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
(A) 9
(B) 15
(C) 41
(D) 40
(E) 5
Solution 1

Zoltan answered 45 questions.

If all of his answers had been correct, his score would have been $45(4)=180$ points.

Since his score was 135 points, then he lost $180-135=45$ 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 $45 \div 5=9$ incorrect answers.

(We can check that 36 correct, 9 incorrect, and 5 unanswered gives a score of $4(36)-1(9)+0(5)$ or 135 points.)

## Solution 2

Suppose that Zoltan answered $x$ questions incorrectly.

Since he answered 45 questions in total, then he answered $45-x$ 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 $4(45-x)-1(x)+0(5)$.

We are told that his score was 135 points.

Hence, $4(45-x)-1(x)+0(5)=135$ and so $180-4 x-x=135$.

Thus, $5 x=45$ or $x=9$.

Therefore, Zoltan answered 9 questions incorrectly.

(We can check that 36 correct, 9 incorrect, and 5 unanswered gives a score of $4(36)-1(9)+0(5)$ or 135 points.)

ANSWER: (A)