1987 AJHSME Problems/Problem 24
Contents
[hide]Problem
A multiple choice examination consists of questions. The scoring is for each correct answer, for each incorrect answer, and for each unanswered question. John's score on the examination is . What is the maximum number of questions he could have answered correctly?
Solution
Solution 1
Let be the number of questions correct, be the number of questions wrong, and be the number of questions left blank. We are given that
Adding equation to double equation , we get
Since we want to maximize the value of , we try to find the largest multiple of less than . This is , so let . Then we have
Finally, we have . We want , so the answer is , or .
See Also
1987 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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