2021 Fall AMC 10B Problem 7
Problem 7 of 25EasierAlgebraNumber TheoryCounting & Probability
Call a fraction not necessarily in 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?
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Solution
A special fraction with denominator equals where We need integer values of
Taking a check of the fourteen possible denominators gives the following pairs that produce integers: Their distinct sums are
There are such integers.
Thus, the answer is C .