Question

Isaac 写下了某个整数两次，另一个整数三次。这五个数的和为 $100$ ，并且其中一个数是 $28$ 。另一个数是多少？

Isaac has written down one integer two times and another integer three times. The sum of the five numbers is $100,$ and one of the numbers is $28.$ What is the other number?

$8$

$11$

$14$

$15$

$18$

答案：A

知识点：丢番图方程整除性

难度评级：1050

解答：

写作 $2x + 3y = 100$ 。如果 $28$ 被写了两次，则 $3y = 100 - 56 = 44$ ，这不是 $3$ 的倍数。

所以 $28$ 被写了三次： $2x = 100 - 84 = 16$ ，得 $x = 8$ 。

因此，正确选项是 A。

Write $2x + 3y = 100.$ If $28$ were written twice, then $3y = 100 - 56 = 44,$ which is not a multiple of $3.$

So $28$ is written three times: $2x = 100 - 84 = 16,$ giving $x = 8.$

Thus, the correct answer is A.

2015 AMC 12B 第 3 题

答案：A

难度评级：1050

解答：

其他年份的第 3 题