2023 AMC 8 Problems/Problem 20

We have the set {3, 3, 8, 16, 28}. To double the range we must find the current range, which is , to then the double is Since we dont want to change the median we need to get a value greater than 8 (as 8 would change the mode) for the smaller and 53 is fixed for the larger as anything less than 3 is not beneficial to the optimization. So taking our optimal values of 53 and 7 we have an answer of -apex304, SohumUttamchandani, wuwang2002, TaeKim