Question

大于二且除以三、四、五或六时余数都为二的最小数，位于哪两个数之间？

The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numbers?

$40\text{ and }50$

$51\text{ and }55$

$56\text{ and }60$

$61\text{ and }65$

$66\text{ and }99$

答案：D

知识点：最小公倍数模运算

难度评级：1240

视频讲解：

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文字解答：

设这个数为 $x$ 。因为它除以 $3,4,5,6$ 时余数都是 $2$ ，所以 $x-2$ 是 $3,4,5,6$ 的公倍数。这表示 $x-2$ 是 $lcm(3,4,5,6)$ 的倍数，而这个最小公倍数是 $60$ 。因此 $x-2$ 必须是 $60$ 的倍数。下一个满足条件的数出现在 $x-2 = 60 \implies x = 62$ 时。

所以正确答案是 D。

Let the number be $x.$ Since it leaves a remainder of $2$ when divided by $3,4,5,6,$ we know $x-2$ is a multiple of $3,4,5,6.$ This means $x-2$ is a multiple of $lcm(3,4,5,6)$ which is $60.$ Therefore, $x-2$ must be a multiple of $60.$ The next number such that this occurs is when $x-2 = 60 \implies x = 62 .$

Thus, the answer is D .

2012 AMC 8 第 15 题

答案：D

难度评级：1240

视频讲解：

文字解答：

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