2011 AMC 10A Problem 3

Problem 3 of 25EasierAlgebra

Suppose

[a\ b]

denotes the average of

a

and

b,

and

\{a\ b\ c\}

denotes the average of

a,

b,

and

c.

What is the value of the following expression?

\{\{1 \ 1 \ 0\} \ [0 \ 1] \ 0\}

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Solution

We have that

\{1 \ 1 \ 0\} = \dfrac{1 + 1 + 0}{3} = \dfrac{2}{3}.

We also get that

[0 \ 1] = \dfrac{1 + 0}{2} = \dfrac{1}{2}.

Finally,

\left\{\dfrac{2}{3} \ \dfrac{1}{2} \ 0\right\} = \dfrac{\dfrac{2}{3} + \dfrac{1}{2} + 0}{3} = \dfrac{7}{18}.

Thus, D is the correct answer.