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Source: — Data Sufficiency |
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by neelgandham » Mon Sep 17, 2012 6:39 am
Is x^4 + y^4 > z^4?
A x^2 + y^2.> z^2
Case 1: If x = 100, y = 100 and z = 0. Then
x^2 + y^2.> z^2 (2*100^2 > 0) and x^4 + y^4 > z^4 (2*100^4 > 0).

Case 2: If x = 4, y = 4 and z = 5
x^2 + y^2.> z^2 (32 > 25) and x^4 + y^4 < z^4 (512 < 625).

Since we don't have a definite answer, Statement I is insufficient to answer the question.
B x + y > z
Case 1: If x = 100, y = 100 and z = 0. Then
x + y > z (2*100 > 0) and x^4 + y^4 > z^4 (2*100^4 > 0).

Case 2: If x = 4, y = 4 and z = 5
x + y > z (8 > 5) and x^4 + y^4 < z^4 (512 < 625).

Since we don't have a definite answer, Statement II is insufficient to answer the question.

Did you observe that I used the same cases in both the statements ? So, statement I + II combined isn't sufficient to answer the question.

IMO E

p.s: Can you cite the source of the question please. I find it a little tougher than the normal GMAT question and hence the query.
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by Ian Stewart » Mon Sep 17, 2012 11:53 am
neelgandham wrote:
p.s: Can you cite the source of the question please. I find it a little tougher than the normal GMAT question and hence the query.
It's one of the harder questions in GMATPrep, so it's a real GMAT question.

It can actually be answered fairly quickly if you recognize where else you've seen the expressions in the question. In any right triangle with sides of length a, b and c, where c is the hypotenuse, we know that a^2 + b^2 = c^2. But we also know in any triangle, the sum of two sides is greater than the third, so a + b > c. That is, it often happens that a + b > c, but a^2 + b^2 is not greater than c^2.

So in this question, we can just borrow numbers from simple right triangles to get a 'no' answer to the question: if we let x^2 = 3, y^2 = 4, and z^2 = 5 (so x = √3, y = √4 and z = √5), we find that x + y > z, x^2 + y^2 > z^2, but that x^4 + y^4 = z^4. So the answer to the question can be 'no', using both statements, and since it can clearly also be 'yes', the two statements are not sufficient together and the answer is E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by neelgandham » Tue Sep 18, 2012 1:28 am
Great explanation! Ta
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by eski » Tue Sep 18, 2012 10:51 am
My ans E

simple way (a+b)^2 = a^2+2ab+b^2 right?

so square option A .

so if we just want a^4+b^4 we have to have 2a^2b^2 removed , which can ONLY be done when either a or b or both are 0,thats not possible which is INSUFFICIENT

Similarly twice square option B .also INSUFF
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