Question

对所有实数 $x$ 和 $y$ ，定义 $x~\diamondsuit~ y$ 为 $|x-y|$ 。求 $(1~\diamondsuit~(2~\diamondsuit~3))-((1~\diamondsuit~2)~\diamondsuit~3)?$

Define $x~\diamondsuit~ y$ to be $|x-y|$ for all real numbers $x$ and $y.$ What is the value of $(1~\diamondsuit~(2~\diamondsuit~3))-((1~\diamondsuit~2)~\diamondsuit~3)?$

$-2$

$-1$

$0$

$1$

$2$

答案：A

知识点：自定义运算绝对值

难度评级：560

解答：

先计算最内层括号，再依次向外计算，即得上述结果。 $0-2=-2$ 。 $\begin{aligned} 1\mathbin\diamondsuit(2\mathbin\diamondsuit3)&=|1-|2-3||=0,\\ (1\mathbin\diamondsuit2)\mathbin\diamondsuit3&=||1-2|-3|=2. \end{aligned}$

所以正确答案是 A。

Working from the innermost operations outward gives $\begin{aligned} 1\mathbin\diamondsuit(2\mathbin\diamondsuit3)&=|1-|2-3||=0,\\ (1\mathbin\diamondsuit2)\mathbin\diamondsuit3&=||1-2|-3|=2. \end{aligned}$ Therefore, the given difference is $0-2=-2.$

Thus, the answer is A .

2022 AMC 10B 第 1 题

答案：A

难度评级：560

解答：

其他年份的第 1 题