AHSME 1970 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 $\text{(A) } 12 \text{(B) } 28 \text{(C) } 70 \text{(D) } 75 \text{(E) } 105$