Question

There are 80 questions in a test. Each correct answer
fetches 1 mark, each wrong answer & unanswered
question attract a penalty of 1/4 mark & 1/8 mark
respectively each. Frodo scored 23 marks in the test.
What is the minimum possible number of the ques-
tion wrongly answered by him?​

Answer 1

Answer:

I think you want to ask how are such questions solved

If x answers were correct and y were wrong

then x-o.5y= 54.5 --- (1)

and

assuming he/she attempted all questions

x+y = 80 ----(2)

solving 1 and 2

1.5y = 25.5 => y = 17

If the number of questions attempted are variable, then you have to put a constraint that x+y can only be an integer

The second constraint is 1.5y should have .5 as the least significant figure (after decimal)

The third constraint is y can never be more than 17

suppose y is 16, then 1.5 y is 24, which breaks the second constraint

suppose y is 15, then 1.5 y is 22.5, which is a valid answer if he/she attempted 77 questions, x is 62 in this case.

(Another way to achieve the same is decreasing the number of x by 1 and y by 2 to get the same result, only varying the number of attempts)

solving this way following are set of answers

------------------------------------------

attempted questions x y

------------------------------------------

80 63 17

77 62 15

74 61 13

71 60 11

68 59 9

65 58 7

62 57 5

59 56 3

56 55 1

Step-by-step explanation:

Answer 2

Answer:

HEY MATE HERE IS YOU ANSWER

Step-by-step explanation:

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.

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