A test has 60 questions. A student scores 1 mark for a correct answer, –1/2 for a wrong answer and –1/4 for not attempting a question. If the net score of a student who attempted 48 questions is 33 marks, then how many questions did he get wrong?*1) 82) 123) 104) None of these
Question
A test has 60 questions. A student scores 1 mark for a correct answer, –1/2 for a wrong answer and –1/4 for not attempting a question. If the net score of a student who attempted 48 questions is 33 marks, then how many questions did he get wrong?*1) 82) 123) 104) None of these
Solution
Let's solve this step by step:
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The student attempted 48 questions, so he did not attempt 60 - 48 = 12 questions. For not attempting a question, he loses 1/4 marks. So, for 12 questions, he loses 12 * (–1/4) = –3 marks.
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The net score of the student is 33 marks. But he lost 3 marks for not attempting 12 questions. So, the total marks he got from the questions he attempted is 33 - (–3) = 36 marks.
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For each correct answer, the student scores 1 mark. So, if he answered all the 48 questions correctly, he would have got 48 * 1 = 48 marks. But he got only 36 marks. So, he lost 48 - 36 = 12 marks.
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For each wrong answer, the student loses 1/2 marks. So, the number of questions he got wrong is 12 / (1/2) = 24.
So, the student got 24 questions wrong. The answer is not in the options given, so the correct answer is 4) None of these.
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