2022 AMC 12B Problem 1 — Solution | LIVE by Po-Shen Loh

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2022 AMC 12B Problem 1

Below is the professionally curated solution for Problem 1 of the 2022 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 12B solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:custom operation absolute value order of operations

Difficulty rating: 890

1.

Define $x \diamond y$ to be $|x - y|$ for all real numbers $x$ and $y.$ What is the value of

$(1 \diamond (2 \diamond 3)) - ((1 \diamond 2) \diamond 3)?$

$-2$

$-1$

$0$

$1$

$2$

Solution:

Since $2 \diamond 3 = |2-3| = 1,$ we get $1 \diamond (2 \diamond 3) = 1 \diamond 1 = 0.$

Since $1 \diamond 2 = |1-2| = 1,$ we get $(1 \diamond 2) \diamond 3 = 1 \diamond 3 = |1-3| = 2.$

The value is $0 - 2 = -2.$

Thus, the correct answer is A.

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