AMC10 2011 A

AMC10 2011 A · Q3

AMC10 2011 A · Q3. It mainly tests Averages (mean).

Suppose $[a\ b]$ denotes the average of $a$ and $b$, and $\{a\ b\ c\}$ denotes the average of $a$, $b$, and $c$. What is $\big\{\{1\ 1\ 0\}\ [0\ 1]\ 0\big\} ?$

设$[a\ b]$表示$a$和$b$的平均值，$\{a\ b\ c\}$表示$a$、$b$和$c$的平均值。求$\big\{\{1\ 1\ 0\}\ [0\ 1]\ 0\big\}$的值？

(A) $\frac{2}{9}$ $\frac{2}{9}$

(B) $\frac{5}{18}$ $\frac{5}{18}$

(D) $\frac{7}{18}$ $\frac{7}{18}$

(E) $\frac{2}{3}$ $\frac{2}{3}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

First note that $\{1\ 1\ 0\} = \frac{2}{3}$ and $[0\ 1] = \frac{1}{2}$. Therefore $\big\{\{1\ 1\ 0\}\ [0\ 1]\ 0\big\} = \{\frac{2}{3}, \frac{1}{2}, 0\} = \frac{\frac{2}{3} + \frac{1}{2} + 0}{3} = \frac{7}{18}$.

首先，$\{1\ 1\ 0\} = \frac{2}{3}$，$[0\ 1] = \frac{1}{2}$。因此$\big\{\{1\ 1\ 0\}\ [0\ 1]\ 0\big\} = \{\frac{2}{3}, \frac{1}{2}, 0\} = \frac{\frac{2}{3} + \frac{1}{2} + 0}{3} = \frac{7}{18}$。

Topics

AR.006 Averages (mean)