Question

The rubric of a test with 30 questions states that for each correct answer, a student gets x marks and for each incorrect answer, a student will lose y marks. Andrea answered 22 questions correctly and 8 questions incorrectly, and she scored 52 points. Mike answered 24 questions correctly and 6 questions incorrectly, and he scored 54 points. Now, calculate the points deducted for each incorrect answer.

Answer 1

Let x be marks for a correct answer and y the marks lost for an incorrect one. From Andrea: 22x − 8y = 52. From Mike: 24x − 6y = 54.

Subtracting gives 2x + 2y = 2 ⇒ x + y = 1 ⇒ x = 1 − y. Substitute into one equation:
24(1 − y) − 6y = 54 ⇒ 24 − 30y = 54 ⇒ y = −1.

So the "points deducted" per incorrect answer is −1, i.e. there is no deduction—in fact 1 point is added for each incorrect answer. (For completeness, x = 2 marks per correct answer.)