1995 AJHSME Problems/Problem 22

Problem

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?

$\text{(A)}\ 162 \qquad \text{(B)}\ 172 \qquad \text{(C)}\ 173 \qquad \text{(D)}\ 174 \qquad \text{(E)}\ 222$

Solution

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: $5\cdot7=35 \text{, } 11\cdot17=187 \text{ X}$ $5\cdot11=55 \text{, } 7\cdot17=119 \text{ X}$ $5\cdot17=85 \text{, } 7\cdot11=77 \text{ }\surd$ $85+77= \boxed{\text{(A)}\ 162}$

1995 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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1995 AJHSME Problems/Problem 22

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