Question

There only $30$ questions in a multiple-choice test. A student get $1$ 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 y be number of unattempted questions. Given x is number of currently insured question.

$\Rightarrow (30-x-y)$ were wrong answered.

$\Rightarrow 4\times x+1\times y+0\times (30-y)=60\Rightarrow 4x+y=60,x\le 30,y\le 30$

Ans $x+y<30$

If x = 9 , y = 24

$\Rightarrow x+y=33>30\therefore \text{Not possible}$

If x = 10 , y = 20

$\Rightarrow x+y=30\Rightarrow x=11,y=16x=12,y=12x=13,y=8x=14,y=4x=15,y=0$

$x=16,y=-4$ Y can't be negative $\therefore$ only 6 Possible values