Each week Manhattan GMAT posts a GMAT question on our blog and follows up with the answer the next day. Are you up for the challenge?
For all positive integers x and y in the expression x&y, the symbol & represents one of the following six operations between x and y in the order shown: addition, subtraction, multiplication, division, exponentiation, or rooting (in this case, x&y would represent x1/y). If the six operations each have an equal chance of being represented, which of the following points in the xy-coordinate plane would have exactly a 50% chance of yielding the same result in the expression x&y (with the other outcomes all different from this result as well as from each other)?
(A) (1, 1)
(B) (1, 2)
(C) (2, 1)
(D) (2, 2)
(E) (3, 1)