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# Is x = y? (1) x^2 = xy (2) x^2 = y^2

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BSchool Forum Moderator
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Is x = y? (1) x^2 = xy (2) x^2 = y^2 [#permalink]

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09 Apr 2016, 22:10
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Difficulty:

55% (hard)

Question Stats:

51% (00:36) correct 49% (00:45) wrong based on 107 sessions

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Is x = y?

(1) x^2 = xy
(2) x^2 = y^2
[Reveal] Spoiler: OA

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Give me a hell yeah ...!!!!!

Last edited by Bunuel on 10 Apr 2016, 09:53, edited 1 time in total.
Renamed the topic and edited the question.

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Math Forum Moderator
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Re: Is x = y? (1) x^2 = xy (2) x^2 = y^2 [#permalink]

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09 Apr 2016, 22:26
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St1: x^2 - xy = 0
x(x - y) = 0 --> x = 0 or x = y
If x = 0 then y can be any value.
Not sufficient

St2: x^2 - y^2 = 0
(x + y)(x - y) = 0 --> x = y or x = -y
Not sufficient

Combining St1 and St2, we can confirm that x will always be equal to y
Sufficient

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Re: Is x = y? (1) x^2 = xy (2) x^2 = y^2 [#permalink]

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10 Apr 2016, 07:31
stonecold wrote:
Is x=y?
[A] x² = xy
[B] x² = y²

Vyshak's solution is great, so I won't re-answer the question.
I just want to point out that the intended TRAP here is that some people will incorrectly take the equation x² = xy and divide both sides by x to get x = y
People who do that will incorrectly conclude that the answer is A.
The problem with taking the equation x² = xy and dividing both sides by x is that you may be dividing both sides by zero, which is a big no-no.
Likewise, if we take this valid equation, (2)(0) = (1)(0) and divide both sides by 0, we can't then conclude that 2 = 1

Cheers,
Brent
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Brent Hanneson – Founder of gmatprepnow.com

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Re: Is x = y? (1) x^2 = xy (2) x^2 = y^2 [#permalink]

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11 Oct 2016, 07:51
stonecold wrote:
Is x = y?

(1) x^2 = xy
(2) x^2 = y^2

1. x^2 - xy = 0
x(x-y)=0
x=0, x=y - 2 outcomes, not sufficient.

2. x^2 = y^2
x=2, y=2 - yes
x=-2, y=2 - no
not sufficient.

1+2
x=0 -> y=0 - ok
x=y -> ok

sufficient.

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Re: Is x = y? (1) x^2 = xy (2) x^2 = y^2 [#permalink]

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18 Aug 2017, 05:27
GMATPrepNow wrote:
stonecold wrote:
Is x=y?
[A] x² = xy
x² = y²

Vyshak's solution is great, so I won't re-answer the question.
I just want to point out that the intended TRAP here is that some people will incorrectly take the equation x² = xy and divide both sides by x to get x = y
People who do that will incorrectly conclude that the answer is A.
The problem with taking the equation x² = xy and dividing both sides by x is that you may be dividing both sides by zero, which is a big no-no.
Likewise, if we take this valid equation, (2)(0) = (1)(0) and divide both sides by 0, we can't then conclude that 2 = 1

Cheers,
Brent

Dear Brent [b]GMATPrepNow ,

Can we conclude that, for this similar questions, it is easier if we use algebraic approach?

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Re: Is x = y? (1) x^2 = xy (2) x^2 = y^2 [#permalink]

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18 Aug 2017, 06:29
stonecold wrote:
Is x = y?

(1) x^2 = xy
(2) x^2 = y^2

1) $$x^2$$ = xy
=> x = 0 or x = y
Insufficient.

2) $$x^2$$ = $$y^2$$
x = y OR x = -y
=> x = 2 , y = 2
OR x = -2 , y = 2
Insufficient.

1+2)
x = y
Sufficient.

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Re: Is x = y? (1) x^2 = xy (2) x^2 = y^2   [#permalink] 18 Aug 2017, 06:29
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# Is x = y? (1) x^2 = xy (2) x^2 = y^2

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