2011 AMC 10B 第 8 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。

8.

某海滩在气温至少为 80F80^{\circ} F 且晴朗时会很拥挤。六月十日该海滩不拥挤。关于这一天的天气条件,可以推出什么?

At a certain beach if it is at least 80F80^{\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 8080^{\circ}F,且天气不晴朗。

The temperature was cooler than 80 80^{\circ} F and it was not sunny.

气温低于 8080^{\circ}F,或者天气不晴朗。

The temperature was cooler than 80 80^{\circ} F or it was not sunny.

如果气温至少为 8080^{\circ} F,那么那天晴朗。

If the temperature was at least 80 80^{\circ} F, then it was sunny.

如果气温低于 8080^{\circ} F,那么那天晴朗。

If the temperature was cooler than 80 80^{\circ} F, then it was sunny.

如果气温低于 8080^{\circ}F,那么那天不晴朗。

If the temperature was cooler than 80 80^{\circ} F, then it was not sunny.

答案:B
知识点:逻辑推理
难度评级:870
解答:

原命题是:若气温至少 80F80^\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 80F80^\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 80F80^\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 80F80^\circ F, or it was not sunny, or both.

Thus, B is the correct answer.

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