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# Is x^4 + y ^4 > z^4 ?

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Director
Joined: 23 Sep 2007
Posts: 769
Is x^4 + y ^4 > z^4 ? [#permalink]

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03 Aug 2008, 19:42
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

how to solve this quickly? especially statement 1

Is $$x^4 + y ^4 > z^4$$ ?

$$1) x^2 + y ^2 > z^2$$

$$2) x + y > z$$
Senior Manager
Joined: 23 May 2006
Posts: 311
Re: Is x^4 + y ^4 > z^4 ? [#permalink]

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03 Aug 2008, 20:05
gmatnub wrote:
how to solve this quickly? especially statement 1

Is $$x^4 + y ^4 > z^4$$ ?

$$1) x^2 + y ^2 > z^2$$

$$2) x + y > z$$

In this problem the property of x,y,z is not provided, hence they can be integers, real number, complex number, rational, irrational, whole number or natural number. Hence this alone gives you a clue that the answer might be E.

Hence now take values that support and do not support the both the statements.

S1. If x= sqrt(-3) and y=sqrt(-7), z=sqrt(-11) -------> -10> -11; however, 3^2 + 7^ < 11^2

S2. If x= 0 and y= 1, z= -2; 1 > -2, However 1 < 4
If x = 2 and y = 2 and z = 2; 4 > 2 and 32 > 16
IMO E
Director
Joined: 10 Sep 2007
Posts: 923
Re: Is x^4 + y ^4 > z^4 ? [#permalink]

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03 Aug 2008, 20:07
Not only x,y,z are not interger but also none of their property is mentioned. They can be anything real number, complex number, rational, irrational, whole number or natural number. So you cannot assume what their property.

What you can assume is set of values supporting question and set of values not supporting question. If you can find both values then question cannot be answered with given statements and Answer is E.

In this case suppose x=sqrt(-3),y=sqrt(-7),z=sqrt(-11)
So 1 is satisfied but x^4+y^4 is not greater than z^4

Similarly x=sqrt(3),y=sqrt(7),z=sqrt(9)
So 1 is satisfied and x^4+y^4 is not greater than z^4.

Finally x=3,y=2,z=1
So 1 is satisfied and main question is also answered +vely.

Above set of data will equally apply for statement 2, so there will be no way to get the value with these two statement so answer E.

There is mathematical way however that is very abstract so I am not putting here, but if you want I can send you.
Director
Joined: 23 Sep 2007
Posts: 769
Re: Is x^4 + y ^4 > z^4 ? [#permalink]

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03 Aug 2008, 20:16
nevermind,

i was too focused on using decimals to test the conditions.

for condition 1, had I used x=3 and y=3 and z=4, I would have had the answer.
Re: Is x^4 + y ^4 > z^4 ?   [#permalink] 03 Aug 2008, 20:16
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# Is x^4 + y ^4 > z^4 ?

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