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

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Intern
Joined: 21 Aug 2011
Posts: 24
GMAT Date: 04-02-2012
GPA: 3.79
WE: Corporate Finance (Investment Banking)
If x and y are different integers and x^2 = xy, which of the  [#permalink]

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10 Mar 2012, 08:22
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25% (medium)

Question Stats:

71% (01:18) correct 29% (01:21) wrong based on 580 sessions

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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
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Joined: 02 Sep 2009
Posts: 58434
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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10 Mar 2012, 08:27
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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).

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Intern
Joined: 17 Jan 2012
Posts: 22
Location: India
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Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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20 Nov 2013, 08:11
Bunuel wrote:

$$x^2=xy$$ --> $$x(x-y)=0$$ --> 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).

Thanks for such a nice explanation....
I was confused about option III but your solutions clarifies it perfectly....
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Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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29 Nov 2015, 11:39
Shko1 wrote:
If x and y are different integers and x^2 = xy, which of the following much be true?

I. x = 0
II. x = 0
III. x = -y

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

Looks like nobody edited original question. According to Bunuel's solution point II should read "Y=0". Please correct
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Posts: 2
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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08 Aug 2016, 11:06
I did the following which led me to confusion:

x^2 = (x^1)(y^1)
x^2/x^1 = y^1
So, x = y

What am I doing incorrectly here?

Thanks
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Joined: 08 Aug 2016
Posts: 1
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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08 Aug 2016, 11:13
In x^2, x may be positive and may be negative , you have to consider both case
But here you have taken x positive only

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

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10 Aug 2016, 09:19
Here as X^2=XY => X=0 or X=y but from question stem as x≠y => x=0
So only A is correct as y cannot be zero (else it will equal to x which is not allowed)
Smash that A
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If x and y are different integers and x^2 = xy, which of the  [#permalink]

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29 Apr 2017, 07:10
This question has been discussed here:

https://gmatclub.com/forum/if-x-and-y-a ... 67779.html
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Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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10 Jan 2018, 13:47
(x)(x)=(x)(y)

Now if x does not = 0 we can divide both sides by x to get x=y. But we know x cannot equal y. Therefore it is impossible for x not to be 0. So x Has to be 0.

Y does not have to be 0. x can =0 and y can equal 3 for example. This eliminates choices 2 and 3.
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Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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09 Feb 2019, 07:34
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

KeyWord: If x and y are different integers

x^2 = xy
x^2 -xy =0
x(x-y) = 0

Only one case is possible i.e. x=0

A
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Re: If x and y are different integers and x^2 = xy, which of the   [#permalink] 09 Feb 2019, 07:34
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