliminate B. D: y=1 Substituting y=1 into $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$, we get: $$x^2 + x^2 - 2x – 2x + 2 = 0$$ $$2x^2 - 4x + 2 = 0$$ $$x^2 - 2x + 1 = 0$$ $$(x-1)^2 = 0$$ $$x=1$$ Success! _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6526 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers such that (xy)^2 + x^2 – 2xy – 2x + 2 = 0, wha [#permalink] ### Show Tags 26 Jul 2018, 23:52 => $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$ $$=> (xy)^2 – 2xy + 1 + x^2 – 2x + 1 = 0$$ $$=> (xy – 1)^2 + (x – 1)^2 = 0$$ $$=> xy = 1$$ and $$x = 1$$. Thus , $$x = 1$$ and $$y = 1$$. Therefore, 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 and y are integers such that (xy)^2 + x^2 – 2xy – 2x + 2 = 0, wha &nbs [#permalink] 26 Jul 2018, 23:52
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