2018 AMC 12B Problem 10
Below is the professionally curated solution for Problem 10 of the 2018 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 12B solutions, or check the answer key.
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Difficulty rating: 1700
10.
A list of positive integers has a unique mode, which occurs exactly times. What is the least number of distinct values that can occur in the list?
Solution:
The mode uses of the entries, leaving Because the mode is unique, every other value appears at most times, so at least distinct non-mode values are needed.
Adding the mode gives This is achievable: use copies each of through ten copies of and one copy of
Thus, the correct answer is D.
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