1995 AJHSME Problems/Problem 22
Problem
The number 
can be written as a product of a pair of positive two-digit numbers. What is the sum of this pair of numbers?
Solution
The prime factorization of 6545 is 5*7*11*17. 5*7*11=385, which is a three digit number, so every two-digit number pair has to be two number of the form pq. Now we do trial and error:
![\[5*7=35 \text{, } 11*17=187 \text{ X}\]](http://latex.artofproblemsolving.com/d/3/a/d3aa90e7a5d7d66b77a8f8850759521cef81cea1.png)
![\[5*11=55 \text{, } 7*17=119 \text{ X}\]](http://latex.artofproblemsolving.com/a/9/a/a9a993b426bc502c2ff60e6c92e70da519d4a779.png)
![\[5*17=85 \text{, } 7*11=77 \text{ }\surd\]](http://latex.artofproblemsolving.com/8/5/5/855fad6873c017c73a49d5fb538f157cd70f353c.png)
![\[85+77=162 \text{(A)}\]](http://latex.artofproblemsolving.com/8/5/f/85f4ddc2e4256a4d95e8339b5d7e08ebab11102b.png)
