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Source: 10B #7/12B #5

November 17, 2021
SFFTFractionsAMCAMC 10number theory

Problem Statement

Call a fraction ab\frac{a}{b}, not necessarily in the simplest form special if aa and bb are positive integers whose sum is 1515. How many distinct integers can be written as the sum of two, not necessarily different, special fractions?
<spanclass=latexbold>(A)</span> 9<spanclass=latexbold>(B)</span> 10<spanclass=latexbold>(C)</span> 11<spanclass=latexbold>(D)</span> 12<spanclass=latexbold>(E)</span> 13<span class='latex-bold'>(A)</span>\ 9 \qquad<span class='latex-bold'>(B)</span>\ 10 \qquad<span class='latex-bold'>(C)</span>\ 11 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ 13