Question

If there are 100 questions in total, and each right answer carries 1 marks, each wrong answer has a negative mark of 1/3, a student attended 88 questions and scored 68 marks. how many questions did student answer correctly?

Answer 1

Answer:

In a test there are 80 questions. A candidate gets 1 mark for each correct answer, and a minus of .5 for each wrong answer. If the candidate scores 54.5 marks, how many correct answers did he have?

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:

Depends on how unattempted questions are marked.

If unattempted questions are not counted as wrong answer the student answered 73 correctly.

If unattempted questions are counted as wrong answer the student answered 76 correctly

Step-by-step explanation:

If unattempted questions are not counted as wrong answer:

let a be the number correctly answered

let b be the number incorrectly answered

a - 1/3 b = 68   =>  a = 68 + 1/3b

a + b = 88

(68 + 1/3b) + b = 88

b = 15

a = 73

If unattempted questions are counted as wrong answer:

a - 1/3 b = 68   =>  a = 68 + 1/3b

a + b = 100

(68 + 1/3b) + b = 100

b = 24

a = 76