AMC8 2001
AMC8 2001 · Q22
AMC8 2001 · Q22. It mainly tests Arithmetic misc, Remainders & modular arithmetic.
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?
在一份20题的测试中，每题正确得5分，每题未答得1分，每题错误得0分。以下哪个分数是不可能的？
(A)
90
90
(B)
91
91
(C)
92
92
(D)
95
95
(E)
97
97
Answer
Correct choice: (E)
正确答案：（E）
Solution
To get a score in the 90s, a student must get 18 or 19 correct answers. If the number is 18, then the other two questions are worth 0+0, 0+1, 1+0 or 1+1, producing total scores of 90, 91 or 92. If the number correct is 19, then the total is 95+0 or 95+1. Therefore, the only possible scores in the 90s are 90, 91, 92, 95 and 96. This leaves 97 as an impossible score.
要得到90分的成绩，学生必须答对18或19题。如果答对18题，则剩下两题得分组合为0+0、0+1、1+0或1+1，总分为90、91或92。如果答对19题，则总分为95+0或95+1，即95或96。因此90分的可能分数只有90、91、92、95、96，97分不可能。
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