ksharma12 wrote:
Is x^4 + y^4 > z^4?
(1) x^2 + y^2 > z^2
(2) x + y > z
We want to determine whether x^4 + y^4 > z^4.
Statement One Alone:x^2 + y^2 > z^2
If we square both sides of the inequality, we will have:
x^4 + 2(x^2)(y^2) + y^4 > z^4
x^4 + y^4 > z^4 – 2(x^2)(y^2)
We still cannot determine whether x^4 + y^4 > z^4, since 2(x^2)(y^2) is a nonnegative quantity.
For example, if x = 0, y = 2, and z = 1, then x^4 + y^4 > z^4, since 0^4 + 2^4 > 1^4.
However, if x = 3, y = 3, and z = 4, then x^4 + y^4 is not greater than z^4, since 3^4 + 3^4 is not greater than 4^4.
Statement one is not sufficient to answer the question.
Statement Two Alone:x + y > z
We cannot determine whether x^4 + y^4 is greater than z^4.
For example, if x = 0, y = 2, and z = 1, then x^4 + y^4 > z^4, since 0^4 + 2^4 > 1^4.
However, if x = 3, y = 3, and z = 4, then x^4 + y^4 is not greater than z^4, since 3^4 + 3^4 is not greater than 4^4.
Statement two is not sufficient to answer the question.
Statements One and Two Together:Using our two statements, we still cannot determine whether x^4 + y^4 is greater than z^4. Using the same numerical examples used earlier, we have:
If x = 0, y = 2, and z = 1, then x^4 + y^4 > z^4.
However, if x = 3, y = 3, and z = 4, then x^4 + y^4 is not greater than z^4.
Answer: E
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