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

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

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New post 04 Nov 2017, 18:23
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C
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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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Which of the following equations has a unique integer solution? A. y [#permalink]

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New post 04 Nov 2017, 21:14
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, 02:09, edited 1 time in total.

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

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New post 05 Nov 2017, 00:58
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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Which of the following equations has a unique integer solution? A. y [#permalink]

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New post 05 Nov 2017, 01:56
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?

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

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New post 05 Nov 2017, 02:00

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

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New post 05 Nov 2017, 02:06
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.

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

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New post 05 Nov 2017, 18:26
=>

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
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Re: Which of the following equations has a unique integer solution? A. y   [#permalink] 05 Nov 2017, 18:26
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Which of the following equations has a unique integer solution? A. y

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