A test consists of 25 MCQs. Each correct answer gives +4 marks and incorrect answer gives -1 mark. If a candidate scores 74 marks, then how many questions were left unattempted?
[amp_mcq option1=”4″ option2=”3″ option3=”5″ option4=”9″ correct=”option1″]
This question was previously asked in
UPSC CAPF – 2022
Total questions: c + i + u = 25
Total score: 4c – i = 74 (unattempted questions contribute 0 marks).
We need to find the value of u. We can test the given options for u.
If u = 4, then c + i = 25 – 4 = 21.
We have the system of equations:
1) c + i = 21
2) 4c – i = 74
Add the two equations: (c + i) + (4c – i) = 21 + 74 => 5c = 95 => c = 19.
Substitute c = 19 into equation 1: 19 + i = 21 => i = 21 – 19 = 2.
Check the score: 4c – i = 4(19) – 2 = 76 – 2 = 74. This matches the given score.
Therefore, the number of unattempted questions is 4.
– Use variables to represent the number of correct, incorrect, and unattempted questions.
– The total number of questions is the sum of correct, incorrect, and unattempted questions.
– The total score is calculated based on the marks per correct and incorrect answer.