AMC12 2007 B

AMC12 2007 B · Q5

AMC12 2007 B · Q5. It mainly tests Linear inequalities, Arithmetic misc.

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?

2007 年 AMC 12 比赛的计分方式为：每题答对得 6 分，答错得 0 分，不作答得 1.5 分。看完 25 道题后，Sarah 决定尝试前 22 题，并将最后 3 题留空不答。她在前 22 题中至少需要答对多少题才能得到至少 100 分？

(A) 13 13

(B) 14 14

(D) 16 16

(E) 17 17

Answer

Correct choice: (D)

正确答案：（D）

Solution

She must get at least $100 - 4.5 = 95.5$ points, and that can only be possible by answering at least $\lceil \frac{95.5}{6}\rceil = 16 \Rightarrow \mathrm {(D)}$ questions correctly.

她至少需要得到 $100 - 4.5 = 95.5$ 分，而这只有在至少答对 $\lceil \frac{95.5}{6}\rceil = 16 \Rightarrow \mathrm {(D)}$ 题时才可能。

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