CAPF AC 2020 Q111: General Mental Ability – Quantitative Aptitude
- (a) 18
- (b) 17
- (c) 16
- (d) 15
Answer: (c) 16
Explanation
Marks with negative marking
Given: the candidate attempts 20 questions and scores 72 marks.
5 marks are awarded for each correct answer and 2 marks are deducted for each wrong answer.
How to think: start from a perfect score and count what each wrong answer costs.
All 20 right would give 100 marks.
Each wrong answer loses the 5 marks and costs 2 more, so it costs 7.
| Step | Working |
|---|---|
| Perfect score | 20 × 5 = 100 |
| Marks lost | 100 − 72 = 28 |
| Cost of one wrong answer | 5 + 2 = 7 |
| Wrong answers | 28 ÷ 7 = 4 |
| Correct answers | 20 − 4 = 16 |
Check by equation: let the correct answers be x.
Then 5x − 2(20 − x) = 72.
So 7x = 112 and x = 16.
Check each option:
| Correct | Wrong | Score |
|---|---|---|
| 18 | 2 | 90 − 4 = 86 |
| 17 | 3 | 85 − 6 = 79 |
| 16 | 4 | 80 − 8 = 72 |
| 15 | 5 | 75 − 10 = 65 |
Answer: (c) 16.
Why each option is right or wrong
- (a) Incorrect. 18 correct gives 90 − 4 = 86 marks, not 72.
- (b) Incorrect. 17 correct gives 85 − 6 = 79 marks.
- (c) CORRECT. 16 correct and 4 wrong give 80 − 8 = 72 marks.
- (d) Incorrect. 15 correct gives 75 − 10 = 65 marks.
Key point
Negative marking: wrong answers = (full marks − score) ÷ (marks for a right answer + penalty). Here (100 − 72) ÷ 7 = 4 wrong, so 16 right.
Remember
One wrong answer costs marks for the question plus the penalty.
Common mistakes
- Taking the cost of a wrong answer as 2; it is 5 + 2 = 7.
- Dividing 72 by 5 and guessing the nearest option.
- Reporting the number of wrong answers (4) when the question asks for correct ones.
Exam tip
Educated guess: each step down in correct answers lowers the score by 7. From 86 at option (a), two steps down is 72.
Sources
- NCERT Class VIII Mathematics — Linear Equations in One Variable
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Algebra)