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# What is the value of x^2 + y^2 ?

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Manager
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What is the value of x^2 + y^2 ? [#permalink]  04 Oct 2010, 17:06
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Difficulty:

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Question Stats:

60% (02:20) correct 40% (01:21) wrong based on 99 sessions
What is the value of $$x^2 + y^2$$?

1. $$x^2 + y^2 = 2xy + 1$$
2. $$x^2 + y^2 = 4 - 2xy$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-2-y-142923.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Nov 2014, 00:45, edited 1 time in total.
Edited the OA.
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Kudos [?]: 616 [0], given: 25

Re: What is the value of x^2 + y^2 ? [#permalink]  04 Oct 2010, 17:51
1) it's given in terms of xy, insufficient

2) again same problem, insufficient

1+2) add together the equations and divide by 2. X^2+y^2=2.5
sufficient

Posted from my mobile device
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Manager
Joined: 24 Jun 2010
Posts: 141
Concentration: Strategy, Technology
Followers: 6

Kudos [?]: 22 [0], given: 26

Re: What is the value of x^2 + y^2 ? [#permalink]  04 Oct 2010, 18:34
shrouded1 wrote:
1) it's given in terms of xy, insufficient

2) again same problem, insufficient

1+2) add together the equations and divide by 2. X^2+y^2=2.5
sufficient

Posted from my mobile device

Yup I get the same thing.. OA must be wrong
Intern
Joined: 27 Jul 2010
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Kudos [?]: 2 [0], given: 0

Re: What is the value of x^2 + y^2 ? [#permalink]  04 Oct 2010, 19:37
Yes.. I get C too.. OA must be wrong..
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Manager
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Kudos [?]: 65 [0], given: 18

Re: What is the value of x^2 + y^2 ? [#permalink]  16 Oct 2010, 06:14
shd be C according to me as well...
Manager
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GPA: 3.9
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Re: What is the value of x^2 + y^2 ? [#permalink]  23 Nov 2014, 07:50
I also end up with C.
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Re: What is the value of x^2 + y^2 ? [#permalink]  24 Nov 2014, 00:45
Expert's post
krazo wrote:
What is the value of $$x^2 + y^2$$?

1. $$x^2 + y^2 = 2xy + 1$$
2. $$x^2 + y^2 = 4 - 2xy$$

What is the value of x^2+y^2 ?

(1) x^2+y^2=2xy+1 --> $$x^2-2xy+y^2=1$$ --> $$(x-y)^2=1$$. If $$x=1$$ and $$y=0$$, then $$x^2+y^2=1$$ but if $$x=2$$ and $$y=1$$, then $$x^2+y^2=5$$. Not sufficient.

(2) x^2+y^2=4-2xy --> $$x^2+2xy+y^2=4$$ --> $$(x+y)^2=4$$. If $$x=2$$ and $$y=0$$, then $$x^2+y^2=4$$ but if $$x=1$$ and $$y=1$$, then $$x^2+y^2=2$$. Not sufficient.

(1)+(2) Sum the equations: $$2(x^2+y^2)=5$$ --> $$x^2+y^2=2.5$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-2-y-142923.html
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Re: What is the value of x^2 + y^2 ?   [#permalink] 24 Nov 2014, 00:45
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