2011 AMC 10A Problems/Problem 3

Problem 3

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

$\textbf{(A)}\ \frac{2}{9} \qquad\textbf{(B)}\ \frac{5}{18} \qquad\textbf{(C)}\ \frac{1}{3} \qquad\textbf{(D)}\ \frac{7}{18} \qquad\textbf{(E)}\ \frac{2}{3}$

Solution

Average $1$ , $1$ , and $0$ to get $\frac23$ . Average $0$ , and $1$ , to get $\frac12$ . Average $\frac23$ , $\frac12$ , and $0$ . to get $\boxed{\textbf{(D)}\ \frac7{18}}$

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2011 AMC 10A Problems/Problem 3

Problem 3

Solution