2018 AMC 10B Problem 14
Problem 14 of 25IntermediateAlgebra
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?
Answer choices
Show solution
Solution
The mode shows up times. To keep the number of distinct values small, let every other value repeat as much as the rules allow, which is times each (any more would tie the mode). With distinct values the list holds at most entries. We need so giving Therefore, the answer is D.