MathDB
Mean and Median

Source: 2018 AMC 12A #6

February 8, 2018
2018 AMC 12AAMCAMC 12AMC 12 Ano posts

Problem Statement

For positive integers mm and nn such that m+10<n+1m+10<n+1, both the mean and the median of the set {m,m+4,m+10,n+1,n+2,2n}\{m, m+4, m+10, n+1, n+2, 2n\} are equal to nn. What is m+nm+n?
<spanclass=latexbold>(A)</span>20<spanclass=latexbold>(B)</span>21<spanclass=latexbold>(C)</span>22<spanclass=latexbold>(D)</span>23<spanclass=latexbold>(E)</span>24<span class='latex-bold'>(A) </span>20\qquad<span class='latex-bold'>(B) </span>21\qquad<span class='latex-bold'>(C) </span>22\qquad<span class='latex-bold'>(D) </span>23\qquad<span class='latex-bold'>(E) </span>24