2022 AMC 8 Problems/Problem 2

Revision as of 14:26, 28 January 2022 by MRENTHUSIASM (talk | contribs) (Reformatted.)

Problem

Consider these two operations: \begin{align*} a \, \blacklozenge \, b &= a^2 - b^2\\ a \, \bigstar \, b &= (a - b)^2 \end{align*} What is the value of $(5 \, \blacklozenge \, 3) \, \bigstar \, 6?$

$\textbf{(A) } {-}20 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 100 \qquad \textbf{(E) } 220$

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 (ProblemsAnswer KeyResources)
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. AMC logo.png