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Difference between revisions of "2018 AMC 10B Problems/Problem 14"
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== Solution ==
 
== Solution ==
  
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To minimize the number of values, we want to maximize the number of times they appear. So, we could have 223 numbers appear 9 times, 1 number appear once, and the mode appear 10 times, giving us a total of 223 + 1 + 1 = <math>\boxed{(D) 225}</math>
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To minimize the number of values, we want to maximize the number of times they appear. So, we could have 223 numbers appear 9 times, 1 number appear once, and the mode appear 10 times, giving us a total of <math>223 + 1 + 1</math> = <math>\boxed{(D) 225}</math>

Revision as of 15:30, 16 February 2018

A list of $2018$ positive integers has a unique mode, which occurs exactly $10$ times. What is the least number of distinct values that can occur in the list?

$\textbf{(A)}\ 202\qquad\textbf{(B)}\ 223\qquad\textbf{(C)}\ 224\qquad\textbf{(D)}\ 225\qquad\textbf{(E)}\ 234$

Solution

To minimize the number of values, we want to maximize the number of times they appear. So, we could have 223 numbers appear 9 times, 1 number appear once, and the mode appear 10 times, giving us a total of $223 + 1 + 1$ = $\boxed{(D) 225}$

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