There are 90 questions in a test. Each correct answer fetches 1 mark, each wrong answer & unanswered question attract a penalty of 1/4 mark… — Answer & Discussion

There are 90 questions in a test. Each correct answer fetches 1 mark, each wrong answer & unanswered question attract a penalty of 1/4 marks & 1/8 marks respectively. Bilbo scored 23 marks in the test. What is the minimum possible number of the questions wrongly answered by him?

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Discussion 1

CCommunity26 May 2019

Here is losing total of 67 marks in test (from the all correct situation)

If he answers a question wrongly, he should drop by 1.25 marks

If he leaves a question unanswered, he is losing 1.125 marks

Going through options, we find that

For option 1)

⇒ Marks lost by questions = 2.5

⇒ Marks required to be lost by unanswered ques. = 64.5

But 64.5 / 1.125 is not an integer.

Hence, it is not possible

For option 2)

⇒ Marks lost by question = 6.25

⇒ Marks required to be lost by unanswered ques. = 60.75

Here, 60.75 / 1.125 is an integer.

Hence, it is possible

Other two options also doesn’t give an integer.

∴ The minimum number of wrong answers is 5