Difference between revisions of "2018 AMC 10B Problems/Problem 14"
(Created page with "A list of <math>2018</math> positive integers has a unique mode, which occurs exactly <math>10</math> times. What is the least number of distinct values that can occur in the...") |
MathMaestro9 (talk | contribs) |
||
| Line 2: | Line 2: | ||
<math>\textbf{(A)}\ 202\qquad\textbf{(B)}\ 223\qquad\textbf{(C)}\ 224\qquad\textbf{(D)}\ 225\qquad\textbf{(E)}\ 234</math> | <math>\textbf{(A)}\ 202\qquad\textbf{(B)}\ 223\qquad\textbf{(C)}\ 224\qquad\textbf{(D)}\ 225\qquad\textbf{(E)}\ 234</math> | ||
| + | |||
| + | == 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 = <math>\boxed{(D) 225}</math> | ||
Revision as of 16:28, 16 February 2018
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
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 = 
