Question

在 AMC $12$ 中，每道答对的题得 $6$ 分，每道答错的题得 $0$ 分，每道未作答的题得 $2.5$ 分。如果 Charlyn 在 $25$ 道题中有 $8$ 道未作答，那么剩下的题中她至少要答对多少道，才能得到至少 $100$ 分？

On the AMC $12,$ each correct answer is worth $6$ points, each incorrect answer is worth $0$ points, and each problem left unanswered is worth $2.5$ points. If Charlyn leaves $8$ of the $25$ problems unanswered, how many of the remaining problems must she answer correctly in order to score at least $100?$

$11$

$13$

$14$

$16$

$17$

答案：C

知识点：不等式取整函数

难度评级：1020

小提示：

$8$ 道空题已经贡献 $2.5 \times 8$ 分。

The $8$ blanks already contribute $2.5 \times 8$ points

大提示：

求每题 $6$ 分的正确答案至少需要多少道，才能补足剩余分数。

Find the smallest number of correct answers whose $6$ points each cover the remaining points

解答：

$8$ 道未作答的题值 $2.5 \times 8 = 20$ 分，所以 Charlyn 还需要从答对的题中得到至少 $100 - 20 = 80$ 分。

每道答对的题值 $6$ 分，而不小于 $80$ 的最小 $6$ 的倍数是 $84 = 6 \times 14$ 。所以她至少需要答对 $14$ 道题。

所以正确答案是 C。

The $8$ unanswered problems are worth $2.5 \times 8 = 20$ points, so Charlyn needs at least $100 - 20 = 80$ more points from correct answers.

Each correct answer is worth $6$ points, and the smallest multiple of $6$ that is at least $80$ is $84 = 6 \times 14.$ So she needs at least $14$ correct answers.

Thus, the correct answer is C.

2004 AMC 12A 第 2 题

答案：C

难度评级：1020

小提示：

大提示：

解答：

其他年份的第 2 题