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# is x^4 + y^4 > z^4 ? 1. x^2 + y^2 > z^2 2. x + y >

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Manager
Joined: 04 Sep 2008
Posts: 249
Location: Kolkata
Schools: La Martiniere for Boys
is x^4 + y^4 > z^4 ? 1. x^2 + y^2 > z^2 2. x + y > [#permalink]

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27 Oct 2008, 22:03
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is x^4 + y^4 > z^4 ?

1. x^2 + y^2 > z^2
2. x + y > z

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Thanks
rampuria

Senior Manager
Joined: 20 Feb 2008
Posts: 294
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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27 Oct 2008, 23:14
I would go for A Stat 1 is sufficient

This holds for x,y,z where x, y and z can be negative, positive or between 0 and 1.

Stat 2 does not hold for negative numbers.
VP
Joined: 30 Jun 2008
Posts: 1026

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28 Oct 2008, 03:50
it is E.

http://www.manhattangmat.com/forums/is-x-4-y-4-z-4-ds-t3616.html

this one is better
http://www.manhattangmat.com/forums/is-x-4-y-4-z-4-t4655.html
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VP
Joined: 05 Jul 2008
Posts: 1401

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28 Oct 2008, 12:21
K. Here is the catch with A

$$x ^2 + y ^2 > Z ^ 2 means x ^4 + y ^4 + 2 (x^2) (y^2) > z ^4$$

just because 2 x ^2 y ^2 is positive does not mean that it is needed to satisfy the equation. The equation could be correct without the need for 2 x ^2 y ^2 under which x ^4 + y ^ 4 will be greater than Z ^4 and if it needs it, the equation is less than z ^4.
Re: DS   [#permalink] 28 Oct 2008, 12:21
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