2021 Fall AMC 12B Problem 3

Problem 3 of 25EasierAlgebra

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?

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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

N = 6,

whose product is

60.

Thus, the correct answer is C.