Question

In a multiple-choice examination, there are 20 questions. Each correct answer is worth 4 marks, while 2 marks are to be deducted for every wrong answer. Further, 1 mark is to be deducted for every unattempted question. One student receives a total of 46 marks in the examination. However, before releasing the marks, the professor realizes that she has, by mistake, deducted 2 marks for every unattempted question and 1 mark for every wrong answer.

After correction, how many marks will the student get?

Accepted Answer

C. Let $x$ be correct, $y$ be wrong, and $z$ be unattempted questions. $x + y + z = 20 \implies z = 20 - (x+y)$. Mistaken score formula: $4x - y - 2z = 46$. $4x - y - 2(20 - x - y) = 46 \implies 6x + y - 40 = 46 \implies 6x + y = 86$. Since $x + y \le 20$ and $x, y \ge 0$ integers: $x = 14 \implies y = 2 \implies z = 4$. Correct score formula: $4x - 2y - z = 5x - y - 20$. Substituting $x = 14, y = 2$: Correct marks $= 4(14) - 2(2) - 4 = 56 - 4 - 4 = 48$.

Multiple-choice examination scoring correction

Explanation

Practise this under exam conditions