1998 AJHSME Problems/Problem 10
Problem
Each of the letters , , , and represents a different integer in the set , but not necessarily in that order. If , then the sum of and is
Solution
There are different ways to approach this problem, and I'll start with the different factor of the numbers of the set .
has factor .
has factors and
has factors and
has factors , , and .
From here, we note that even though all numbers have the factor , only has another factor other than in the set (ie. )
We could therefore have one fraction be and another .
The sum of the numerators is
See also
1998 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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