1961 AHSME Problem 20

The set of points satisfying the pair of inequalities y>2x and y>4-x is contained entirely in quadrants:

\textbf{(A)}\ \text{I and II}\qquad \textbf{(B)}\ \text{II and III}\qquad \textbf{(C)}\ \text{I and III}\qquad \textbf{(D)}\ \text{III and IV}\qquad \textbf{(E)}\ \text{I and IV}

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