2000 AMC 8 第 2 题

先试着解答 2000 AMC 8 第 2 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 2000 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。

2.

下列哪个数小于它的倒数?
Which of these numbers is less than its reciprocal?
−2-2
−1-1
00
11
22
答案:A
知识点:不等式
小提示:
检查 00 是否有倒数。
Check whether 00 has a reciprocal
大提示:
比较 −2-2 和 −12-\frac{1}{2}。
Compare −2-2 with −12-\frac{1}{2}
解答:
00 没有倒数,11 和 −1-1 的倒数都是它们本身。
22 的倒数是 12\frac{1}{2},但 22 不小于 12\frac{1}{2}。
因为 −2<−12-2 < -\frac 12,所以 −2-2 是唯一小于其倒数的选项。
所以正确答案是 A。
00 has no reciprocal, and 11 and −1-1 are their own reciprocals.
The reciprocal of 22 is 12,\frac{1}{2}, but 22 is not less than 12.\frac{1}{2}.
Therefore, as −2<−12,-2 < -\frac 12, we know that −2-2 is the only one of the answer choices that is less than its reciprocal.
Thus, A is the correct answer.
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