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

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Manager
Joined: 05 Sep 2007
Posts: 144
Location: New York
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if x and y are different integers and x^2=xy, which of the [#permalink]  24 Sep 2007, 07:33
if x and y are different integers and x^2=xy, which of the following must be true?
1.x=0
2.y=0
3.x=-y
A.1 only
B.2 only
C.3 only
D.1 & 3 only
E.1,2 & 3.
Director
Joined: 22 Aug 2007
Posts: 572
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Kudos [?]: 14 [0], given: 0

Re: Integers [#permalink]  24 Sep 2007, 08:12
el1981 wrote:
if x and y are different integers and x^2=xy, which of the following must be true?
1.x=0
2.y=0
3.x=-y
A.1 only
B.2 only
C.3 only
D.1 & 3 only
E.1,2 & 3.

got A,

I think the key phrase is "X and Y are different intengers".

1: 0^2=O. ANY INTENGER, always true.
2: ANY INTENGER^2=0^2, can not be, cuz if Y is zero, X must be something else, as stem says.
3: (-Y)^2=-Y.Y, can be true only if Y is zero, stem does not give such info.

thus only 1st...
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
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[#permalink]  24 Sep 2007, 08:33
I say C..

the question is asking |x|=xy

for any X...and for any Y...

x=-y

x=0 is just a subset of all the possible values of x that would work..

x=-y works for all values of X...
Director
Joined: 22 Aug 2007
Posts: 572
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Kudos [?]: 14 [0], given: 0

[#permalink]  24 Sep 2007, 09:10
fresinha12 wrote:
I say C..

the question is asking |x|=xy

for any X...and for any Y...

x=-y

x=0 is just a subset of all the possible values of x that would work..

x=-y works for all values of X...

Can u please elborate on the text in red...? how is it deducted from the stem?
Director
Joined: 06 Sep 2006
Posts: 745
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Re: Integers [#permalink]  24 Sep 2007, 09:14
x^2 - xy = 0
x (x -y) = 0
x=0 or x - y = 0; x=y
x=y cant be true because x and y are different integers.
only x=0 stands.
A.
Manager
Joined: 05 Sep 2007
Posts: 144
Location: New York
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Kudos [?]: 18 [0], given: 0

[#permalink]  24 Sep 2007, 09:44
the answer is A.
Thank you guys. Now i got it.
[#permalink] 24 Sep 2007, 09:44
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# if x and y are different integers and x^2=xy, which of the

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