AHSME 1961 Problem 23

Points $P$ and $Q$ are both in the line segment $AB$ and on the same side of its midpoint. $P$ divides $AB$ in the ratio $2:3$, and $Q$ divides $AB$ in the ratio $3:4$. If $PQ=2$, then the length of $AB$ is: $\textbf{(A)}\ 60 \textbf{(B)}\ 70 \textbf{(C)}\ 75 \textbf{(D)}\ 80 \textbf{(E)}\ 85$