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 positive integers k and n, the “k-power remainder of n” is defined as r in the following equation:
n = kw + r, where w is the largest integer such that r is not negative. For instance, the 3-power remainder of 13 is 4, since 13 = 32 + 4. In terms of k and w, what is the largest possible value of r that satisfies the given conditions?
(A) (k – 1)kw – 1
(B) kw – 1
(C) (k + 1)kw – 1
(D) kw+1 – 1
(E) (k + 1)kw+1 – 1