Only one of the two — Aptitude Question
Only one of the two: Of 100 people, 60 read newspaper A, 45 read newspaper B and 20 read both. Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
Of 100 people, 60 read newspaper A, 45 read newspaper B and 20 read both. How many read exactly one newspaper?
Options
- 55
- 65
- 75
- 85
Show the answer and the worked solution
Correct answer: B. 65
Worked solution
- Only A = 60 − 20 = 40; only B = 45 − 20 = 25.
- Exactly one = 40 + 25 = 65.
Answer: 65.
The idea
'Exactly one' removes the overlap from both groups, so it is the union minus the intersection: 85 − 20 = 65.
Shortcut. Exactly one = A + B − 2 × both = 105 − 40 = 65, since the 20 readers of both are counted twice in 60 + 45.
Common trap. "85" — computing the union 60 + 45 − 20, which counts readers of at least one newspaper and still includes the 20 who read both.