1959 AMC 12 第 46 题

先试着解答 1959 AMC 12 第 46 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1959 AMC 12 解答,或核对答案

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 dd 天的假期中观察到:

(1)(1) 上午或下午共下雨 77 次;

(2)(2) 若下午下雨,则当天上午晴朗;

(3)(3) 有五个晴朗的下午;

(4)(4) 有六个晴朗的上午。

dd 等于:

A student on vacation for dd days observed that

(1)(1) it rained 77 times, morning or afternoon;

(2)(2) when it rained in the afternoon, it was clear in the morning;

(3)(3) there were five clear afternoons;

(4)(4) there were six clear mornings.

Then dd equals:

77

99

1010

1111

1212

答案:B
知识点:基本计数补集计数
难度评级:1590
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 (2)(2) 保证下雨的下午与下雨的上午不会发生在同一天

Condition (2)(2) ensures that a rainy afternoon and rainy morning never occur on the same day

解答:

下雨的上午有 d6d-6 个,下雨的下午有 d5d-5 个。由条件 (2)(2),可知这些下雨时段互不重合,总数为 77。因此 (d6)+(d5)=7 (d-6)+(d-5)=7\text{,}所以 2d=182d=18,且 d=9d=9

因此,正确答案是 B

There are d6d-6 rainy mornings and d5d-5 rainy afternoons. By condition (2),(2), these are distinct rainy occasions, and their total is 7.7. Hence (d6)+(d5)=7, (d-6)+(d-5)=7, so 2d=182d=18 and d=9.d=9.

Thus, the correct answer is B.

← 第 45 题#45
完整试卷

其他年份的第 46 题

1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1955 AMC 12 · 1956 AMC 12 · 1957 AMC 12 · 1958 AMC 12