In a bar survey, the rectangle represents everyone in the bar. The circle…
2024
In a bar survey, the rectangle represents everyone in the bar. The circle represents people who like apple juice, the triangle represents people who like orange juice, and the pentagon represents people who like pineapple juice. The disjoint region counts are: apple only = 15, apple and orange = 8, orange only = 9, orange and pineapple = 6, pineapple only = 18, and rectangle-only (inside the bar but outside all three juice shapes) = 42. How many people in the bar like neither apple juice nor orange juice?
Answer: B. 60 — CONCEPTFor two sets A and B inside a universal set U, “neither A nor B” means the complement U \ (A ∪ B). Every disjoint region outside both A and B is…
- A.
52
- B.
60
- C.
64
- D.
48
Attempted by 460 students.
Show answer & explanation
Correct answer: B
CONCEPT
For two sets A and B inside a universal set U, “neither A nor B” means the complement U \ (A ∪ B). Every disjoint region outside both A and B is counted, even when it belongs to a third set.
APPLICATION
Take the rectangle as the universal set and exclude every region that lies in the apple circle or the orange triangle.
The remaining disjoint regions are pineapple only, containing 18 people, and rectangle-only, containing 42 people.
Add the remaining region counts: 18 + 42 = 60.
CROSS-CHECK
All six disjoint regions contain 15 + 8 + 9 + 6 + 18 + 42 = 98 people.
The apple-or-orange union contains 15 + 8 + 9 + 6 = 38 people.
Its complement therefore contains 98 − 38 = 60 people.
RESULT
Therefore, 60 people like neither apple juice nor orange juice.
Explore the full course: Tcs Ignite Smart Hiring Test Series