AMC10 2007 B

AMC10 2007 B · Q6

AMC10 2007 B · Q6. It mainly tests Averages (mean), Interest / growth (simple).

The 2007 AMC 10 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 only 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 10的评分规则是：每题正确得6分，每题错误得0分，每题未答得1.5分。Sarah看过25道题后，决定尝试前22道，只留最后3道未答。为了得到至少100分，她必须在前22道题中正确解出多少道？

(A) 13 13

(B) 14 14

(D) 16 16

(E) 17 17

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Sarah will receive 4.5 points for the three questions she leaves unanswered, so she must earn at least $100-4.5=95.5$ points on the first 22 problems. Because $$15<\frac{95.5}{6}<16,$$ she must solve at least 16 of the first 22 problems correctly. This would give her a score of 100.5.

答案（D）：Sarah 因为有三道题未作答，将获得 4.5 分，因此她在前 22 题中至少需要获得 $100-4.5=95.5$ 分。因为 $$15<\frac{95.5}{6}<16,$$ 她必须在前 22 题中至少答对 16 题。这样她的得分将是 100.5 分。

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