CAPF AC 2020 Q124: General Mental Ability – Quantitative Aptitude
In a group of 100 children, 64 children like to play cricket, 53 children like to play football and 20 children like to play both cricket and football. How many children do NOT like to play cricket or football?
- (a) 3
- (b) 5
- (c) 7
- (d) 9
Answer: (a) 3
Explanation
Children who like neither game
Given: in a group of 100 children, 64 like to play cricket, 53 like to play football and 20 like to play both cricket and football.
How to think: adding 64 and 53 counts the 20 children who like both games twice.
Subtract them once to get the children who like at least one game.
The rest like neither.
| Step | Working |
|---|---|
| Cricket or football | 64 + 53 − 20 = 97 |
| Neither | 100 − 97 = 3 |
The group split up:
| Part | Children |
|---|---|
| Only cricket | 64 − 20 = 44 |
| Only football | 53 − 20 = 33 |
| Both | 20 |
| Neither | 3 |
| Total | 44 + 33 + 20 + 3 = 100 |
Answer: (a) 3.
Why each option is right or wrong
- (a) CORRECT. 64 + 53 − 20 = 97 like a game, so 100 − 97 = 3 like neither.
- (b) Incorrect. 5 does not make the four parts add up to 100.
- (c) Incorrect. 7 does not make the four parts add up to 100.
- (d) Incorrect. 9 does not make the four parts add up to 100.
Key point
n(A or B) = n(A) + n(B) − n(A and B). Here 64 + 53 − 20 = 97; neither = 100 − 97 = 3.
Remember
Either = A + B − both; neither = total − either.
Common mistakes
- Adding 64 and 53 without subtracting the 20 counted twice.
- Subtracting the 20 twice and getting 77 instead of 97.
- Giving 97, the number who like a game, as the answer.
Exam tip
Draw two overlapping circles. Fill the overlap first (20), then the two sides (44 and 33), then the outside.
Sources
- NCERT Class XI Mathematics — Sets (practical problems on union and intersection)
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Logical Venn Diagrams)