Difference between revisions of "1995 AJHSME Problems/Problem 22"
Mrdavid445 (talk | contribs) (Created page with "==Problem== The number <math>6545</math> can be written as a product of a pair of positive two-digit numbers. What is the sum of this pair of numbers? <math>\text{(A)}\ 162 \q...") |
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<math>\text{(A)}\ 162 \qquad \text{(B)}\ 172 \qquad \text{(C)}\ 173 \qquad \text{(D)}\ 174 \qquad \text{(E)}\ 222</math> | <math>\text{(A)}\ 162 \qquad \text{(B)}\ 172 \qquad \text{(C)}\ 173 \qquad \text{(D)}\ 174 \qquad \text{(E)}\ 222</math> | ||
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| + | ==Solution== | ||
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| + | 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: | ||
| + | <cmath>5*7=35 \text{, } 11*17=187 \text{ X}</cmath> <cmath>5*11=55 \text{, } 7*17=119 \text{ X}</cmath> <cmath>5*17=85 \text{, } 7*11=77 \text{ }\surd </cmath> <cmath>85+77=162 \text{(A)}</cmath> | ||
Revision as of 13:32, 5 July 2012
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)
