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# If x and y are different integers and x^2 = xy, which of the

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If x and y are different integers and x^2 = xy, which of the [#permalink]  10 Mar 2012, 07:22
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If x and y are different integers and x^2 = xy, which of the following much be true?

I. x = 0
II. x = 0
III. x = -y

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
[Reveal] Spoiler: OA
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Re: Arithmetic; Algebra on rational numbers help [#permalink]  10 Mar 2012, 07:27
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Shko1 wrote:
If x and y are different integers and (x^2)=xy, which of the following much be true?

I. X = 0
II. Y = 0
III. X = -Y

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

$$x^2=xy$$ --> $$x(x-y)=0$$ --> either $$x=0$$ or $$x=y$$ but since given that $$x$$ and $$y$$ are different numbers than the second option is out and we have: $$x=0$$. So, only I is always true (in fact because of the same reason that $$x$$ and $$y$$ are different numbers II and III are never true).

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Re: Arithmetic; Algebra on rational numbers help [#permalink]  20 Nov 2013, 07:11
Bunuel wrote:

$$x^2=xy$$ --> $$x(x-y)=0$$ --> either $$x=0$$ or $$x=y$$ but since given that $$x$$ and $$y$$ are different numbers than the second option is out and we have: $$x=0$$. So, only I is always true (in fact because of the same reason that $$x$$ and $$y$$ are different numbers II and III are never true).

Thanks for such a nice explanation....
I was confused about option III but your solutions clarifies it perfectly....
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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]  10 Dec 2014, 09:45
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Re: If x and y are different integers and x^2 = xy, which of the   [#permalink] 10 Dec 2014, 09:45
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