1993 AHSME Problem 16

Consider the non-decreasing sequence of positive integers 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,\cdots in which the n^{th} positive integer appears n times. The remainder when the 1993^{rd} term is divided by 5 is

\text{(A) } 0\quad \text{(B) } 1\quad \text{(C) } 2\quad \text{(D) } 3\quad \text{(E) } 4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.