2004 AMC 12A 第 2 题

先试着解答 2004 AMC 12A 第 2 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2004 AMC 12A 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

2.

在 AMC 1212 中,每道答对的题得 66 分,每道答错的题得 00 分,每道未作答的题得 2.52.5 分。如果 Charlyn 在 2525 道题中有 88 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 100100 分?
On the AMC 12,12, each correct answer is worth 66 points, each incorrect answer is worth 00 points, and each problem left unanswered is worth 2.52.5 points. If Charlyn leaves 88 of the 2525 problems unanswered, how many of the remaining problems must she answer correctly in order to score at least 100?100?
1111
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1414
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答案:C
知识点:不等式取整函数
小提示:
88 道空题已经贡献 2.5×82.5 \times 8 分。
The 88 blanks already contribute 2.5×82.5 \times 8 points
大提示:
求每题 66 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 66 points each cover the remaining points
解答:
88 道未作答的题值 2.5×8=202.5 \times 8 = 20 分,所以 Charlyn 还需要从答对的题中得到至少 100−20=80100 - 20 = 80 分。
每道答对的题值 66 分,而不小于 8080 的最小 66 的倍数是 84=6×1484 = 6 \times 14。所以她至少需要答对 1414 道题。
所以正确答案是 C。
The 88 unanswered problems are worth 2.5×8=202.5 \times 8 = 20 points, so Charlyn needs at least 100−20=80100 - 20 = 80 more points from correct answers.
Each correct answer is worth 66 points, and the smallest multiple of 66 that is at least 8080 is 84=6×14.84 = 6 \times 14. So she needs at least 1414 correct answers.
Thus, the correct answer is C.
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