Difference between revisions of "2001 AMC 8 Problems/Problem 22"
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The highest possible score is if you get every answer right, to get <math> 5(20)=100 </math>. The second highest possible score is if you get <math> 19 </math> questions right and leave the remaining one blank, to get a <math> 5(19)+1(1)=96 </math>. Therefore, no score between <math> 96 </math> and <math> 100 </math>, exclusive, is possible, so <math> 97 </math> is not possible, <math> \boxed{\text{E}} </math>. | The highest possible score is if you get every answer right, to get <math> 5(20)=100 </math>. The second highest possible score is if you get <math> 19 </math> questions right and leave the remaining one blank, to get a <math> 5(19)+1(1)=96 </math>. Therefore, no score between <math> 96 </math> and <math> 100 </math>, exclusive, is possible, so <math> 97 </math> is not possible, <math> \boxed{\text{E}} </math>. | ||
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| + | ==Solution 2== | ||
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| + | 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 <math> \boxed{\text{E}} </math>. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2001|num-b=21|num-a=23}} | {{AMC8 box|year=2001|num-b=21|num-a=23}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:15, 16 June 2024
Contents
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
