1997 AHSME Problem 20

Which one of the following integers can be expressed as the sum of 100 consecutive positive integers?

\textbf{(A)}\ 1,\!627,\!384,\!950\qquad\textbf{(B)}\ 2,\!345,\!678,\!910\qquad\textbf{(C)}\ 3,\!579,\!111,\!300\qquad\textbf{(D)}\ 4,\!692,\!581,\!470\qquad\textbf{(E)}\ 5,\!815,\!937,\!260

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