Data Sufficiency

sachindia wrote:If X, Y, and Z are positive integers, is (X - Y)(Y - Z)(X - Z) > 0?

(1) X² + YZ = XY + XZ
(2) XY - Y² = XZ - YZ

Statement 1: X² + YZ = XY + XZ
--> X² - XY + YZ - XZ = 0
--> X(X - Y) - Z(X - Y) = 0
--> (X - Y)(X - Z) = 0

Hence, either (X - Y) = 0 or (X - Z) = 0
In both cases, (X - Y)(Y - Z)(X - Z) = 0

Sufficient

Statement 2: XY - Y² = XZ - YZ
--> XY - Y² - XZ + YZ = 0
--> Y(X - Y) - Z(X - Y) = 0
--> (X - Y)(Y - Z) = 0

Hence, either (X - Y) = 0 or (Y - Z) = 0
In both cases, (X - Y)(Y - Z)(X - Z) = 0

Sufficient

The correct answer is D.