2021 Fall AMC 10B Problems/Problem 7
Problem
Call a fraction 
, not necessarily in the simplest form special if 
and 
are positive integers whose sum is 
. How many distinct integers can be written as the sum of two, not necessarily different, special fractions?
Solution
Listing out all special fractions, we get:
Simplifying and grouping based on their denominators gives
}
}
}
See Also
| 2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
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| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
