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

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Retired Moderator
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What is the value of x^2 + y^2 ? [#permalink]

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26 Aug 2012, 09:56
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65% (hard)

Question Stats:

54% (02:24) correct 46% (01:33) wrong based on 74 sessions

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

(1) $$x^2 + y^2 = 2xy + 1$$
(2) $$x^2 + y^2 = 4 - 2xy$$

[Reveal] Spoiler:
I don't agree with the OA.
If we add (1) and (2):

(1) $$x^2 -2xy + y^2 = 1$$
(2) $$x^2 +2xy+ y^2 = 4$$
-------------------------------------
Total: $$2x^2 +2y^2 = 5$$

Then: $$x^2 + y^2 = \frac{5}{2}$$

Please, your comments.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 01 Dec 2014, 03:57, edited 1 time in total.
Edited the OA.
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Re: What is the value of x^2 + y^2 ? [#permalink]

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26 Aug 2012, 10:41
When trying to solve for x and y, it doesn't appear that we can find a solution for x^2 + y^2
2xy + 1 = 4 - 2xy

4xy = 3
xy = 3/4

However, the approach of canceling out 2xy DOES remove the xy variable and leaves us cleanly with x^2 + y^2. We indeed have the value as you mentioned...perhaps the source for the OA is incorrect.
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Re: What is the value of x^2 + y^2 ? [#permalink]

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30 Nov 2014, 13:20
metallicafan wrote:
What is the value of $$x^2 + y^2$$ ?
(1) $$x^2 + y^2 = 2xy + 1$$
(2) $$x^2 + y^2 = 4 - 2xy$$

I don't agree with the OA.
If we add (1) and (2):

(1) $$x^2 -2xy + y^2 = 1$$
(2) $$x^2 +2xy+ y^2 = 4$$
-------------------------------------
Total: $$2x^2 +2y^2 = 5$$

Then: $$x^2 + y^2 = \frac{5}{2}$$

Please, your comments.

+1 for C. I did the same as you did.
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Re: What is the value of x^2 + y^2 ? [#permalink]

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30 Nov 2014, 23:32
metallicafan wrote:
What is the value of $$x^2 + y^2$$ ?
(1) $$x^2 + y^2 = 2xy + 1$$
(2) $$x^2 + y^2 = 4 - 2xy$$

I don't agree with the OA.
If we add (1) and (2):

(1) $$x^2 -2xy + y^2 = 1$$
(2) $$x^2 +2xy+ y^2 = 4$$
-------------------------------------
Total: $$2x^2 +2y^2 = 5$$

Then: $$x^2 + y^2 = \frac{5}{2}$$

Please, your comments.

well metallicafan,
i see nothing wrong with your approach, but i solved this the following way...
(1) x^2 + y^2 = 2.x.y + 1
=> (x - y)^2 = 1
=> x - y = 1 or -1 insuff

(2) x^2 + y^2 = 4 - 2.x.y
=> (x + y)^2 = 4
=> x + y = 2 or -2 insuff

combining the two,
since the above equations can have multiple values when we solve for x and y, hence, insufficient.
answer is E. is this a GMATPrep question?? because i dont think the real gmat would confuse students like this.

happy to help, a kudos if you like.
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Re: What is the value of x^2 + y^2 ? [#permalink]

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01 Dec 2014, 01:40
arnabs wrote:
metallicafan wrote:
What is the value of $$x^2 + y^2$$ ?
(1) $$x^2 + y^2 = 2xy + 1$$
(2) $$x^2 + y^2 = 4 - 2xy$$

I don't agree with the OA.
If we add (1) and (2):

(1) $$x^2 -2xy + y^2 = 1$$
(2) $$x^2 +2xy+ y^2 = 4$$
-------------------------------------
Total: $$2x^2 +2y^2 = 5$$

Then: $$x^2 + y^2 = \frac{5}{2}$$

Please, your comments.

well metallicafan,
i see nothing wrong with your approach, but i solved this the following way...
(1) x^2 + y^2 = 2.x.y + 1
=> (x - y)^2 = 1
=> x - y = 1 or -1 insuff

(2) x^2 + y^2 = 4 - 2.x.y
=> (x + y)^2 = 4
=> x + y = 2 or -2 insuff

combining the two,
since the above equations can have multiple values when we solve for x and y, hence, insufficient.
answer is E. is this a GMATPrep question?? because i dont think the real gmat would confuse students like this.

happy to help, a kudos if you like.

But don't you get an answer of 5/2 for$$x^2 + y^2$$ if you take any of the combinations?, Note that we are asked to find $$x^2 + y^2$$
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Re: What is the value of x^2 + y^2 ? [#permalink]

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01 Dec 2014, 02:36
santorasantu wrote:
arnabs wrote:
metallicafan wrote:
What is the value of $$x^2 + y^2$$ ?
(1) $$x^2 + y^2 = 2xy + 1$$
(2) $$x^2 + y^2 = 4 - 2xy$$

I don't agree with the OA.
If we add (1) and (2):

(1) $$x^2 -2xy + y^2 = 1$$
(2) $$x^2 +2xy+ y^2 = 4$$
-------------------------------------
Total: $$2x^2 +2y^2 = 5$$

Then: $$x^2 + y^2 = \frac{5}{2}$$

Please, your comments.

well metallicafan,
i see nothing wrong with your approach, but i solved this the following way...
(1) x^2 + y^2 = 2.x.y + 1
=> (x - y)^2 = 1
=> x - y = 1 or -1 insuff

(2) x^2 + y^2 = 4 - 2.x.y
=> (x + y)^2 = 4
=> x + y = 2 or -2 insuff

combining the two,
since the above equations can have multiple values when we solve for x and y, hence, insufficient.
answer is E. is this a GMATPrep question?? because i dont think the real gmat would confuse students like this.

happy to help, a kudos if you like.

But don't you get an answer of 5/2 for$$x^2 + y^2$$ if you take any of the combinations?, Note that we are asked to find $$x^2 + y^2$$

hmmm, yes you do. yeah should be C. my bad
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Re: What is the value of x^2 + y^2 ? [#permalink]

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01 Dec 2014, 04:11
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What is the value of x^2 + y^2 ?

(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy

----------------------------------------------------------------------------------------------------------------------------------------
Good tricky question almost carried away and started finding (x+y) ^2

but finally marked correct ans C

1. x^2 + y^2 = 2xy+1 --> value of 2XY is not known hence not sufficient
2. x^2 + y^2 = 4-2xy --> value of 2XY is not known hence not sufficient

Combining (1+2)
2x^2+2y^2 = 5
i.e x^2 + y^2 = 5/2 hence sufficient

Regards
SG
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Re: What is the value of x^2 + y^2 ? [#permalink]

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02 Dec 2014, 00:56
St1. x^2+y^2=2xy+1 is INSUFFICIENT

St2. x^2+y^2=4-2xy is INSUFFICIENT

St1+St2
means 2xy+1=4-2xy
4xy=3
xy=3/4
putting it in the first equation gives 2*3/4+1=5/2

C
Re: What is the value of x^2 + y^2 ?   [#permalink] 02 Dec 2014, 00:56
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# What is the value of x^2 + y^2 ?

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