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2021 AMC 10D Question 7

AMC10 · 2021 AMC 10D

Question 7

Call a fraction $\frac{a}{b},$ not necessarily in simplest form, *special* if $a$ and $b$ are positive integers whose sum is $15.$ How many distinct integers can be written as the sum of two, not necessarily different, special fractions?
  1. $ \ 9 $
  2. $ \ 10 $
  3. $ \ 11 $
  4. $ \ 12 $
  5. $ \ 13 $