AMC 8 2023 Problem 20

AMC8 2023 年第 20 题

统计与数据图表★★★☆☆

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 the two additional numbers?

将两个整数加入数据列表3，3，8，11，28使得它的极差加倍，而众数和中位数保持不变．问所添加的两个数之和的最大可能值是多少？

A.56
B.57
C.58
D.60
E.61

正确答案 · Correct Answer

解析 · Solution

Solution 1

To double the range, we must find the current range, which is 28 - 3 = 25, to then double to: 2(25) = 50. Since we do not want to change the median, we need to get a value less than 8 (as 8 would change the mode) for the smaller, which will be 7. This fixes 53 for the larger value. Anything less than 3 is not beneficial to the optimization because you want to get the largest range without changing the mode. So, taking our optimal values of 7 and 53, we have an answer of 7 + 53 = 60., SohumUttamchandani, wuwang2002, TaeKim, CrystalFlower, CHECKMATE2021, lazypanda5050

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