A test has 50 questions. A student scores 1 mark for a correct answer, `-1/3` for a wrong answer and `-1/6`for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

Options

A. 6
B. 12
C. 9
D. 3

Answer

D

Explanation

Let the number of questions answered correctly = x
The number of questions answered wrongly = y
and the number of question unanswered = z
Then, according to the question
`x + y + z = 50 ......(i)`
`x - 1/3 y - 1/6z = 32 `
or, `6x – 2y - z = 192 ... (ii) `
adding (i) & (ii), we get
`7x - y = 242 `or, `y = 7x – 242 ... (iii)`
Putting `x = 35 `in (iii), we get
`y=7 xx 35 - 242 = 245 - 242 = 3 `
So, `y = 3 `is the minimum value of y as for any value of `x gt 35, y` start increasing.
[`because` Putting `x gt 35` i.e. 34, 33 etc., we get the negative value of y i.e not possible.]
Therefore, the minimum number of question answered wrongly = minimum value of y = 3.