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 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 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 F,且天气不晴朗。
The temperature was cooler than F and it was not sunny.
气温低于 F,或者天气不晴朗。
The temperature was cooler than F or it was not sunny.
如果气温至少为 F,那么那天晴朗。
If the temperature was at least F, then it was sunny.
如果气温低于 F,那么那天晴朗。
If the temperature was cooler than F, then it was sunny.
如果气温低于 F,那么那天不晴朗。
If the temperature was cooler than F, then it was not sunny.
答案:B
解答:
原命题是:若气温至少 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 ,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 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 , or it was not sunny, or both.
Thus, B is the correct answer.
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