If X, Y and Z are positive integers, is X greater than Z â€“ Y?
(1) X â€“ Z â€“ Y > 0.
(2) Z2 = X2 + Y2
(1) --> X> Z+Y > Z-Y (because Z and Y are positive integers ---> Z+Y> Z-Y) ---> answer to the question: YES ---> suff
(2) Z^2 = X^2 + Y^2 --> X^2 = Z^2 - Y^2 = (Z-Y) ( Z+Y) > (Z-Y) (Z-Y)
---> X^2 > (Z-Y)^2 ---> (X- (Z-Y)) * (X+ (Z-Y)) > 0
---> 2 cases:
X> Z-Y AND X > Y-Z
OR X< Z-Y AND X < Y-Z ( This can't happen because either Z-Y or Y-Z must be smaller than 0 ---> X <0 ---> against the assumption in the problem)
---> The only case is X> Z-Y ---> suff
Go for D.
Well, i had some flaw in the red part.
Correct it :
Z^2 = X^2+ Y^2 --> X^2= Z^2 - Y^2 --> X^2= (Z-Y) * (Z+Y)
---> X= [(Z-Y) * (Z+Y)]/ X = (Z-Y) * ( ( Z+Y) / X)
+If Z-Y < 0 ---> Z-Y < 0 < X --> Z-Y< X
+If Z-Y > 0
If the bold part < 1 ( that is Z+Y< X) --> X< Z-Y ---> Z+Y < X< Z-Y --> Z+Y < Z-Y ---> unreasonable --> this case can't happen
If the bold part >1 ( that is Z+Y > X) ---> X > Z-Y
--> finally, we still conclude that X> Z-Y
I'm still stuck to D.
Honestly, I didn't get your "bold part" approach. One thing for sure is that you shouldn't take gmat questions that serious. Remember that you have less than 2 minutes for each question.