AMC 8 1991 Problem 19
AMC8 1991 年第 19 题
统计与数据图表★★★☆☆
The average (arithmetic mean) of 10 different positive whole numbers is 10 . The largest possible value of any of these numbers is
10 个不同的正整数平均数为 10。这些数中最大可能值是多少？
- A.10
- B.50
- C.55
- D.90
- E.91
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
If the average of the numbers is 10, then their sum is 10×10=100.
To maximize the largest number of the ten, we minimize the other nine. Since they must be distinct, positive whole numbers, we let them be 1,2,3,4,5,6,7,8,9. Their sum is 45.
The sum of nine of the numbers is 45, and the sum of all ten is 100 so the last number must be .
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