1986 AMC 8 第 22 题
先试着解答 1986 AMC 8 第 22 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 1986 AMC 8 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。
22.
艾伦、贝丝、卡洛斯和戴安娜正在讨论本评分期数学课可能得到的成绩。艾伦说：“如果我得 A，那么贝丝会得 A。”贝丝说：“如果我得 A，那么卡洛斯会得 A。”卡洛斯说：“如果我得 A，那么戴安娜会得 A。”这些话都是真的，但只有两名学生得了 A。哪两名学生得了 A？
Alan, Beth, Carlos, and Diana were discussing their possible grades in mathematics class this grading period. Alan said, “If I get an A, then Beth will get an A.” Beth said, “If I get an A, then Carlos will get an A.” Carlos said, “If I get an A, then Diana will get an A.” All of these statements were true, but only two of the students received an A. Which two received A’s?
艾伦、贝丝
Alan, Beth
贝丝、卡洛斯
Beth, Carlos
卡洛斯、戴安娜
Carlos, Diana
艾伦、戴安娜
Alan, Diana
贝丝、戴安娜
Beth, Diana
答案：C
小提示：
如果链条中较早的学生得 A，那么他后面的所有学生也必须得 A
If a student earlier in the chain gets an A, everyone after them in the chain must also get an A
大提示：
要正好有两个 A，这两个必须是链条最后的学生
For exactly two A’s, the two must be the last students in the chain
解答：
这些陈述形成一条链：艾伦得 A 会推出贝丝得 A，贝丝得 A 会推出卡洛斯得 A，卡洛斯得 A 会推出戴安娜得 A。如果艾伦得 A，则四人都得 A；如果贝丝得 A，则三人得 A。
正好有两个 A 的唯一方式是链条最后两人得 A，即卡洛斯和戴安娜。
所以正确答案是 C。
The statements form a chain: Alan’s A forces Beth’s, Beth’s forces Carlos’s, and Carlos’s forces Diana’s. If Alan got an A, all four would; if Beth got an A, three would.
The only way to have exactly two A’s is for them to be the last two in the chain, Carlos and Diana.
Thus, the correct answer is C .
其他年份的第 22 题
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- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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