2021 AMC 10B Fall Problem 4

Below is the professionally curated solution for Problem 4 of the 2021 AMC 10B Fall, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10B Fall solutions, or check the answer key.

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Concepts:absolute value linear equation

Difficulty rating: 870

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:

Let $N=m-s$ be the noon temperature difference. At $4{:}00$ , the new difference is $(m-5)-(s+3)=N-8$ .

The temperatures then differ by $2$ degrees, so $|N-8|=2$ . Hence $N=6$ or $N=10$ , and the product of all possible values is $6\cdot10=60$ .

Thus, the answer is C .

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