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# Is x^2 equal to xy?

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Director
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Is x^2 equal to xy? [#permalink]

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21 May 2008, 00:44
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Question Stats:

65% (01:13) correct 35% (01:08) wrong based on 180 sessions

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Is x^2 equal to xy?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-2-equal-to-xy-88034.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 28 Oct 2014, 04:10, edited 2 times in total.
Edited the question and added the OA.

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

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21 May 2008, 00:57
prasannar wrote:
Is x^2 equal to xy?
(1) x2 – y2 = (x + 5)(y - 5)
(2) x = y

D,

1) Assuming x2 - y2 is a typo for x^2-y^2,

(x+y)(x-y) = (-5 + y) (x - (-5) )
i.e. x =-5 & y = -5

2) is suff

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Re: Is x^2 equal to xy? [#permalink]

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21 May 2008, 01:01
alpha_plus_gamma wrote:
(x+y)(x-y) = (-5 + y) (x - (-5) )
i.e. x =-5 & y = -5

you seem right!
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Re: Is x^2 equal to xy? [#permalink]

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21 May 2008, 02:49
Given OA is B.

I too picked D and got nailed down by the OA.

Patman how did you get to B, plz explain
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Re: Is x^2 equal to xy? [#permalink]

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21 May 2008, 04:34
(1)x^2-y^2=(x+y)(x-y)=(x + 5)(y - 5)
so y=5 but no information abt x so insufficient

(2) x=y
multiplying both sides by x
x^2=xy sufficient

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Re: Is x^2 equal to xy? [#permalink]

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21 May 2008, 06:52
this should be B..

x^2-y^2=(x-y)(x+y)..

we have (x+5)(y-5)... (y-5) is not equal to (x-y)

here x is negative...so insuff

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Re: Is x^2 equal to xy? [#permalink]

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27 Oct 2014, 19:43
prasannar wrote:
Is x^2 equal to xy?
(1) x2 – y2 = (x + 5)(y - 5)
(2) x = y

ritula wrote:
(1)x^2-y^2=(x+y)(x-y)=(x + 5)(y - 5)
so y=5 but no information abt x so insufficient

(2) x=y
multiplying both sides by x
x^2=xy sufficient

FN wrote:
this should be B..

x^2-y^2=(x-y)(x+y)..

we have (x+5)(y-5)... (y-5) is not equal to (x-y)

here x is negative...so insuff

Can someone please explain this DS problem in more detail?
Bunuel ??... Please can you help! TY

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Re: Is x^2 equal to xy? [#permalink]

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28 Oct 2014, 04:07
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Expert's post
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dmmk wrote:
prasannar wrote:
Is x^2 equal to xy?
(1) x2 – y2 = (x + 5)(y - 5)
(2) x = y

ritula wrote:
(1)x^2-y^2=(x+y)(x-y)=(x + 5)(y - 5)
so y=5 but no information abt x so insufficient

(2) x=y
multiplying both sides by x
x^2=xy sufficient

FN wrote:
this should be B..

x^2-y^2=(x-y)(x+y)..

we have (x+5)(y-5)... (y-5) is not equal to (x-y)

here x is negative...so insuff

Can someone please explain this DS problem in more detail?
Bunuel ??... Please can you help! TY

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-2-equal-to-xy-88034.html
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Re: Is x^2 equal to xy?   [#permalink] 28 Oct 2014, 04:07
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