AMC8 2000

AMC8 2000 · Q2

AMC8 2000 · Q2. It mainly tests Linear inequalities, Absolute value.

Which of these numbers is less than its reciprocal?

以下哪个数小于它的倒数？

(A) -2 -2

(B) -1 -1

(D) 1 1

(E) 2 2

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The number $0$ has no reciprocal, and $1$ and $-1$ are their own reciprocals. This leaves only $2$ and $-2$. The reciprocal of $2$ is $\frac{1}{2}$, but $2$ is not less than $\frac{1}{2}$. The reciprocal of $-2$ is $-\frac{1}{2}$, and $-2$ is less than $-\frac{1}{2}$.

答案（A）：数字 $0$ 没有倒数，而 $1$ 和 $-1$ 的倒数是它们本身。因此只剩下 $2$ 和 $-2$。$2$ 的倒数是 $\frac{1}{2}$，但 $2$ 并不小于 $\frac{1}{2}$。$-2$ 的倒数是 $-\frac{1}{2}$，并且 $-2$ 小于 $-\frac{1}{2}$。

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