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Difference between revisions of "2011 AMC 10A Problems/Problem 3"

(Created page with '== Problem 3 == Suppose [<math>a</math> <math>b</math>] denotes the average of <math>a</math> and <math>b</math>, and {<math>a</math> <math>b</math> <math>c</math>} denotes the …')
(No difference)

Revision as of 19:37, 10 February 2011

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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