2021 AMC 12B Fall Problem 16
Below is the professionally curated solution for Problem 16 of the 2021 AMC 12B Fall, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12B Fall solutions, or check the answer key.
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Difficulty rating: 2100
16.
Suppose are positive integers such that and What is the sum of all possible distinct values of
Solution:
The gcd sum of is large, so the numbers share substantial common factors. Searching the partitions of that meet the condition gives exactly two solution types.
The triple has sum and The triple has sum and
The sum of the distinct values is
Thus, the correct answer is B.
Problem 16 in Other Years
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