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2021 Fall AMC 12B Problem 3

Problem 3 of 25EasierAlgebraProblem-Solving Techniques

At noon on a certain day, Minneapolis is NN degrees warmer than St. Louis. At 4:004{:}00 the temperature in Minneapolis has fallen by 55 degrees while the temperature in St. Louis has risen by 33 degrees, at which time the temperatures in the two cities differ by 22 degrees. What is the product of all possible values of N?N?

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Solution

At noon the gap is N.N. Minneapolis then loses 55 degrees and St. Louis gains 3,3, so the gap changes by 8.8. The new absolute difference is ∣N−8∣=2.|N - 8| = 2. This gives N=10N = 10 or N=6,N = 6, whose product is 60.60. Thus, the correct answer is C.
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