Question

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 $N?$

$10$

$30$

$60$

$100$

$120$

Answer: C

Concepts:absolute value linear equation

Difficulty rating: 870

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 .

2021 AMC 10B Fall Problem 4

Answer: C

Difficulty rating: 870

Solution:

Problem 4 in Other Years