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# Is x^2 equal to xy?

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Is x^2 equal to xy? [#permalink]

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15 Dec 2009, 23:28
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Difficulty:

25% (medium)

Question Stats:

70% (02:17) correct 30% (01:19) wrong based on 162 sessions

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Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y
[Reveal] Spoiler: OA
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Is x^2 equal to xy? [#permalink]

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16 Dec 2009, 06:39
Expert's post
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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02 Aug 2010, 08:08
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
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02 Aug 2010, 20:23
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.
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04 Oct 2010, 00:21
X=5 =>> y=+/-5
But if you substitute back in eqn only y=5 is valid

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Is X^2 equal to xy? [#permalink]

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26 Sep 2013, 08:00
Is $$X^2$$ equal to $$xy$$?

1) $$X^2 - Y^2 = ( x+5) ( y-5)$$
2) $$x=y$$

[Reveal] Spoiler:
Fairly easy question but I was wondering how do manipulate statement 1 am I missing something cos it seems insufficient on surface without any calculations?

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Re: Is X^2 equal to xy? [#permalink]

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26 Sep 2013, 08:37
Expert's post
fozzzy wrote:
Is $$X^2$$ equal to $$xy$$?

1) $$X^2 - Y^2 = ( x+5) ( y-5)$$
2) $$x=y$$

[Reveal] Spoiler:
Fairly easy question but I was wondering how do manipulate statement 1 am I missing something cos it seems insufficient on surface without any calculations?

Merging similar topics.
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Re: Is x^2 equal to xy? [#permalink]

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02 Feb 2014, 17:06
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
Re: Is x^2 equal to xy?   [#permalink] 02 Feb 2014, 17:06
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