Two subjects — Mathematical Reasoning Aptitude Question
Two subjects: In a class of 60 students, 35 study physics, 30 study chemistry and 15 study both. Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
In a class of 60 students, 35 study physics, 30 study chemistry and 15 study both. How many study neither?
Options
- 5
- 10
- 15
- 20
Show the answer and the worked solution
Correct answer: B. 10
Worked solution
- At least one subject = 35 + 30 − 15 = 50.
- Neither = 60 − 50 = 10.
Answer: 10.
The idea
Add the two groups and subtract the overlap once, then take the complement. Forgetting to remove the overlap gives 65, which is impossible.
Shortcut. Physics-only is 35 − 15 = 20, so physics-only plus all 30 chemists gives 50 students in at least one subject; 60 − 50 = 10.
Common trap. "5" — computing 35 + 30 − 60 = 5, which is the smallest overlap the numbers force, not the number studying neither.