AMC 8 2012 Problem 11

AMC8 2012 年第 11 题

统计与数据图表★★★☆☆

The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and

x

are all equal. What is the value of

x

正整数 3,4,5,6,6,7 和 x 组成的一组数，它们的平均数、中位数、唯一的众数都相等。那么 x 的值是多少？

A. $\hspace{.05in}5$
B. $\hspace{.05in}6$
C. $\hspace{.05in}7$
D. $\hspace{.05in}11$
E. $\hspace{.05in}12$

正确答案 · Correct Answer

解析 · Solution

Solution 1

Because the mode is unique, it must be 6 6, so the mean must also be 6 6. The sum of the seven numbers is 31 + 𝑥 31+x, which must be equal to 7 × 6 = 42 7×6=42. Therefore 𝑥 = 11 x=11. The median of the numbers 3, 4, 5, 6, 6, 7, 11 3,4,5,6,6,7,11 is also 6 6. Answer: 𝐷 D .

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