Math Gold Medalist

Lor

2023 AMC 8 

Problem 20

Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of two additional numbers?

$\textbf{(A)}\ 56 \qquad \textbf{(B)}\ 57 \qquad \textbf{(C)}\ 58 \qquad \textbf{(D)}\ 60 \qquad \textbf{(E)}\ 61$

Casework

Mod, Median, Range, Mean, …

   Solution