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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 19 Sep 2006, 09:01
If x and y are different integers and x^2 = xy, which of the following must be true?
I. x = 0
II. y = 0
III. x = -y

(A) I only (B) II only (C) III only (D) I & III only (E) I, II, & III
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 [#permalink] New post 19 Sep 2006, 09:09
Given X and Y are different integers.

X^2=XY
X^2-XY=0
X(X-Y)=0
i.e either X=0 or X-Y=0(this can't be the case bcoz X and Y are distinct

So X must be 0
i.e option A
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Last edited by cicerone on 25 Sep 2008, 00:22, edited 1 time in total.
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 [#permalink] New post 19 Sep 2006, 09:43
Agree with A.
Same reasoning as cicerone
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 [#permalink] New post 19 Sep 2006, 13:14
A as well

My method was to pick numbers

If x and y are different integers and x^2 = xy, which of the following must be true?

I. x = 0
so 0^2=0(y) ... correct as anything multiplied by 0 will yield 0

II. y = 0
so x^2 = x(0) not possible as x cannot equal 0 and equation will not work out... see if you pick 2 it would be 2^2=2(0) doesn't work

III. x = -y

so x=1 and y=-1 then 1=(1)(-1) doesn't work either

Hence answer is A
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 [#permalink] New post 21 Sep 2006, 07:54
If x and y are different integers and x^2 = xy, which of the following must be true?
I. x = 0
II. y = 0
III. x = -y

(A) I only (B) II only (C) III only (D) I & III only (E) I, II, & III

x^2 = xy thus

x(x-y) = 0

either x = 0 or x = y but the stem states they are different intigers thus x= 0 and this is definite

A is my answer
  [#permalink] 21 Sep 2006, 07:54
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