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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: 745
Followers: 1

Kudos [?]: 18 [0], given: 0

If x and y are different integers and x^2 = xy, which of the [#permalink]  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
Senior Manager
Joined: 28 Aug 2006
Posts: 302
Followers: 10

Kudos [?]: 99 [0], given: 0

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, 00:22, edited 1 time in total.
Manager
Joined: 24 Oct 2005
Posts: 169
Followers: 31

Kudos [?]: 127 [0], given: 0

Agree with A.
Same reasoning as cicerone
Senior Manager
Joined: 13 Sep 2006
Posts: 282
Location: New York
Followers: 1

Kudos [?]: 8 [0], given: 0

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

SVP
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 126 [0], given: 39

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

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