In a town, 25% of families own a phone and 15% own a car; 65% own neither. Exactly 2000 families own both a phone and a car. Consider the statements: (i) 10% own both, (ii) 35% own either a car or a phone, (iii) 40,000 families live in the town. Which statements are correct?

Introduction / Context: This is an inclusion–exclusion application coupled with converting counts to percentages. The ”neither” percent gives ”either” directly, and the given counts anchor the town’s population.

Given Data / Assumptions:

• % with phone = 25.
• % with car = 15.
• % with neither = 65 ⇒ % with either = 35.
• Families owning both = 2000.

Concept / Approach: Use inclusion–exclusion: P(phone ∪ car) = P(phone) + P(car) − P(both). Since 65% own neither, P(phone ∪ car) = 35%. Plug known phone and car percentages to get P(both). Then use the 2000 count to find total families.

Step-by-Step Solution:

Verification / Alternative check: Check: 25 + 15 − 5 = 35% aligns with ”either,” consistent with 65% ”neither.”

Why Other Options Are Wrong: Any option including (i) is invalid since both% is 5%, not 10%. ”Only II” omits the correct (iii).

Common Pitfalls: Mixing ”either” with ”exactly one,” or forgetting that ”neither” immediately gives ”either.”

Final Answer: II and III