Question

Carroll 老师承诺：即将到来的考试中，所有选择题都答对的人都会得到 A。下面哪一个陈述在逻辑上必然成立？

Ms. Carroll promised that anyone who got all the multiple choice questions right on the upcoming exam would receive an A on the exam. Which one of these statements necessarily follows logically?

如果 Lewis 没有得到 A，那么他所有选择题都答错了。

If Lewis did not receive an A, then he got all of the multiple choice questions wrong.

如果 Lewis 没有得到 A，那么他至少答错了一道选择题。

If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.

如果 Lewis 至少答错了一道选择题，那么他没有得到 A。

If Lewis got at least one of the multiple choice questions wrong, then he did not receive an A.

如果 Lewis 得到了 A，那么他所有选择题都答对了。

If Lewis received an A, then he got all of the multiple choice questions right.

如果 Lewis 得到了 A，那么他至少答对了一道选择题。

If Lewis received an A, then he got at least one of the multiple choice questions right.

答案：B

知识点：逻辑推理

难度评级：900

解答：

老师只承诺：如果所有选择题都答对，就一定得到 A；她没有规定得到 A 的其他途径。

因此，即使没有答对所有选择题，也仍有可能得到 A。同样，即使只答错一道选择题，也仍有可能得不到 A。老师承诺的逆否命题是：如果没有得到 A，那么并非所有选择题都答对，也就是至少答错了一道。因此选项 A、C、D、E 都不一定成立。所以正确答案是 B。

The promise says that getting every multiple choice question right guarantees an A. Its contrapositive is that anyone who did not receive an A must not have gotten every multiple choice question right. In other words, that person got at least one multiple choice question wrong.

Thus, B is the correct answer.

2017 AMC 10A 第 6 题

答案：B

难度评级：900

解答：

其他年份的第 6 题