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:
$\textbf{(A)}\ 60\qquad \textbf{(B)}\ 70\qquad \textbf{(C)}\ 75\qquad \textbf{(D)}\ 80\qquad \textbf{(E)}\ 85$
Draw diagram as shown, where $P$ and $Q$ are on the same side.  Let $AP = x$ and $QB = y$.
Since $P$ divides $AB$ in the ratio $2:3$, $\frac{x}{y+2} = \frac{2}{3}$.  Since $Q$ divides $AB$ in the ratio $3:4$, $\frac{x+2}{y} = \frac{3}{4}$.  Cross multiply to get a [system of equations](https://artofproblemsolving.com/wiki/index.php/System_of_equations).
\[3x = 2y+4\]
\[4x+8=3y\]
Solve the system to get $x = 28$ and $y = 40$.  Thus, $AB = 40 + 28 + 2 = 70$, so the answer is $\boxed{\textbf{(B)}}$.