2021 AMC 12B Fall 第 3 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
3.
某天中午，Minneapolis 比 St. Louis 暖 度。到 ，Minneapolis 的温度下降了 度，而 St. Louis 的温度上升了 度，此时两城市温度相差 度。所有可能的 值的乘积是多少？
At noon on a certain day, Minneapolis is degrees warmer than St. Louis. At the temperature in Minneapolis has fallen by degrees while the temperature in St. Louis has risen by degrees, at which time the temperatures in the two cities differ by degrees. What is the product of all possible values of
小提示：
中午的温差是 ；追踪两个温度变化如何改变这个差。
At noon the difference is ; track how each change affects the gap
大提示：
新温差为 。
The new difference is
解答：
中午温差为 。之后 Minneapolis 的温度下降 度，St. Louis 的温度上升 度，所以温差改变了 度。新的绝对温差为 。
由此得到 或 ，乘积为 。
所以正确答案是 C。
At noon the gap is Minneapolis then loses degrees and St. Louis gains so the gap changes by The new absolute difference is
This gives or whose product is
Thus, the correct answer is C.
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