Question

二〇〇七年 AMC 12 的计分方式为：每答对一题得 $6$ 分，答错得 $0$ 分，空题得 $1.5$ 分。Sarah 看过 $25$ 道题后，决定尝试前 $22$ 题，最后 $3$ 题留空。为了至少得到 $100$ 分，她在前 $22$ 题中至少要答对多少题？

The 2007 AMC 12 contests will be scored by awarding $6$ points for each correct response, $0$ points for each incorrect response, and $1.5$ points for each problem left unanswered. After looking over the $25$ problems, Sarah has decided to attempt the first $22$ and leave the last $3$ unanswered. How many of the first $22$ problems must she solve correctly in order to score at least $100$ points?

$13$

$14$

$15$

$16$

$17$

答案：D

知识点：不等式

难度评级：1120

解答：

三道空题给 $3\cdot1.5=4.5$ 分。

所以 Sarah 需要从答对题中得到至少 $100-4.5=95.5$ 分。因为她至少要答对 $16$ 题，此时得分为 $16\cdot6+4.5=100.5$ 。 $15\lt\dfrac{95.5}{6}\lt16,$

所以正确答案是 D。

The three unanswered problems give $3\cdot1.5=4.5$ points.

So Sarah needs at least $100-4.5=95.5$ points from correct answers. Since $15\lt\dfrac{95.5}{6}\lt16,$ she must solve at least $16$ problems correctly, which would give her $16\cdot6+4.5=100.5$ points.

Thus, the correct answer is D.

2007 AMC 12B 第 5 题

答案：D

难度评级：1120

解答：

其他年份的第 5 题