1959 AMC 12 第 46 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。
46.
一名学生在为期 天的假期中观察到:
上午或下午共下雨 次;
若下午下雨,则当天上午晴朗;
有五个晴朗的下午;
有六个晴朗的上午。
则 等于:
A student on vacation for days observed that
it rained times, morning or afternoon;
when it rained in the afternoon, it was clear in the morning;
there were five clear afternoons;
there were six clear mornings.
Then equals:
小提示:
根据晴朗上午和下午的数量,分别计算下雨的上午与下午
Count rainy mornings and rainy afternoons from the numbers of clear half-days
大提示:
条件 保证下雨的下午与下雨的上午不会发生在同一天
Condition ensures that a rainy afternoon and rainy morning never occur on the same day
解答:
下雨的上午有 个,下雨的下午有 个。由条件 ,可知这些下雨时段互不重合,总数为 。因此 所以 ,且 。
因此,正确答案是 B。
There are rainy mornings and rainy afternoons. By condition these are distinct rainy occasions, and their total is Hence so and
Thus, the correct answer is B.