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 casework

Difficulty rating: 1090

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.

2021 AMC 12B Fall Problem 3

Answer: C

Difficulty rating: 1090

Solution:

Problem 3 in Other Years