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Problem 2 (2022 AMC 8)

AMC 8Easy

From module Defined Operations

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Understand the scale
Scale 0.5: Easiest math competition problems, often solvable even for early middle school students without experience. 1: Problems strictly for beginners, often at a moderate middle school level. 1.5: Problems for stronger beginner students, on the level of the middling problems in most middle school contests. 2: For motivated beginners, harder questions from the previous categories. 2.5: More advanced beginner problems, hardest questions from previous categories. 3: Early intermediate problems that require more creative thinking. 3.5: Tougher early intermediate problems that consistently stretch into higher-level creative thinking or conceptual knowledge. 4: Intermediate-level problems. 4.5: Upper intermediate problems approaching the upper bound for non-invitational sprint math competitions. 5: More difficult AIME problems or simple proof-based Olympiad-style problems. 6: High-level AIME-styled questions or introductory Olympiad-level questions. 7: Tougher Olympiad-level questions, may require more technical knowledge. 8: High-level Olympiad-level questions. 9: Expert Olympiad-level questions. 9.5: The hardest problems appearing on Olympiads which the strongest students could reasonably solve. 10: Historically notorious problems, generally unsuitable for even very hard competitions because they are exceedingly tedious, long, and difficult.
Defined OperationsOrder of Operations

Problem

Consider these two operations: a⧫b=a2−b2,a★b=(a−b)2.a \blacklozenge b = a^2 - b^2, \qquad a \bigstar b = (a - b)^2. What is (5⧫3)★6(5 \blacklozenge 3) \bigstar 6?

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

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