AHSME 1961 Problem 20

The set of points satisfying the pair of inequalities $y>2x$ and $y>4-x$ is contained entirely in quadrants: $\textbf{(A)}\ \text{I and II} \textbf{(B)}\ \text{II and III} \textbf{(C)}\ \text{I and III} \textbf{(D)}\ \text{III and IV} \textbf{(E)}\ \text{I and IV}$