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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

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⇒ Solutions

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 ÷ 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.)

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 − 4x − x = 135.
Thus, 5x = 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.)

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Answer : (A) 9

Solution :

Let the number of answers Zoltan answered correctly be x and that answered incorrectly be y.

Answers not attempted = 50 - 45 = 5

His score : 135

x + y = 45 ---Eq.1 (Total questions attempted) And 4x - y = 135 ---Eq.2 (Marks according tomarking scheme)