Question

Larry 的老师让他把数字代入 $a$ 、 $b$ 、 $c$ 、 $d$ 和 $e$ ，再计算表达式并求值。Larry 忽略了括号，但加减号本身算对了，并且碰巧得到了正确结果。他给 $a$ 、 $b$ 、 $c$ 、 $d$ 代入的数分别是 $1$ 、 $2$ 、 $3$ 、 $4$ 。他给 $e$ 代入了什么数？ $a-(b-(c-(d+e)))$

Lucky Larry's teacher asked him to substitute numbers for $a,$ $b,$ $c,$ $d,$ and $e$ in the expression $a-(b-(c-(d+e)))$ and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for $a,$ $b,$ $c,$ and $d$ were $1,$ $2,$ $3,$ and $4,$ respectively. What number did Larry substitute for $e?$

$-5$

$-3$

$0$

$3$

$5$

答案：D

知识点：运算顺序一次方程

难度评级：1280

解答：

忽略括号时，Larry 会得到 $1 - 2 - 3 - 4 + e = e - 8.$

按括号正确计算， $\begin{align*} &1 - (2 -(3 - (4 + e)))\\ & = 1 - (2 - (-1 - e))\\ &= 1 - (3 + e) \\ &=-2 - e.\end{align*}$

两者相等，所以 $e - 8 = -2 - e$ $e = 3.$

所以正确答案是 D。

Ignoring the parentheses, Larry would get $1 - 2 - 3 - 4 + e = e - 8.$

Evaluating with the parentheses, one would get $\begin{align*} &1 - (2 -(3 - (4 + e)))\\ & = 1 - (2 - (-1 - e))\\ &= 1 - (3 + e) \\ &=-2 - e.\end{align*}$

Both of these values are the same, so $e - 8 = -2 - e$ $e = 3.$

Thus, D is the correct answer.

2010 AMC 10B 第 9 题

答案：D

难度评级：1280

解答：

其他年份的第 9 题