2022 AMC 8 Problem 2 — Solution | LIVE by Po-Shen Loh

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2022 AMC 8 Problem 2

Attempt Problem 2 of the 2022 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 8 solutions, or check the answer key.

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2.

Consider these two operations: $\begin{align*} a\,\blacklozenge\,b &= a^2 - b^2 \\ a \star b &= (a - b)^2 \end{align*}$

Compute the value:

$(5\,\blacklozenge\,3) \star 6$

$-20$

$4$

$16$

$100$

$220$

Answer: D

Concepts:custom operation order of operations

Difficulty rating: 560

Solution:

Using the definitions, $\begin{align*} (5\,\blacklozenge\,3) \star 6 &= (5^2-3^2) \star 6 \\ &=16 \star 6 \\ &=(16-6)^2\\ &= 100\end{align*}$

Thus, the correct answer is D.

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