2023 AMC 8
Complete problem set with solutions and individual problem pages
Problem 20 Hard
Two integers are inserted into the list to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?
- A.
- B.
- C.
- D.
- E.
Answer:D
To double the range, we must find the current range, which is , to then double to: . Since we do not want to change the median, we need to get a value less than (as would change the mode) for the smaller, making fixed for the larger. Anything less than is not beneficial to the optimization because you want to get the largest range without changing the mode. So, taking our optimal values of and , we have an answer of .
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