2016 AMC 8 Problem 19

The sum of 25 consecutive even integers is 10,000. What is the largest of these 25 consecutive integers?

\textbf{(A)}\ 360\qquad\textbf{(B)}\ 388\qquad\textbf{(C)}\ 412\qquad\textbf{(D)}\ 416\qquad\textbf{(E)}\ 424

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