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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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Difficulty:   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
Math Expert V
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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6
3
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
Concentration: General Management, International Business
GMAT 1: 650 Q48 V31 WE: Information Technology (Telecommunications)
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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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....
Senior Manager  B
Joined: 02 Dec 2014
Posts: 354
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33 WE: Sales (Telecommunications)
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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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. 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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Intern  B
Joined: 04 Mar 2015
Posts: 2
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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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
Intern  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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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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Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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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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Manager  S
Status: On a 600-long battle
Joined: 22 Apr 2016
Posts: 136
Location: Hungary
Schools: Erasmus '19
GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23 If x and y are different integers and x^2 = xy, which of the  [#permalink]

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This question has been discussed here:

https://gmatclub.com/forum/if-x-and-y-a ... 67779.html
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Manager  B
Joined: 17 Jul 2016
Posts: 54
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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(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.
Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If x and y are different integers and x^2 = xy, which of the  [#permalink]

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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

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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Many of life's failures happen with people who do not realize how close they were to success when they gave up. 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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If x and y are different integers and x^2 = xy, which of the

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