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# Which of the following equations has a unique integer solution? A. y

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6611
GMAT 1: 760 Q51 V42
GPA: 3.82
Which of the following equations has a unique integer solution? A. y  [#permalink]

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04 Nov 2017, 17:23
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Difficulty:

55% (hard)

Question Stats:

44% (01:09) correct 56% (01:20) wrong based on 55 sessions

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[GMAT math practice question]

Which of the following equations has a unique integer solution?

A. $$y=3x$$
B. $$y=(\frac{x}{3})+4$$
C. $$y=\sqrt{2}x$$
D. $$y=\frac{1}{2}x$$
E. $$y=\frac{-1}{x}+2$$

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"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" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1217 Location: India GPA: 3.82 Which of the following equations has a unique integer solution? A. y [#permalink] ### Show Tags Updated on: 05 Nov 2017, 01:09 MathRevolution wrote: [GMAT math practice question] Which of the following equations has a unique integer solution? A. $$y=3x$$ B. $$y=(\frac{x}{3})+4$$ C. $$y=\sqrt{2}x$$ D. $$y=\frac{1}{2}x$$ E. $$y=\frac{-1}{x}+2$$ For Option A,B, D & E there can be multiple integer solution depending upon the value of $$x$$. Hence they are out. Option C both $$x$$ & $$y$$ can be integer in only one scenario $$x=y=0$$ Hence the answer is option C Originally posted by niks18 on 04 Nov 2017, 20:14. Last edited by niks18 on 05 Nov 2017, 01:09, edited 1 time in total. Math Expert Joined: 02 Sep 2009 Posts: 51035 Re: Which of the following equations has a unique integer solution? A. y [#permalink] ### Show Tags 04 Nov 2017, 23:58 niks18 wrote: MathRevolution wrote: [GMAT math practice question] Which of the following equations has a unique integer solution? A. $$y=3x$$ B. $$y=(\frac{x}{3})+4$$ C. $$y=\sqrt{2}x$$ D. $$y=\frac{1}{2}x$$ E. $$y=\frac{-1}{x}+2$$ Hi Bunuel Can you calrify Option C $$y=\sqrt{2}x$$; if $$x=\sqrt{2}$$, $$y$$ is $$2$$ but if $$x=\sqrt{8}$$, $$y=4$$. Again multiple solutions possible. For Option A,B, D & E there can be multiple integer solution depending upon the value of $$x$$. Hence they are out. So we don't have an equation with unique solution. Kindly clarify where I am going wrong Please pay attention to the highlighted part. _________________ PS Forum Moderator Joined: 25 Feb 2013 Posts: 1217 Location: India GPA: 3.82 Which of the following equations has a unique integer solution? A. y [#permalink] ### Show Tags 05 Nov 2017, 00:56 Bunuel wrote: niks18 wrote: MathRevolution wrote: [GMAT math practice question] Which of the following equations has a unique integer solution? A. $$y=3x$$ B. $$y=(\frac{x}{3})+4$$ C. $$y=\sqrt{2}x$$ D. $$y=\frac{1}{2}x$$ E. $$y=\frac{-1}{x}+2$$ Hi Bunuel Can you calrify Option C $$y=\sqrt{2}x$$; if $$x=\sqrt{2}$$, $$y$$ is $$2$$ but if $$x=\sqrt{8}$$, $$y=4$$. Again multiple solutions possible. For Option A,B, D & E there can be multiple integer solution depending upon the value of $$x$$. Hence they are out. So we don't have an equation with unique solution. Kindly clarify where I am going wrong Please pay attention to the highlighted part. Thanks Bunuel for the hint so this means that both x & y should be an integer? Math Expert Joined: 02 Sep 2009 Posts: 51035 Re: Which of the following equations has a unique integer solution? A. y [#permalink] ### Show Tags 05 Nov 2017, 01:00 niks18 wrote: Thanks Bunuel for the hint so this means that both x & y should be an integer? Yes. I think it should be clear from my reply above. _________________ PS Forum Moderator Joined: 25 Feb 2013 Posts: 1217 Location: India GPA: 3.82 Re: Which of the following equations has a unique integer solution? A. y [#permalink] ### Show Tags 05 Nov 2017, 01:06 Bunuel wrote: niks18 wrote: Thanks Bunuel for the hint so this means that both x & y should be an integer? Yes. I think it should be clear from my reply above. Thanks, will edit my solution. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6611 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following equations has a unique integer solution? A. y [#permalink] ### Show Tags 05 Nov 2017, 17:26 => A. x = 0, y = 0 / x = 1, y = 3 B. x = 0, y = 4 / x = 3, y = 5 C. $$y=\sqrt{2}x$$ has a unique integer solution, that is, x = 0 and y = 0. If x is not 0, y is an irrational number, which is not an integer. D. x = 0, y = 0 / x = 2, y = 1 E. x = 1, y = 1 / x = -1, y = 3 Therefore, the answer is C. Answer : C _________________ 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: Which of the following equations has a unique integer solution? A. y &nbs [#permalink] 05 Nov 2017, 17:26
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