CAPF AC 2022 Q44: General Mental Ability – Quantitative Aptitude
A test consists of 25 MCQs. Each correct answer gives +4 marks and each incorrect answer gives −1 mark. If a candidate scores 74 marks, then how many questions were left unattempted?
- (a) 4
- (b) 3
- (c) 5
- (d) 9
Answer: (a) 4
Explanation
Unattempted questions in a test
Given: a test has 25 questions; a correct answer gives +4 and a wrong answer −1; the candidate scores 74; find the number left unattempted.
How to think: let c be correct and w be wrong.
Then 4c − w = 74, and c + w cannot be more than 25.
Try values of c just above 74 ÷ 4.
| Correct (c) | Wrong (w = 4c − 74) | Attempted | Possible? |
|---|---|---|---|
| 18 | −2 | Not valid | No, wrong answers cannot be negative |
| 19 | 2 | 21 | Yes |
| 20 | 6 | 26 | No, more than 25 questions |
So 19 were correct and 2 wrong.
Unattempted: 25 − 21 = 4.
Answer: (a) 4.
Why each option is right or wrong
- (a) CORRECT. 19 correct and 2 wrong give 74 marks, leaving 4 unattempted.
- (b) Incorrect. 3 unattempted means 22 attempted, and no split of 22 gives 74.
- (c) Incorrect. 5 unattempted means 20 attempted, and no split of 20 gives 74.
- (d) Incorrect. 9 unattempted leaves only 16 attempted, worth at most 64 marks.
Key point
Marking-scheme problems: write score = 4c − w with c + w ≤ total, then test the few whole-number values of c that fit. Only one will satisfy both conditions.
Remember
19 right, 2 wrong, 4 left: 76 − 2 = 74.
Common mistakes
- Assuming all 25 were attempted and solving 4c − (25 − c) = 74, which gives a fraction.
- Forgetting that wrong answers reduce the score.
- Giving the number of wrong answers (2) instead of the unattempted ones.
Exam tip
Educated guess: 74 ÷ 4 is 18.5, so at least 19 answers were correct. 19 × 4 = 76, which is 2 too many, so 2 were wrong. 19 + 2 = 21 attempted, leaving 4.
Sources
- NCERT Class X Mathematics — Pair of Linear Equations in Two Variables
- R. S. Aggarwal, Quantitative Aptitude — Problems on Numbers