2021 AMC 12B Fall Problem 3

Below is the professionally curated solution for Problem 3 of the 2021 AMC 12B Fall, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12B Fall solutions, or check the answer key.

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Concepts:absolute value casework

Difficulty rating: 1090

At noon on a certain day, Minneapolis is $N$ degrees warmer than St. Louis. At $4{:}00$ the temperature in Minneapolis has fallen by $5$ degrees while the temperature in St. Louis has risen by $3$ degrees, at which time the temperatures in the two cities differ by $2$ degrees. What is the product of all possible values of $N?$

$10$

$30$

$60$

$100$

$120$

Solution:

At noon the gap is $N.$ Minneapolis then loses $5$ degrees and St. Louis gains $3,$ so the gap changes by $8.$ The new absolute difference is $|N - 8| = 2.$

This gives $N = 10$ or $N = 6,$ whose product is $60.$

Thus, the correct answer is C.

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