Question

There are $30$ questions in a multiple-choice set. A student gets $1$ mark for each unattempted question, $0$ mark for each wrong answer and $4$ marks for each correct answer. A student answered $x$ questions correctly and scored $60$. Then the number of possible value of $x$ is __.

• A. $15$
• B. $10$
• C. $6$
• D. $5$

Answer 1

The correct option is C $6$

Let the number of correct answers $=a$

Let the number of unattempted questions$=b$

Number of incorrect answers $=c$

$\therefore a+b+c=304a+b+0\left(c\right)=604a+b=60$

We will proceed by decresing $a$ by one and increaing the unattempted questions so that our total points remain the same same and total questions remain same

If $a>15$, then $b$ will take negative value and which is not possible.

So, we have $a\le 15$

When $a=15$ then $b=0$

$a=14$ then $b=4$

$a=13$ then $b=8$

$a=12$ then $b=12$

$a=11$ then $b=16$

$a=10$ then $b=20$

If $a=9$ then $b=24$. So, we get total questions $=9+24=33>30$ which is not true.

So, $10\le a\le 15$

Thus six cases are possible

Hence, option $C$ is correct.