GMAT Kolaveri wrote:Is x^4 + y^4 > z^4 ?
(1) x^2 + y^2 > z^2
(2) x+y > z
[spoiler]OA:E[/spoiler]
Best approach here is the picking numbers approach.
(1) x² + y² > z²
If x = 3, y = 0, z = 2, then x^4 + y^4 = 3^4 + 0^4 = 81 and z^4 = 16. Here x^4 + y^4 > z^4.
If x² = 3, y² = 4, z² = 5, then x^4 + y^4 = 3² + 4² = 9 + 16 = 25 and z^4 = 5² = 25. Here x^4 + y^4 = z^4.
No definite answer, NOT sufficient.
(2) x + y > z
If x = 3, y = 0, z = 2, then x^4 + y^4 = 3^4 + 0^4 = 81 and z^4 = 16. Here x^4 + y^4 > z^4.
If x = 1, y = 1, z = -2, then x^4 + y^4 = 2 and z^4 = (-2)^4 = 16. Here x^4 + y^4 < z^4.
No definite answer, NOT sufficient.
Combining (1) and (2):
If x = 3, y = 0, z = 2, then x^4 + y^4 = 3^4 + 0^4 = 81 and z^4 = 16. Here x^4 + y^4 > z^4.
If x² = 3, y² = 4, z² = 5, then x = √3, y = 2, x + y = √3 + 2 and z = √5, which will be 2.2 approx, but x + y = √3 + 2, which will be more than 3. So, the conditions in both the statements are being satisfied. Here x^4 + y^4 = 3² + 4² = 9 + 16 = 25 and z^4 = 5² = 25. Here x^4 + y^4 = z^4.
No definite answer, NOT sufficient.
The correct answer is
E.
