Question

数字零、一、二、三、四、五、六、七、八、九各使用一次，组成两个五位数，使它们的和尽可能大。下列哪一个可能是其中一个数？

Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?

$76531$

$86724$

$87431$

$96240$

$97403$

答案：C

知识点：位值最优化

难度评级：1480

视频讲解：

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文字解答：

要让两个五位数的和最大，从左到右的各位数字应尽可能大。因此两个数的第一位必须取自 $9,8$ ，第二位取自 $7,6$ ，第三位取自 $5,4$ ，第四位取自 $3,2$ ，最后一位取自 $1,0$ 。

给出的数中，唯一满足这种位置要求的是 $87431$ 。

所以正确答案是 C。

To construct two five digit numbers, first digits of the numbers from the left must be as great as possible. Therefore, the leftmost unused number must be either of the greatest two numbers. This means the first digit must be either of $9,8,$ the second digit must be either of $7,6,$ the third digit must be either of $5,4,$ the fourth digit must be either of $3,2$ and the last digit must be either of $1,0.$

The only one of the given numbers that satisfy this is $87431.$

Thus, the answer is C .

2012 AMC 8 第 16 题

答案：C

难度评级：1480

视频讲解：

文字解答：

其他年份的第 16 题