We all know that whole numbers will satisfy both statements and the question stem
I guess it's already been pointed out, but that's not always the case. Try x = 6, y = 8, z = 9.
It seems easiest to me to notice the relationship between the statements and triangles. The sum of two sides of a triangle is always greater than the third side, but the sum of the squares of the sides is not always greater than the square of the third side- the Pythagorean Theorem tells us that the sum of the squares of the two shortest sides is never
greater than the square of the longest side if we look at the sides of a right angled triangle. That is, we've all seen dozens of examples (right angled triangles) where a+b > c but a^2 + b^2 = c^2.
So, let x^2, y^2 and z^2 be the sides of a 3-4-5 triangle and you get an example immediately that proves the answer to the original question should be E:
x^2 = 3 (i.e. x = root(3))
y^2 = 4 (i.e. y = 2)
z^2 = 5 (i.e. z = root(5))
It's easy to check that x+y > z, and we already know that x^2+y^2 > z^2 and x^4 + y^4 = z^4 (i.e. it's not greater than z^4). E.
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