This is indeed a tough TOUGH DS problem, and testing numbers is definitely a great way to go about it, considering you have an average of only 2 minutes a question on the Quant section.
I fooled around with the question a little bit more, though, and I think there's an interesting way you can arrive very quickly at answer E (although this would certainly be difficult to do in a time-pressure situation). Just for fun...
Is x^4 + y^4 > z^4 ?
(1) x^2 + y^2 > z^2
(2) x+y > z
This is a Yes/No DS question, meaning that we can if we can answer both Yes and No to the prompt with the information given, then that information is insufficient. One thing that's easy to forget is that showing x^4 + y^4 < z^4 is not the only way to answer No to the prompt. The answer would also be No if x^4 + y^4 were EQUAL to z^4.
Notice that this (along with Statement 1) bares an uncanny resemblance to the Pythagorean Theorem. That got me thinking about using Pythagorean triples.
There are no restrictions on x, y, or z, so use x = sqrt(3), y = sqrt(4), z = sqrt(5). These are values that satisfy both Statements (1) and (2), and thus they are legal.
In that case, x^4 + y^4 = z^4, and we would get a No.
Now, all we have to do is find a Yes, and that is very easy to do:
Choose ridiculously large values of x and y and a very small value for z. x = 100, y = 100, and z = 1 will work just fine.
Those values satisfy both Statements (1) and (2) and answer Yes to the prompt.
We are done! Answer: E
Rich Zwelling
GMAT Instructor, Veritas Prep
