1998 AHSME Problem 30

For each positive integer n, let

a_n = \frac{(n+9)!}{(n-1)!}

Let k denote the smallest positive integer for which the rightmost nonzero digit of a_k is odd. The rightmost nonzero digit of a_k is

\mathrm{(A) \ }1 \qquad \mathrm{(B) \ }3 \qquad \mathrm{(C) \ }5 \qquad \mathrm{(D) \ } 7 \qquad \mathrm{(E) \ } 9

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