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Banking Exams Exam  >  Banking Exams Questions  >  Out of 60 families living in a building, all ... Start Learning for Free
Out of 60 families living in a building, all those families which own a car own a scooter as well. No family has just a scooter and a bike. 16 families have both a car and a bike. Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. What is the sum of the maximum and minimum number of families that own only a bike?
  • a)
    24
  • b)
    34
  • c)
    54
  • d)
    44
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Out of 60 families living in a building, all those families which own ...
From the information given in the question, the following Venn Diagram can be constructed:

So, in order to maximize the number of families that own only a bike, we can put the remaining 44 families in ‘only bike’ region.
Similarly, in order to minimize the number of families that own only a bike, we can put the remaining 44 families in ‘only scooter’ region.
So, the maximum number of families that own only a bike is 44 and the minimum number of families that own only a bike is 0.
So, sum = 44 + 0 = 44
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Most Upvoted Answer
Out of 60 families living in a building, all those families which own ...
To solve this problem, we need to analyze the given information step by step.

1. Number of families with a car and a scooter:
Since all the families that own a car also own a scooter, we can say that the number of families with a car is equal to the number of families with a car and a scooter. Let's represent this number as c.

2. Number of families with a car and a bike:
From the given information, we know that 16 families have both a car and a bike. Let's represent this number as x.

3. Number of families with just a scooter:
Since no family has just a scooter and a bike, all the families that own a scooter also own a car. Therefore, the number of families with just a scooter is 0.

4. Number of families with just a bike:
Let's represent the number of families with just a bike as b.

5. Total number of families:
The total number of families is given as 60.

6. Number of families that own exactly one type of vehicle:
From the information given, the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. Therefore, b > c + x.

Now, let's calculate the values of c and b using the given information:

c = Number of families with a car = Number of families with a car and a scooter
x = Number of families with a car and a bike = 16
b > c + x

Since no family has just a scooter, c = 0.

b > 0 + 16
b > 16

Now, let's find the maximum and minimum values of b:

Maximum value of b:
The maximum value of b can be 59 since all the families own at least one type of vehicle and the number of families with exactly one type of vehicle is more than the number of families with more than one type of vehicle.

Minimum value of b:
The minimum value of b can be 17 since b > 16.

Therefore, the sum of the maximum and minimum number of families that own only a bike is 59 + 17 = 76.

The correct answer is not present among the given options (a, b, c, d).
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Out of 60 families living in a building, all those families which own a car own a scooter as well. No family has just a scooter and a bike. 16 families have both a car and a bike. Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. What is the sum of the maximum and minimum number of families that own only a bike?a)24b)34c)54d)44Correct answer is option 'D'. Can you explain this answer?
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Out of 60 families living in a building, all those families which own a car own a scooter as well. No family has just a scooter and a bike. 16 families have both a car and a bike. Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. What is the sum of the maximum and minimum number of families that own only a bike?a)24b)34c)54d)44Correct answer is option 'D'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Out of 60 families living in a building, all those families which own a car own a scooter as well. No family has just a scooter and a bike. 16 families have both a car and a bike. Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. What is the sum of the maximum and minimum number of families that own only a bike?a)24b)34c)54d)44Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of 60 families living in a building, all those families which own a car own a scooter as well. No family has just a scooter and a bike. 16 families have both a car and a bike. Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. What is the sum of the maximum and minimum number of families that own only a bike?a)24b)34c)54d)44Correct answer is option 'D'. Can you explain this answer?.
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