AMC 8 1986 Problem 22
AMC8 1986 年第 22 题
逻辑推理（跨域）★★★☆☆
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?
Alan、Beth、Carlos 和 Diana 正在讨论本评分周期他们可能的数学成绩。Alan 说："如果我得了 A，那么 Beth 会得 A。" Beth 说："如果我得了 A，那么 Carlos 会得 A。" Carlos 说："如果我得了 A，那么 Diana 会得 A。" 所有这些陈述都是真的，但只有两名学生得了 A。哪两人得了 A？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
If Alan got an A, then Beth, and therefore Carlos and Diana would also get A's. But only two students actually got A's, so Alan did not get an A.
If Beth got an A, then Carlos, and therefore Diana would get also get A's. Once again, this is impossible since only two students got A's. Therefore, Beth did not get an A.
By process of elimination, must have gotten A's.
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