2010 AMC 10B Problems/Problem 15
Contents
[hide]Problem
On a -question multiple choice math contest, students receive points for a correct answer, points for an answer left blank, and point for an incorrect answer. Jesse’s total score on the contest was . What is the maximum number of questions that Jesse could have answered correctly?
Solution
Let be the amount of questions Jesse answered correctly, be the amount of questions Jesse left blank, and be the amount of questions Jesse answered incorrectly. Since there were questions on the contest, . Since his total score was , . Also, . We can substitute this inequality into the previous equation to obtain another inequality: . Since is an integer, the maximum value for is .
Solution 2
We can plug in each answer choice and find our what is the greatest one that works. We start of with Answer Choice since it is the largest one.
E is right, Jesse got questions right.
If Jesse got questions right, then he gains points, he then needs to get another wrong to achieve a score of . However, this is impossible as the test only contains questions, and he needs questions in order to achieve this.
D is right, Jesse got questions right.
If Jesse got questions right, then he gains points, he then needs to get another wrong in order to achieve a score of . However, this is impossible as the test only contains questions, and he needs questions in order to achieve this.
C is right, Jesse got questions right.
If Jesse got questions right, then he gains points, he then needs to get another wrong in order to achieve a score of . This is possible since this only requires questions. The other questions remain blank and earn him points.
- SAMANTAP
Video Solution
https://youtu.be/vYXz4wStBUU?t=549
~IceMatrix
See Also
2010 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.