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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] New post 10 Mar 2012, 08:22
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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. Y = 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] New post 10 Mar 2012, 08:27
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).

Answer: A.
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Re: Arithmetic; Algebra on rational numbers help   [#permalink] 10 Mar 2012, 08:27
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