Question

A test has 50 questions. A student scores 1 mark for a correct answer, $\frac{-1}{3}$ for a wrong answer, and $\frac{-1}{6}$ 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

• A. 6
• B. 3
• C. 2
• D. 5

Answer 1

The correct option is B

3

Let the number of correct answers be 'x', number of wrong answers be 'y' and number of questions not attempted be 'z'.

Thus,x+y+z=50 .............(i)

And $x-\frac{y}{3}-\frac{z}{6}=32$

The second equation can be written as,
6x-2y-z=192 ...................(ii)
Adding the two equations we get,
$7x-y=242\Rightarrow x=\frac{242}{7}+\frac{y}{7}=\frac{242+y}{7}$

Since, x and y are both integers, y cannot be 1 or 2. The minimum value that y can have is 3.
Hence option (b)