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2023 AMC 8 Problems/Problem 20

Revision as of 18:25, 24 January 2023 by Starleague (talk | contribs)

We have the set {3, 3, 8, 16, 28}. To double the range we must find the current range, which is $28 - 3 = 25$, to then the double is $2(25) = 50$ 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 $53 + 7 = \boxed{\text{(D)}60}$ -apex304, SohumUttamchandani, wuwang2002, TaeKim

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