Each week Manhattan GMAT posts a 700 level GMAT question on our blog and follows up with the answer the next day. Are you up for the challenge?
For any operation ? that acts on two numbers x and y, the commutator is defined as x?y – y?x. For which of the following operations is the commutator not equal to zero for some values of x and y?
I. x?y = xy
II. x?y = (x – y)2
III. x?y = x3 + 3x2y + 3xy2 + y3
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III