jainrahul1985 wrote:Is x^4 + y^4 > z^4 ?
(1) x^2 + y^2 > z^2
(2) x+y > z
OA E
It is very easy to find examples where the answer is "yes": just choose ridiculously large values for x and y, and small values for z. x=100, y=100, z=1 will satisfy both statements, and the answer to the question stem will be "yes".
so the main challenge in this question is to find a "no" answer:
Stat. (1): define what you're looking for. A No answer means that we need an x and a y that are greater than z when all are squared, but are NOT greater than z when all are raised to the power of 4. How could such a "flip" happen? It might be easier to think of x^4 as the square of x^2, and then simply look for examples of x^2 and y^2 that when squared will not be greater than than a z^2 squared. So if x^2 and y^2 are both 1 (so that even when we square them again to x^4 and y^4, we'll still get 1+1=2), we can then choose a z^2 that is smaller than 1+1 (to satisfy stat (1), but, when squared, will yield a z^4 that is GREATER than 1+1, leaving a no answer. Take a z^2 that is close to 2: z^2=1.9 will be closer to 4 when squared, and definitely greater than x^4+y^4=1+1. Since we have both a yes and a no answer, Stat. (1) is insufficient.
Stat. (2) Use the same numbers. x=1, y=1, z=1.9 will satisfy stat. (2), but yield a "no" answer when raised to the power of 4. Since we have both a yes and a no answer, Stat. (2) is insufficient.
1+2 combined: since the same sets of numbers satisfy both statements, the combination of the statements still allows both a yes and and a no, and is still insufficient. The answer is
E.
