Difference between revisions of "2023 AMC 8 Problems/Problem 20"

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~Star League (https://starleague.us)
 
~Star League (https://starleague.us)
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==Video Solution by OmegaLearn (Using Smart Sequence Analysis)==
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https://youtu.be/qNsgNa9Qq9M

Revision as of 21:50, 24 January 2023

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

Animated Video Solution

https://youtu.be/ItntB7vEafM

~Star League (https://starleague.us)

Video Solution by OmegaLearn (Using Smart Sequence Analysis)

https://youtu.be/qNsgNa9Qq9M