1970 AHSME Problem 9

Points P and Q are on line segment AB, and both points are on the same side of the midpoint of AB. Point P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If PQ=2, then the length of segment AB is

\textbf{(A) }12\qquad \textbf{(B) }28\qquad \textbf{(C) }70\qquad \textbf{(D) }75\qquad \textbf{(E) }105

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