Question

There are $30$ questions in a multiple-choice test.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 $6$

A student gets $4$ marks for correct answer and $1$ marks for unattempted question. given he answer $x$ question correctly. Let he answers $y$ question incorrect then total marks will be

$4x+(30-x-y)=60$

$3x-y=30$

And we have total number of questions $=30$

So $x+y\le 30$

We know that $x$ and $y$ both should be non negative integers.

Combining all situation we have 6 solution of (x,y) that is $(10,0),(11,3),(12,6),(13,9),(14,12),(15,15)$