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.