AMC 8 2001 Problem 21
AMC8 2001 年第 21 题
统计与数据图表★★★☆☆
The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is
一组五个不同正整数的平均值是 15。中位数是 18。这五个整数中最大的那个数的最大可能值为
- A.19
- B.24
- C.32
- D.35
- E.40
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Since there is an odd number of terms, the median is the number in the middle, specifically, the third largest number is 18, and there are 2 numbers less than 18 and 2 numbers greater than 18. The sum of these integers is 5(15)=75, since the mean is 15. To make the largest possible number with a given sum, the other numbers must be as small as possible. The two numbers less than 18 must be positive and distinct, so the smallest possible numbers for these are 1 and 2. The number right after 18 also needs to be as small as possible, so it must be 19. This means that the remaining number, the maximum possible value for a number in the set, is .
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