2018 AMC 12A Problem 7

For how many (not necessarily positive) integer values of n is the value of 4000\cdot \left(\tfrac{2}{5}\right)^n an integer?

\textbf{(A) }3 \qquad \textbf{(B) }4 \qquad \textbf{(C) }6 \qquad \textbf{(D) }8 \qquad \textbf{(E) }9 \qquad

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