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# R = 1 + 2xy + x^2y^2, what is the value of xy?

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R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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14 Oct 2010, 20:56
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$$R = 1 + 2*x*y + x^2*y^2$$, what is the value of $$x*y$$?

(1) R = 0
(2) x > 0
[Reveal] Spoiler: OA

Last edited by Engr2012 on 03 Sep 2015, 07:37, edited 3 times in total.
Formatted the question.
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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15 Oct 2010, 02:20
satishreddy wrote:
R=1+2xy+x^y^, what is the value of xy

1) R=0
2) x>0

OA : A

I think the question you posted is incomplete.

what does y^ mean?? There will be some digit aftger y^.
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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15 Oct 2010, 03:30
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satishreddy wrote:
R=1+2xy+x^2*y^2, what is the value of xy

1) R=0
2) x>0

OA : A

Question should be:

R=1+2xy+x^2*y^2, what is the value of xy?

(1) R=0 --> $$1+2xy+x^2*y^2=0$$ --> $$(xy+1)^2=0$$ --> $$xy=-1$$. Sufficient.
(2) x>0 --> Clearly insufficient.

 ! Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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18 Oct 2010, 00:39
Certainly a tricky one. Thanks for posting
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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05 Mar 2015, 01:09
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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03 Sep 2015, 07:29
x^2y^2

I thought x^((2y)^2) so I answered E

I think it should be written specifically: x^2*y^2
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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03 Sep 2015, 07:38
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trung0808 wrote:
x^2y^2

I thought x^((2y)^2) so I answered E

I think it should be written specifically: x^2*y^2

Thank you for raising this issue. I have formatted the question.
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R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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04 Sep 2015, 04:37
Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.

R=1+2xy+(xy)^2, what is the value of x∗y ?

(1) R = 0
(2) x > 0

==> transforming the original condition and the question by variable approach method, we have, R=(1+xy)^2, 1+xy=R, -R, then xy=R-1, xy=-R-1. if we know R we can find xy
In case of 1), if R=0 then xy=-1, a unique answer. Therefore it is sufficient. Thus A is the answer.
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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04 Sep 2015, 04:58
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.

R=1+2xy+(xy)^2, what is the value of x∗y ?

(1) R = 0
(2) x > 0

==> transforming the original condition and the question by variable approach method, we have, R=(1+xy)^2, 1+xy=R, -R, then xy=R-1, xy=-R-1. if we know R we can find xy
In case of 1), if R=0 then xy=-1, a unique answer. Therefore it is sufficient. Thus A is the answer.

If you know our own innovative logics to find the answer, you don’t need to

actually solve the problem.
http://www.mathrevolution.com
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http://www.mathrevolution.com/gmat/lesson

Also, put the quoted post in proper formatting, so that your actual post is clearly visible.

Thanks
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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10 Nov 2016, 13:05
R=1+2xy+x^2*y^2, what is the value of x∗y ?
(1) R = 0
(2) x > 0
R=1+2xy+x^2*y^2=(1+xy)^2
1- R=0 ⇒ 1+xy=0 ⇒ xy=-1 -- SUFFICIENT
2- x>0 -- Irrelevant
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy? [#permalink]

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28 Jan 2017, 14:07

R=1+2xy+x^2y^2 => (1+xy)^2

Statement I

R=0, therefore (1+xy)^2=0
xy=-1

Statement II
x>0

It does not gives us any specific value of x or y or R

Not Sufficient.

Hence A.
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Re: R = 1 + 2xy + x^2y^2, what is the value of xy?   [#permalink] 28 Jan 2017, 14:07
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