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Evaluating averages of [a,b] and {a,b,c}

Source: AMC 10 2011 a Problem 3

June 25, 2011

AMC

Problem Statement

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\}

?

<span class='latex-bold'>(A)</span>\ \frac{2}{9} \qquad<span class='latex-bold'>(B)</span>\ \frac{5}{18} \qquad<span class='latex-bold'>(C)</span>\ \frac{1}{3} \qquad<span class='latex-bold'>(D)</span>\ \frac{7}{18} \qquad<span class='latex-bold'>(E)</span>\ \frac{2}{3}

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