A music test included 50 multiple choice questions. Zoltan’s score was calculated by
adding 4 points for each correct answer,
subtracting 1 point for each incorrect answer, and
adding 0 points for each unanswered question.
Zoltan answered 45 of the 50 questions and his score was 135 points. The number of questions that Zoltan answered incorrectly is
Pick one
Solution 1
Zoltan answered 45 questions.
If all of his answers had been correct, his score would have been points.
Since his score was 135 points, then he lost points.
For each incorrect answer, he lost 5 points compared to a correct answer, since a correct answer adds 4 points and an incorrect answer subtracts 1 point.
Therefore, Zoltan had incorrect answers.
(We can check that 36 correct, 9 incorrect, and 5 unanswered gives a score of or points.)
Solution 2
Suppose that Zoltan answered questions incorrectly.
Since he answered 45 questions in total, then he answered questions correctly.
Since the test included 50 questions and he answered 45, then he did not answer 5 questions.
Using the marking scheme, his score was .
We are told that his score was 135 points.
Hence, and so .
Thus, or .
Therefore, Zoltan answered 9 questions incorrectly.
(We can check that 36 correct, 9 incorrect, and 5 unanswered gives a score of or points.)