2011 AMC 10A Problems/Problem 3: Difference between revisions
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== Problem | == Problem == | ||
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 average of <math>a</math>, <math>b</math>, and <math>c</math>. What is {{1 1 0} [0 1] 0}? | 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 average of <math>a</math>, <math>b</math>, and <math>c</math>. What is <math>\{\{\text{1 1 0}\} \text{ [0 1] } 0\}?</math> | ||
<math> \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} </math> | <math> \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} </math> | ||
== Solution == | |||
Average <math>1</math>, <math>1</math>, and <math>0</math> to get <math>\frac23</math>. Average <math>0</math>, and <math>1</math>, to get <math>\frac12</math>. Average <math>\frac23</math>, <math>\frac12</math>, and <math>0</math>. to get <math>\boxed{\textbf{(D)}\ \frac7{18}}</math> | Average <math>1</math>, <math>1</math>, and <math>0</math> to get <math>\frac23</math>. Average <math>0</math>, and <math>1</math>, to get <math>\frac12</math>. Average <math>\frac23</math>, <math>\frac12</math>, and <math>0</math>. to get <math>\boxed{\textbf{(D)}\ \frac7{18}}</math> | ||
==Video Solution== | |||
https://youtu.be/JKO9YzQULvM | |||
~savannahsolver | |||
== See Also == | |||
{{AMC10 box|year=2011|ab=A|num-b=2|num-a=4}} | |||
{{MAA Notice}} | |||
Latest revision as of 14:48, 16 January 2021
Problem
Suppose [
] denotes the average of and , and { 
} denotes the average of , , and . What is ![$\{\{\text{1 1 0}\} \text{ [0 1] } 0\}?$](http://latex.artofproblemsolving.com/b/e/c/becf15b17d9cd21e842633baa69800b452281da1.png)
Solution
Average 
, , and 
to get 
. Average , and , to get 
. Average , , and . to get 
Video Solution
~savannahsolver
See Also
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America. 
