Difference between revisions of "2022 AMC 8 Problems/Problem 2"
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What is the value of <math>(5 \, \blacklozenge \, 3) \, \bigstar \, 6?</math> | What is the value of <math>(5 \, \blacklozenge \, 3) \, \bigstar \, 6?</math> | ||
| − | <math>\textbf{(A) } {-}20\qquad\textbf{(B) } 4\qquad\textbf{(C) } 16\qquad\textbf{(D) } 100\qquad\textbf{(E) } 220</math> | + | <math>\textbf{(A) } {-}20 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 100 \qquad \textbf{(E) } 220</math> |
==Solution== | ==Solution== | ||
| − | We get that <math>(5 \, \blacklozenge \, 3) = 5^2 - 3^2 = 16</math>, so <cmath>(5 \, \blacklozenge \, 3) \, \bigstar \, 6 = 16 \, \bigstar \, 6 = (16 - 6)^2 = 10^2 = \boxed{\textbf{(D) }100}.</cmath> | + | We get that <math>(5 \, \blacklozenge \, 3) = 5^2 - 3^2 = 16</math>, so <cmath>(5 \, \blacklozenge \, 3) \, \bigstar \, 6 = 16 \, \bigstar \, 6 = (16 - 6)^2 = 10^2 = \boxed{\textbf{(D) } 100}.</cmath> |
<i>pog</i> | <i>pog</i> | ||
Revision as of 11:13, 28 January 2022
Problem
Consider these two operations:
What is the value of 
Solution
We get that 
, so ![\[(5 \, \blacklozenge \, 3) \, \bigstar \, 6 = 16 \, \bigstar \, 6 = (16 - 6)^2 = 10^2 = \boxed{\textbf{(D) } 100}.\]](http://latex.artofproblemsolving.com/e/a/4/ea43c3bb240d6eb0d0a04c1d8e8c879db4564121.png)
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. 
