Difference between revisions of "2022 AMC 8 Problems/Problem 2"
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==Solution== | ==Solution== | ||
| − | + | We have | |
| − | + | <cmath>\begin{align*} | |
| − | + | (5 \, \blacklozenge \, 3) \, \bigstar \, 6 &= \left(5^2-3^2) \, \bigstar \, 6 \\ | |
| + | &= 16 \, \bigstar \, 6 \\ | ||
| + | &= (16-6)^2 \\ | ||
| + | &= \boxed{\textbf{(D) } 100}. | ||
| + | \end{align*}</cmath> | ||
<i>pog</i> | <i>pog</i> | ||
Revision as of 15:26, 28 January 2022
Problem
Consider these two operations:
What is the value of 
Solution
We have
\begin{align*}
(5 \, \blacklozenge \, 3) \, \bigstar \, 6 &= \left(5^2-3^2) \, \bigstar \, 6 \\
&= 16 \, \bigstar \, 6 \\
&= (16-6)^2 \\
&= \boxed{\textbf{(D) } 100}.
\end{align*} (Error compiling LaTeX. Unknown error_msg)
pog
See Also
| 2022 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
