Question

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

Answer 1

⇒ 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.) 

≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥

⇒ 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 − 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.)

Answer: (A) 

Answer 2

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)

Eq.1 + Eq.2 

5x = 180
x = 36

So, he answered 36 questions correctly.

Questions attempted incorrectly = 45 - 36 = 9


So, the answer is (A) 9.