1998 AJHSME Problems/Problem 10
Problem 10
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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All AJHSME/AMC 8 Problems and Solutions |