AMC 8 2001 Problem 22
AMC8 2001 年第 22 题
特殊数与不定方程★★★☆☆
On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is NOT possible?
在一项有 20 个问题的测试中，每个正确答案得 5 分，每个未回答的问题得 1 分，每个错误答案得 0 分。则以下哪个得分是不可能的？
- A.90
- B.91
- C.92
- D.95
- E.97
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
The highest possible score is if you get every answer right, to get 5(20)=100. The second highest possible score is if you get 19 questions right and leave the remaining one blank, to get a 5(19)+1(1)=96. Therefore, no score between 96 and 100, exclusive, is possible, so 97 is not possible, .
We can equivalently construct the following rules: You have 100 point at first, but if you give the wrong answer, you will lose 5 points, if you don't answer a question you will lose 4 points. Obviously, you can lose 10 points, 9 points, 8 points, 5 points or 4 points, but you cannot lose 3 points. The answer is .
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