Difference between revisions of "2011 AMC 10B Problems/Problem 15"
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== Solution == | == Solution == | ||
− | + | Simplify each operation and see which ones hold true. | |
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<cmath>\begin{align*} | <cmath>\begin{align*} | ||
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\text{III.} \qquad x @ (y @ z) &= (x @ y) @ (x @ z)\\ | \text{III.} \qquad x @ (y @ z) &= (x @ y) @ (x @ z)\\ | ||
x @ \frac{y+z}{2} &= \frac{x+y}{2} @ \frac{x+z}{2}\\ | x @ \frac{y+z}{2} &= \frac{x+y}{2} @ \frac{x+z}{2}\\ | ||
− | \frac{2x+y+z}{4} & | + | \frac{2x+y+z}{4} &= \frac{2x+y+z}{4} |
\end{align*}</cmath> | \end{align*}</cmath> | ||
− | <math>\boxed{\textbf{( | + | <math>\boxed{\textbf{(E)} \text{II and III only}}</math> |
== See Also== | == See Also== |
Latest revision as of 10:06, 13 July 2021
Problem
Let denote the "averaged with" operation: . Which of the following distributive laws hold for all numbers and ?
Solution
Simplify each operation and see which ones hold true.
See Also
2011 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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All AMC 10 Problems and Solutions |
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