2015 AMC 8 Problem 14

Which of the following integers cannot be written as the sum of four consecutive odd integers?

\textbf{(A)}\text{ 16}\qquad\textbf{(B)}\text{ 40}\qquad\textbf{(C)}\text{ 72}\qquad\textbf{(D)}\text{ 100}\qquad\textbf{(E)}\text{ 200}

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