1971 AHSME Problem 12

For each integer N>1, there is a mathematical system in which two or more positive integers are defined to be congruent if they leave the same non-negative remainder when divided by N. If 69,90, and 125 are congruent in one such system, then in that same system, 81 is congruent to

\textbf{(A) }3\qquad \textbf{(B) }4\qquad \textbf{(C) }5\qquad \textbf{(D) }7\qquad \textbf{(E) }8

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