Question

某天中午，Minneapolis 比 St. Louis 暖 $N$ 度。到 $4{:}00$ ，Minneapolis 的温度下降了 $5$ 度，而 St. Louis 的温度上升了 $3$ 度，此时两城市温度相差 $2$ 度。所有可能的 $N$ 值的乘积是多少？

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 $N?$

$10$

$30$

$60$

$100$

$120$

答案：C

知识点：绝对值分类讨论

难度评级：1090

小提示：

中午的温差是 $N$ ；追踪两个温度变化如何改变这个差。

At noon the difference is $N$ ; track how each change affects the gap

大提示：

新温差为 $|N - 5 - 3| = 2$ 。

The new difference is $|N - 5 - 3| = 2$

解答：

中午温差为 $N$ 。之后 Minneapolis 的温度下降 $5$ 度，St. Louis 的温度上升 $3$ 度，所以温差改变了 $8$ 度。新的绝对温差为 $|N - 8| = 2$ 。

由此得到 $N = 10$ 或 $N = 6$ ，乘积为 $60$ 。

所以正确答案是 C。

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 第 3 题

答案：C

难度评级：1090

小提示：

大提示：

解答：

其他年份的第 3 题