GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Aug 2018, 06:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6027
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]

### Show Tags

25 Jul 2018, 01:12
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:08) correct 35% (02:48) wrong based on 37 sessions

### HideShow timer Statistics

[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"  Math Revolution Discount Codes Manhattan GMAT Discount Codes Jamboree Discount Codes ##### Most Helpful Community Reply RC Moderator Status: Perfecting myself for GMAT Joined: 22 May 2017 Posts: 432 Concentration: Nonprofit Schools: Haas '21 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, 01:23 3 2 $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$ => $$(xy)^2 + x^2 – 2xy – 2x + 1 + 1 = 0$$ => $$(xy)^2 – 2(xy) + 1 + x^2 – 2x + 1 = 0$$ => $$(xy-1)^2 + (x-1)^2 = 0$$ => (xy - 1) = 0 and (x - 1) = 0 => y = $$\frac{1}{x}$$ and x = 1 => y = 1 and x = 1 Hence option D _________________ If you like my post press kudos +1 New - RC Butler - 2 RC's everyday Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag. ##### General Discussion Manager Joined: 04 Aug 2010 Posts: 235 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, 03:41 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: 6027 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 27 Jul 2018, 00:52 => $$(xy)^2 + x^2 – 2xy – 2x + 2 = 0$$ $$=> (xy)^2 – 2xy + 1 + x^2 – 2x + 1 = 0$$ $$=> (xy – 1)^2 + (x – 1)^2 = 0$$ $$=> xy = 1$$ 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"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If x and y are integers such that (xy)^2 + x^2 – 2xy – 2x + 2 = 0, wha &nbs [#permalink] 27 Jul 2018, 00:52
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.