cans wrote:What is the remainder when the positive integer n is divided by the positive integer k, where
k>1?
(1) n=(k+1)^3 (i.e. cube of (k+1))
(2) k=5

When you expand (k+1)^3, every term you get will be a multiple of k except for the 1^3 = 1 term at the end. So (k+1)^3 will be 1 greater than a multiple of k, and thus the remainder will be 1 when it is divided by k. So the answer is A, since Statement 2 alone is of no help.

In fact, for the same reason, if k > 1, then (k+1)^n will always give you a remainder of 1 when you divide it by k, assuming n and k are positive integers.