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

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Joined: 02 Sep 2009
Posts: 39661
If x and y are different integers and x^2 = xy, which of the [#permalink]

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21 Feb 2014, 01:00
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) l only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III

Problem Solving
Question: 106
Category: Arithmetic; Algebra Operations on rational numbers; Second-degree equations
Page: 75
Difficulty: 600

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Math Expert
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Posts: 39661
Re: If x and y are different integers and x^2 = xy, which of the [#permalink]

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21 Feb 2014, 01:01
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SOLUTION

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

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21 Feb 2014, 02:18
1
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Given Facts -
1. x and y are different integers
2. x^2 = xy

I - x=0
then x^2 = 0
and xy = 0 , for any value of y
thus x^2 = xy - True for any value of y

II - y = 0
if x=1 then x^2 = 1
and xy = 0
Thus x^2 not equal to xy and thus not true for any value of x

III - x = -y
x^2 = (-y)^2 = y^2
xy = (-y)*(y)=-y^2
Thus x^2 not equal to xy and thus not true for any value of x,y

Hence since I only is true for all values Option (A) is the correct answer.
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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]

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21 Feb 2014, 09:35
1
KUDOS
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

Sol.: From the question stem,
x^2 – xy = 0
x ( x – y) = 0
⇨ Either x = 0 or x = y
Since x and y are two different integers, => x= 0.
Hence (A)
Math Expert
Joined: 02 Sep 2009
Posts: 39661
Re: If x and y are different integers and x^2 = xy, which of the [#permalink]

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22 Feb 2014, 06:14
SOLUTION

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) l 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 as 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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Joined: 09 Sep 2013
Posts: 15951
Re: If x and y are different integers and x^2 = xy, which of the [#permalink]

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28 Sep 2015, 21:11
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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 Apr 2017, 02:36
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are different integers and x^2 = xy, which of the   [#permalink] 29 Apr 2017, 02:36
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# If x and y are different integers and x^2 = xy, which of the

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