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Is x^4 + y^4 > Z^4 ?

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kourakis
 Post subject: Is x^4 + y^4 > Z^4 ?
 Post Posted: Sun Aug 14, 2011 5:00 pm 
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Students


Posts: 8
(1) x^2 + y^2 > z^2
(2) x + y > z

OA is E.

Here is my approach to the problem (I chose A):

Test numbers:

Start with statement (2):

x=1, Y=2, Z=1 YES
x=-1, Y=-2, Z=-10 NO
Therefore, Insufficient

Go to statement (1)

(+) or (-) does not matter, since numbers are squared. We need to try fractions, zero, and one - by inspection though, doesn't a number that is raised to the fourth always decrease (fraction) or increase (integer) when raised to a higher power? Therefore, if the given (2) inequality is true, then the question in hand should always validate that?
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RonPurewal
 Post subject: Re: Is x^4 + y^4 > Z^4 ?
 Post Posted: Mon Aug 15, 2011 2:27 am 
Offline
ManhattanGMAT Staff


Posts: 7146
here's a long thread on that problem; this link will take you to my solution:

post18074.html#p18074

i will lock this thread; if you have further questions, please post them there. thanks.
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