2001 AMC 8 Problems/Problem 22
Contents
[hide]Problem
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?
Solution
The highest possible score is if you get every answer right, to get . The second highest possible score is if you get questions right and leave the remaining one blank, to get a . Therefore, no score between and , exclusive, is possible, so is not possible, .
Solution 2
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 .
See Also
2001 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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