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Is x^4 + y^4 > z^4?

This topic has 1 expert reply and 0 member replies

Is x^4 + y^4 > z^4?

Post Wed Sep 20, 2017 6:58 am
Is x^4 + y^4 > z^4?

(1) x^2 + y^2 > z^2
(2) x + y > z

The OA is E.

How can I determine that the statements together are not sufficient? Why aren't sufficient?

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Top Reply
Post Wed Sep 20, 2017 8:41 am
Vincen wrote:
Is x^4 + y^4 > z^4?

(1) x^2 + y^2 > z^2
(2) x + y > z
Statements combined:

Case 1: x=1, y=0, z=0
Statement 1:
1² + 0² > 0²
1 + 0 > 0
1 > 0.
Statement 2:
1 + 0 > 0
1 > 0.
Plugging Case 1 into the question stem, we get:
1⁴ + 0⁴ > 0⁴
1 + 0 > 0
1 > 0.
In this case, the answer to the question stem is YES.

√3 ≈ 1.7.
√5 ≈ 2.2.

Case 2: x=√3, y=√4, z=√5
Statement 1:
(√3)² + (√4)² > (√5)²
3 + 4 > 5
7 > 5.
Statement 2:
√3 + √4 > √5
1.7 + 2 > 2.2
3.7 > 2.2.
Plugging Case 2 into the question stem, we get:
(√3)⁴ + (√4)⁴ = (√5)⁴
3² + 4² > 5²
9 + 16 > 25
25 > 25.
In this case, the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.

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Thanked by: Vincen
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