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

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If x and y are different integers and x^2 = xy, which of the [#permalink]  21 Feb 2014, 00:00
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Difficulty:

15% (low)

Question Stats:

75% (02:07) correct 25% (01:12) wrong based on 234 sessions
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
Joined: 02 Sep 2009
Posts: 29105
Followers: 4725

Kudos [?]: 49694 [2] , given: 7403

Re: If x and y are different integers and x^2 = xy, which of the [#permalink]  21 Feb 2014, 00:01
2
KUDOS
Expert's post
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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Kudos [?]: 31 [1] , given: 28

Re: If x and y are different integers and x^2 = xy, which of the [#permalink]  21 Feb 2014, 01:18
1
KUDOS
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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Kudos [?]: 4 [1] , given: 256

Re: If x and y are different integers and x^2 = xy, which of the [#permalink]  21 Feb 2014, 08:35
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: 29105
Followers: 4725

Kudos [?]: 49694 [0], given: 7403

Re: If x and y are different integers and x^2 = xy, which of the [#permalink]  22 Feb 2014, 05:14
Expert's post
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] 22 Feb 2014, 05:14
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