Is x^2 equal to xy? : GMAT Data Sufficiency (DS)
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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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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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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.

Answer: B.
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Re: Algebra DS [#permalink]

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New post 02 Aug 2010, 07:08
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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Re: Algebra DS [#permalink]

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New post 02 Aug 2010, 19:23
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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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Re: ALGEBRA [#permalink]

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New post 03 Oct 2010, 23:21
X=5 =>> y=+/-5
But if you substitute back in eqn only y=5 is valid

Please post OA
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Is X^2 equal to xy? [#permalink]

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New post 26 Sep 2013, 07:00
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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New post 26 Sep 2013, 07:37
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Re: Is x^2 equal to xy? [#permalink]

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New post 02 Feb 2014, 16:06
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

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Re: Is x^2 equal to xy? [#permalink]

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New post 26 Jun 2016, 05:41
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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New post 08 Jul 2016, 02:42
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] 08 Jul 2016, 02:42
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