AMC 8 2004 Problem 11
AMC8 2004 年第 11 题
统计与数据图表★★★☆☆
The numbers -2, 4, 6, 9 and 12 are rearranged according to these rules:
1. The largest isn't first, but it is in one of the first three places.
2. The smallest isn't last, but it is in one of the last three places.
3. The median isn't first or last.
What is the average of the first and last numbers?
对－2，4，6，9 和 12 这些数按照如下规则重新排序：
最大的数不在第一个位置，但它位于前三个位置中的某个位置。
最小的数不在最后一个位置，但它位于后三个位置中的某个位置。
中位数不在第一个或者最后一个位置。
那么第一个数和最后一个数的平均值是多少？
- A.3.5
- B.5
- C.6.5
- D.7.5
- E.8
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
From rule 1, the largest number, 12, can be second or third. From rule 2, because there are five places, the smallest number -2 can either be third or fourth. The median, 6 can be second, third, or fourth. Because we know the middle three numbers, the first and last numbers are 4 and 9, disregarding their order. Their average is (4+9)/2 = 6.5.
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