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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: 4920
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:

75% (hard)

Question Stats:

36% (00:33) correct 64% (01:32) wrong based on 44 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. $$y=\frac{-1}{x}+2$$
[Reveal] Spoiler: OA

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 948
Location: India
GPA: 3.82
Which of the following equations has a unique integer solution? A. y [#permalink]

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04 Nov 2017, 20:14
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

Last edited by niks18 on 05 Nov 2017, 01:09, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Which of the following equations has a unique integer solution? A. y [#permalink]

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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.
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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 948
Location: India
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Which of the following equations has a unique integer solution? A. y [#permalink]

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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: 43917
Re: Which of the following equations has a unique integer solution? A. y [#permalink]

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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: 948
Location: India
GPA: 3.82
Re: Which of the following equations has a unique integer solution? A. y [#permalink]

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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: 4920
GPA: 3.82
Re: Which of the following equations has a unique integer solution? A. y [#permalink]

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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

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Re: Which of the following equations has a unique integer solution? A. y   [#permalink] 05 Nov 2017, 17:26
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