In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and –2 for every incorrect answer and 0 for not supplying any answer. If Yash secured 94 marks in a test, what are the possibilities of his marking correct or wrong answer?

Given is that, there are total 50 questions in a test.

Marks awarded for correct answer = 2

Marks awarded for incorrect answer = -2

Marks awarded for unattempting an answer = 0

Score of Yash in the test = 94

We can find minimum correct answers in Yash’s test paper.

So, minimum correct answer is given by

⇒

⇒ Minimum answers = 47

So possibilities are:

(i). Yash attempted 47 answers correct, while (50 – 47 =) 3 unattempted.

Check: Marks on 47 correct answers = 47 × 2 = 94

Marks on remaining 3 unattempted answers = 3 × 0 = 0

Total marks of Yash should be 94.

Total marks = Marks on 47 correct answers + Marks on 3 unattempted answers

⇒ Total marks = 94 + 0

⇒ Total marks = 94

(ii). Yash attempted 48 answers correct, while 1 answer wrong and 1 unattempted.

Check: Marks on 48 correct answers = 48 × 2 = 96

Marks on 1 wrong answer = 1 × -2 = -2

Marks on 1 unattempted answer = 1 × 0

Total marks should come out to be 94.

Total marks = Marks on 48 correct answers + Marks on 1 wrong answer + Marks on 1 unattempted

⇒ Total marks = 96 – 2 + 0

⇒ Total marks = 94