2011 AMC 10B 第 8 题

Question

某海滩在气温至少为

80^{\circ} F

且晴朗时会很拥挤。六月

10

日该海滩不拥挤。关于六月

10

日的天气条件，可以推出什么？

At a certain beach if it is at least

80^{\circ} F

and sunny, then the beach will be crowded. On June

10

the beach was not crowded. What can be concluded about the weather conditions on June

10?

气温低于

80^{\circ}

F，且天气不晴朗。

The temperature was cooler than

80^{\circ}

F and it was not sunny.

气温低于

80^{\circ}

F，或者天气不晴朗。

The temperature was cooler than

80^{\circ}

F or it was not sunny.

如果气温至少为

80^{\circ}

F，那么那天晴朗。

If the temperature was at least

80^{\circ}

F, then it was sunny.

如果气温低于

80^{\circ}

F，那么那天晴朗。

If the temperature was cooler than

80^{\circ}

F, then it was sunny.

如果气温低于

80^{\circ}

F，那么那天不晴朗。

If the temperature was cooler than

80^{\circ}

F, then it was not sunny.

答案：B

知识点：逻辑推理

难度评级：870

小提示：

使用“炎热且晴朗则拥挤”的逆否命题。

Use the contrapositive of “hot and sunny implies crowded”

大提示：

不拥挤表示两个条件中至少有一个不成立。

Not crowded means at least one of the two conditions failed

解答：

原命题是：若气温至少

80^\circ F

且晴朗，则海滩拥挤。

因为海滩不拥挤，这两个条件不可能同时成立。因此气温低于

80^\circ F

，或者天气不晴朗，或者两者都成立。

所以正确答案是 B。

The statement says that if the weather was at least

80^\circ F

and sunny, then the beach was crowded.

Because the beach was not crowded, the two conditions could not both have been true. Therefore the temperature was cooler than

80^\circ F

, or it was not sunny, or both.

Thus, B is the correct answer.

2011 AMC 10B 第 8 题

答案：B

难度评级：870

小提示：

大提示：

解答：

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