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x^4 + y^4 =

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by Brent@GMATPrepNow » Thu Jan 15, 2009 7:02 am
Source: Beat The GMAT Practice Questions

If x + y = 3, and x^2 + y^2 = 5 then x^4 + y^4 =
(A) 11
(B) 13
(C) 17
(D) 19
(E) 22
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x^4+y^4 =

by katz » Thu Jan 15, 2009 7:20 am
x^2 + y^2 = (x+y)^2 - 2xy
5 = 9 - 2xy
=> xy = 2

x^4 + y^4 = (x^2+y^2)^2 - 2(xy)^2
= 25 - 2(2)^2
= 25 - 8
= 17

Therefore the answer would be "C".
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by Brent@GMATPrepNow » Thu Jan 15, 2009 7:23 am
Yep - the correct answer is C.
Here's my solution as well:

x+y=3 means that (x+y)^2=9
We get x^2 + 2xy + y^2 = 9
Since we’re given that x^2 + y^2 = 5, then 2xy=4 which means that xy=2
If x^2 + y^2 = 5, then (x^2 + y^2)^2 = 25
We get x^4 + 2x^2y^2 + y^4 = 25
We already know that xy=2, so 2x^2y^2 = 8
So we get x^4 + 8 + y^4 = 25, which means that x^4 + y^4 = 17
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by Mr2Bits » Thu Jan 15, 2009 7:33 am
C : 17

X =2 Y = 1
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by Brent@GMATPrepNow » Thu Jan 15, 2009 8:28 am
Mr2Bits wrote:C : 17

X =2 Y = 1
Ha ha ha, that is too funny.
I meant create a question that students couldn't plug in a few numbers to see which ones fit and it turns out that (2,1) works.
Back to the drawing board for me :D

I should have made it something like: x + y = 5, and x^2 + y^2 = 7
Nice catch!
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by Mr2Bits » Thu Jan 15, 2009 9:20 am
Brent Hanneson wrote:
Mr2Bits wrote:C : 17

X =2 Y = 1
Ha ha ha, that is too funny.
I meant create a question that students couldn't plug in a few numbers to see which ones fit and it turns out that (2,1) works.
Back to the drawing board for me :D

I should have made it something like: x + y = 5, and x^2 + y^2 = 7
Nice catch!
Yea, I saw it immediately and had to double take it to make sure I wasn't wrong. I have come to the conclusion that when taking the GMAT the obvious answer is most likely incorrect and there is some trick or piece that I'm missing
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