2011 AMC 10A Problems/Problem 3

Problem

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

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

Solution

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

Video Solution

https://youtu.be/JKO9YzQULvM

~savannahsolver

2011 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2011 AMC 10A Problems/Problem 3

Contents

Problem

Solution

Video Solution

See Also