Question

两个自然数的和为 $17{,}402$ 。其中一个数能被 $10$ 整除。如果擦去这个数的个位数字，就得到另一个数。这两个数的差是多少？

The sum of two natural numbers is $17{,}402.$ One of the two numbers is divisible by $10.$ If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?

$10{,}272$

$11{,}700$

$13{,}362$

$14{,}238$

$15{,}426$

答案：D

知识点：位值一次方程

难度评级：1120

解答：

较大的数末尾是 $0$ ，擦去这个数字会除以 $10$ 得到较小的数。因此较大的数是较小数的 $10$ 倍。设较小的数为 $x$ 则两数之和为 $x + 10x = 11x = 17{,}402$ ，得 $x = 1{,}582$ 。

两个数是 $1{,}582$ 和 $15{,}820$ ，它们的差为 $15{,}820 - 1{,}582 = 14{,}238$ 。

因此，正确答案是 D。

The larger number ends in $0,$ and erasing that digit divides it by $10$ to give the smaller number. So the larger number is $10$ times the smaller. Writing the smaller number as $x,$ the sum is $x + 10x = 11x = 17{,}402,$ giving $x = 1{,}582.$

The two numbers are $1{,}582$ and $15{,}820,$ whose difference is $15{,}820 - 1{,}582 = 14{,}238.$

Thus, the correct answer is D.

2021 AMC 12A Spring 第 3 题

答案：D

难度评级：1120

解答：

其他年份的第 3 题