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

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Director
Joined: 06 Sep 2006
Posts: 734

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

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19 Sep 2006, 10:01
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Kudos [?]: 49 [0], given: 0

Senior Manager
Joined: 28 Aug 2006
Posts: 303

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19 Sep 2006, 10:09
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
_________________

Last edited by cicerone on 25 Sep 2008, 01:22, edited 1 time in total.

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Manager
Joined: 24 Oct 2005
Posts: 169

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19 Sep 2006, 10:43
Agree with A.
Same reasoning as cicerone

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Senior Manager
Joined: 13 Sep 2006
Posts: 279

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Location: New York

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19 Sep 2006, 14:14
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

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Retired Moderator
Joined: 05 Jul 2006
Posts: 1749

Kudos [?]: 443 [0], given: 49

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21 Sep 2006, 08:54
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

Kudos [?]: 443 [0], given: 49

21 Sep 2006, 08:54
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# If x and y are different integers and x^2 = xy, which of the

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