Please explain it

15. 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) 12
(C) 9
(D) 3
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Dear Student,

Let x be the number of questions answered correctly, and,
Let y be the number of questions answered wrong.

Therefore,
Number of questions not attempted = Total number of questions - Number of questions answered correctly - number of questions answered wrong =  50-x-y

Now,
We need to find the smallest possible value of y. 

$$\begin{gathered} Score = x*1 + y*\left(\frac{-1}{3}\right) + (50-x-y)*\left(\frac{-1}{6}\right)= 32 \\ \Rightarrow x-\frac{y}{3}-\frac{50-x-y}{6} = 32 \\ \Rightarrow \frac{6x-2y-(50-x-y)}{6}=32 \\ \Rightarrow 7x-y-50 = 32*6 = 192 \\ \Rightarrow 7x-y = 192+50 = 242 \end{gathered}$$​

Now,
7*34 = 238, which is less than 242, so. x has to be at least 35, or else y will be negative. 
So, the smallest value of y occurs when x=35,
In that case,
7x - 242 = 7*35-242 =245-242 = 3
 
So the smallest value of y or the smallest possible number of wrong answers is 3.

Regards