Is x^4 + y^4 > z^4?
Statement 1: x² + y² > z²
Statement 2: x+y > z.
Try to plug in combinations that satisfy both statements.
An easy value to raise to the 4th power is a root.
√2 ≈ 1.4.
√3 ≈ 1.7.
Let x=1, y=1 and z=1.
Statement 1:
1² + 1² > 1².
2 > 1.
Satisfied.
Statement 2:
1+1 > 1.
2 > 1.
Satisfied.
Question stem:
1^4 + 1^4 > 1^4.
2 > 1.
YES.
Let x=√2, y=√3 and z=√4=2.
Statement 1:
√2² + √3² > 2².
5 > 4.
Satisfied.
Statement 2:
√2+√3 > 2.
3.1 > 2.
Satisfied.
Question stem:
(√2)^4 + (√3)^4 > 2^4.
13 > 16.
NO.
Since the combinations above satisfy both statements, and in the first case the answer is YES, and in the second case the answer is NO, INSUFFICIENT.
The correct answer is
E.
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