Problem-Solving and Data AnalysisHardOverlapping sets
Problem-Solving and Data Analysis practice question
In a survey of 50 people, 30 like coffee, 20 like tea, and 8 like both. How many like neither?
Answer: 8
People who like coffee OR tea = 30 + 20 − 8 = 42 (subtract the overlap once). Neither = 50 − 42 = 8. Subtracting the 'both' group prevents double-counting.
Common wrong answers
- If you answered 0
- You did 50 − 30 − 20 and never added back the 8 people counted in both groups; coffee-or-tea is 42, so 8 like neither.
- If you answered 16
- You removed the overlap of 8 twice (30 + 20 − 8 − 8 = 34). It should be subtracted once: 42 like at least one, leaving 50 − 42 = 8.
- If you answered 42
- That's the number who like coffee or tea (30 + 20 − 8). The question asks for the rest: 50 − 42 = 8.
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