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Intern  Joined: 22 Nov 2008
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Is x^2 equal to xy?  [#permalink]

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17 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:44) correct 30% (01:46) wrong based on 545 sessions

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Project DS Butler: Day 39: Data Sufficiency (DS78)

Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

Originally posted by dobinnoli on 15 Dec 2009, 23:28.
Last edited by gmatbusters on 14 Dec 2018, 10:56, edited 1 time in total.
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Joined: 02 Sep 2009
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Re: Is x^2 equal to xy?  [#permalink]

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4
4
Is x^2 equal to xy?

Question: is $$x^2=xy$$? --> $$x(x-y)=0$$ --> Equation holds true if $$x=0$$ or/and $$x=y$$.

So, basically question asks: Is $$x=0$$ or/and $$x=y$$ true?

Obviously statement (2) is sufficient, as it gives directly that $$x=y$$.

(1) x^2 – y^2 = (x + 5)(y - 5) --> $$(x+y)(x-y)=(x + 5)(y-5)$$

If $$y=5$$ --> $$(x+5)(x-5)=(x+5)(5-5)$$ --> $$(x+5)(x-5)=0$$ --> Either $$x=5=y$$ and in this case answer to the question is YES OR $$x=-5$$, hence $$x$$ is not equal to $$y$$ (nor to zero) and in this case answer to the question is NO. So two different answers.

Not sufficient.

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##### General Discussion
Intern  Joined: 03 Mar 2010
Posts: 34
Re: Is x^2 equal to xy?  [#permalink]

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Statement 1:
(x,y)=(5,5) --> x²=xy
(x,y)=(-5,5) --> x²<>xy
not sufficient

Statement 2:
x=y --> xx=xy or x²=xy
sufficient

B
Intern  Joined: 10 Apr 2008
Posts: 19
Re: Is x^2 equal to xy?  [#permalink]

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1
I agree with bogos.

Stmt1:
x^2 - y^2 = (x+5)(x-5)
x^2 - y^2 = x^2 - 25
0 = y^2 - 25
y = +5, -5

plugin a possible value of y into the equation x^2 - y^2 = x^2 - 25
you can see when that y can be -5 and x can 5. But plugging in the same value into x^2 = xy would yield 25 = -25.
Intern  Joined: 12 Oct 2009
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Re: Is x^2 equal to xy?  [#permalink]

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X=5 =>> y=+/-5
But if you substitute back in eqn only y=5 is valid

SVP  Joined: 06 Sep 2013
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Re: Is x^2 equal to xy?  [#permalink]

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dobinnoli wrote:
Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

Is x(x-y)=0

So is x=0 or x=y?

Statement 1

Obviously x is not equal to y otherwise LHS and RHS should be zero

Is x = 0

Is -y^2 = -25, could be but we don't know

Statement 2

x=y, yes. This is correct and sufficient

B
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Re: Is x^2 equal to xy?  [#permalink]

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Omg, can someone please post detailed explanation for this one? I don't understand why are we using Y=5 to evaluate the (x+y)(x-y)=(x+5)(y-5) why not use 10 or 40 or something else? why 5? Does it have something to do with question stem?

Im totally confused here
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Re: Is x^2 equal to xy?  [#permalink]

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iliavko wrote:
Omg, can someone please post detailed explanation for this one? I don't understand why are we using Y=5 to evaluate the (x+y)(x-y)=(x+5)(y-5) why not use 10 or 40 or something else? why 5? Does it have something to do with question stem?

Im totally confused here

I guess we are using 5 in order to make (x+y)(x-y) = 0, which is the easiest way to figure out the possible values of x
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Re: Is x^2 equal to xy?  [#permalink]

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Project DS Butler: Day 39: Data Sufficiency (DS78)

Bumping for DS Butler Project
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Is x^2 equal to xy?  [#permalink]

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ScottTargetTestPrep @EMPOWERgmat can you please explain this question?
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Re: Is x^2 equal to xy?  [#permalink]

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What is ur doubt in this question, because explanation has already been provided in the thread.

Rocknrolla21 wrote:
ScottTargetTestPrep @EMPOWERgmat can you please explain this question?

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Re: Is x^2 equal to xy?  [#permalink]

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gmatbusters I don't understand how we proved that statement 1 is insufficient.

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Re: Is x^2 equal to xy?  [#permalink]

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To prove that St 1 is insufficient, see the beautiful explanation provided by Bunuel here

Rocknrolla21 wrote:
gmatbusters I don't understand how we proved that statement 1 is insufficient.

Posted from my mobile device

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Re: Is x^2 equal to xy?  [#permalink]

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dobinnoli wrote:

Project DS Butler: Day 39: Data Sufficiency (DS78)

Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

Statement One Only:

x^2 – y^2 = (x + 5)(y - 5)

If y = 5, we have:

x^2 - 25 = (x + 5)(0)

x^2 - 25 = 0

(x + 5)(x - 5) = 0

x = 5 or x = -5

If x = 5, then x^2 and xy will be equal since both are 25. However, if x = -5, then x^2 and xy will not be equal since the former is 25 and the latter is -25. Statement one alone is not sufficient.

Statement Two Only:

x = y

Since x = y, if we multiply both sides by x, we have:

x * x = y * x

x^2 = xy

Statement two alone is sufficient.

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