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In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :
(a) 5% families own both a car and a phone.
(b) 35% families own either a car or a phone.
(c) 40,000 families live in the town.
Then,
  • a)
    Only (a) and (b) are correct.
  • b)
    Only (a) and (c) are correct.
  • c)
    Only (b) and (c) are correct.
  • d)
    All (a), (b) and (c) are correct.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In a certain town, 25% of the families own a phone and 15% own a car ;...
Given information:
- 25% of families own a phone
- 15% of families own a car
- 65% of families own neither a phone nor a car
- 2,000 families own both a car and a phone
- 40,000 families live in the town

To solve this problem, we can use a Venn diagram with three sets: phone owners, car owners, and neither. We can fill in the information we know:

- Let x be the number of families that own a phone only
- Let y be the number of families that own a car only
- Let z be the number of families that own neither a phone nor a car

Then we have:

- 0.25(40,000) = x + 2,000 (25% of families own a phone, including those who own both)
- 0.15(40,000) = y + 2,000 (15% of families own a car, including those who own both)
- 0.65(40,000) = z (65% of families own neither)

Solving for x, y, and z, we get:

- x = 8,000
- y = 2,000
- z = 22,000

Now we can check the statements:

(a) 5% families own both a car and a phone.
- This statement is false. We know that 2,000 families own both a car and a phone, which is 2,000/40,000 = 5% of all families. However, this does not mean that 5% of all families own both. Some of these families also own a phone or a car separately.

(b) 35% families own either a car or a phone.
- This statement is true. We can add up the number of families that own a phone only, a car only, or both: x + y + 2,000 = 12,000. This is 12,000/40,000 = 30% of all families. However, we need to add the number of families that own neither to get the percentage that own either: 12,000 + 22,000 = 34,000, which is 34,000/40,000 = 85% of all families. Therefore, 35% of families own either a car or a phone.

(c) 40,000 families live in the town.
- This statement is true. It is given in the problem.

Therefore, the correct answer is (d) All (a), (b) and (c) are correct.
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In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :(a) 5% families own both a car and a phone.(b) 35% families own either a car or a phone.(c) 40,000 families live in the town.Then,a)Only (a) and (b) are correct.b)Only (a) and (c) are correct.c)Only (b) and (c) are correct.d)All (a), (b) and (c) are correct.Correct answer is option 'D'. Can you explain this answer?
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In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :(a) 5% families own both a car and a phone.(b) 35% families own either a car or a phone.(c) 40,000 families live in the town.Then,a)Only (a) and (b) are correct.b)Only (a) and (c) are correct.c)Only (b) and (c) are correct.d)All (a), (b) and (c) are correct.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :(a) 5% families own both a car and a phone.(b) 35% families own either a car or a phone.(c) 40,000 families live in the town.Then,a)Only (a) and (b) are correct.b)Only (a) and (c) are correct.c)Only (b) and (c) are correct.d)All (a), (b) and (c) are correct.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :(a) 5% families own both a car and a phone.(b) 35% families own either a car or a phone.(c) 40,000 families live in the town.Then,a)Only (a) and (b) are correct.b)Only (a) and (c) are correct.c)Only (b) and (c) are correct.d)All (a), (b) and (c) are correct.Correct answer is option 'D'. Can you explain this answer?.
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