stop@800 explained well above why the first statement is sufficient.

The second statement is also sufficient. If we know that x, y and z are positive, and that the Pythagorean relationship holds:

x^2 + y^2 = z^2

then we know that we can make a right angled triangle with sides x, y and z, where z is the hypotenuse. And in any triangle, the sum of two sides is always larger than the third side:

x + y > z
x > z - y

So the answer should be D.

cubicle_bound_misfit wrote:Hi Ian,

in GMATLAND, ain't 0 a positive integer?

Also, the question stem does not say X Y Z are all different.

how can phythagoras be used then?

No, 0 is not a positive integer. It is an integer, but it isn't positive, and it isn't negative.

If you have two lines of length x and y, and you connect them at right angles, the hypotenuse z will automatically satisfy

x^2 + y^2 = z^2

That's Pythagoras. It doesn't matter if x and y are different or equal. So you can make a triangle with sides x, y and z, and x+y must be greater than z.

(and while it's not especially important, in this question, x actually must be different from y if the second statement is true, because we know x, y and z are all integers -- if x were an integer and equal to y, then z would need to be equal to root(2)*x, which wouldn't be an integer).