AMC 8 Daily Practice - New Patterns

Complete problem set with solutions and individual problem pages

Problem 5 Medium

An operation "* " is defined as follows: For any rational numbers x, y and z, x * x = 0, x * (y * z) = (x * y) + z, where "+" denotes ordinary addition. What is the value of 2023 * 2022?

  • A.

    0

  • B.

    1

  • C.

    2

  • D.

    3

  • E.

    4

Answer:B

 To compute 2023 * 2022:

1. Start with the definition 2022 * 2022 = 0.

2. Rewrite 2023 * 2022 by strategically adding and subtracting 2022.

2023 * 2022 = 2023 * 2022 + 2022 - 2022 =2023 * (2022 * 2022) -2022 = 2023 * 0 - 2022= 2023 * (2023 * 2023) - 2022 = (2023 * 2023) + 2023 - 2022 = 0+2023-2022 = 1

Final Answer:   \boxed{1}

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Problem 3 AMC 8 Daily Practice - New Patterns
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