The number $6545$ can be written as a product of a pair of positive two-digit numbers.  What is the sum of this pair of numbers?
$\text{(A)}\ 162 \qquad \text{(B)}\ 172 \qquad \text{(C)}\ 173 \qquad \text{(D)}\ 174 \qquad \text{(E)}\ 222$
The prime factorization of $6545$ is $5\cdot7\cdot11\cdot17  =385\cdot17$, which contains a three digit number, but we want 6545 to be expressed as ab x cd. Now we do trial and error: 
\[5\cdot7=35 \text{,   } 11\cdot17=187 \text{  X}\] \[5\cdot11=55 \text{,   } 7\cdot17=119 \text{  X}\] \[5\cdot17=85 \text{,   } 7\cdot11=77 \text{ }\surd\] \[85+77= \boxed{\text{(A)}\ 162}\]