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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
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    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.

    _________________
    Mitch Hunt
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    Thanked by: Vincen
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