Question

在这个加法题中，每个字母代表一个不同数字。如果 $T = 7$ ，且字母 $O$ 表示一个偶数，那么 $W$ 唯一可能的值是多少？ $\begin{array}{cccc}&T & W & O\\ +&T & W & O\\ \hline F& O & U & R\end{array}$

In this addition problem, each letter stands for a different digit. $\begin{array}{cccc}&T & W & O\\ +&T & W & O\\ \hline F& O & U & R\end{array}$ If $T = 7$ and the letter $O$ represents an even number, what is the only possible value for $W?$

$0$

$1$

$2$

$3$

$4$

答案：D

知识点：数字谜分类讨论

难度评级：1380

解答：

因为两个 $T$ 都是 $7$ ，所以 $O$ 是 $4$ 或 $5$ 。由于 $O$ 是偶数，得到 $O = 4$ 。

于是 $R = 4 + 4 = 8$ 。还知道 $W + W$ 不会进位，否则 $O$ 会是 $5$ 。

因此 $W$ 小于 $5$ ，且不能是 $4$ 或 $1$ 。如果 $W = 0$ ，则 $U = 0$ ，两个字母会代表同一个数字。如果 $W = 2$ ，则 $U = 4$ ，这也不允许。

所以 $W = 3$ 。

所以正确答案是 D。

Since both $T$ 's are $7,$ we get that $O$ is either $4$ or $5.$ Since $O$ is even, we get that $O = 4.$

Then, we get that $R = 4 + 4 = 8.$ We also know that $W + W$ doesn't carry over, since otherwise $O$ would be $5.$

Therefore, $W$ is less than $5$ and cannot be $4$ or $1.$ If $W = 0,$ then $U = 0,$ which gives two letters the same digit. If $W = 2,$ then $U = 4,$ which is also not allowed.

This makes $W = 3.$

Thus, D is the correct answer.

2003 AMC 8 第 14 题

答案：D

难度评级：1380

解答：

其他年份的第 14 题