Set Theory

1) In a party, 150 people attended. Out of these 68% like coke and 36% like Pepsi.
How many people like both coke and pepsi?

Show Solution

Total number of people = 102 + 54 – both coke and pepsi
150 = 102 + 54 – both coke and pepsi
Both coke and pepsi = 156 – 150 = 6. Hence (a).

2) In a party, 150 people attended. Out of these 68% like coke and 36% like Pepsi.
How many people like only coke?

Show Solution
Only coke = 102 – 6 = 96. Hence (b).

3) In a class of 95 students, 43 speak Telugu, 35 speak both French and Telugu, and all the studentsspeak at least one of the two languages. Find the number of students who speak French but not Telugu.

Show Solution

From the above ven diagram, number of students who speak French but not Telugu = 52.
Hence (d).

4) In a group of 130 members, 45 read The Hindu newspaper and 19 have read both Hindu and Times of India newspaper. 12 do not read any newspaper.
Find the number of members who read only Times of India.

Show Solution

Total = Only Hindu + Only Times of india + both Hindu and Times of india + none
130 = 26 + only Times of india + 19 + 12
Only Times of india = 73. Hence (c).

5) In a group of 130 members, 45 read The Hindu newspaper and 19 have read both Hindu and Times of India newspaper. 12 do not read any newspaper.
How many members read atleast one newspaper?

Show Solution
At least one newspaper = 26 + 73 + 19 = 118. Hence (b).

6) In an AGM, set of persons was found to be higher officials. Some of them are CEOs, Managers and
Founders.The following diagram represents the classification of persons in each designation.

How many Managers are Founders but not CEOs?

Show Solution
Managers are Founders but not CEOs → Intersection part of Rectangle and Circle and ignore the Triangle part.Hence, the number of Managers are Founders but not CEOs = 20. Hence (c).

7) In an AGM, set of persons was found to be higher officials. Some of them are CEOs, Managers and
Founders.The following diagram represents the classification of persons in each designation.

How many persons attended the AGM?

Show Solution
Number of persons who attended the AGM, add all the numbers inside the diagram = 25 + 35
+ 5 + 13 + 2 + 20 = 100. Hence (b).

8) 110 students went to theme park where they could ride on the roller coaster,
Centrox and Cable car. It was known that 35 of them took all the rides, and 60 of them took at least two
Of the three rides. Each ride costs Rs.2, and the total receipts were of the theme park were Rs.350
How many students took exactly one ride?

Show Solution

Students took at least two of the three rides = d + e + f + 35 = 60
Only two rides = d + e + f = 25
Each ride costs Rs.2
Total receipt from students those who took all the three rides = 35 * 6 = Rs.210
Total receipt from students those who took only two rides = 25 * 4 = Rs.100
Total receipt from students those who took all the three rides and those who took only two rides=210 + 100 = Rs.310
Total collection = Rs.350
Balance amount Rs.40 was collected from those students those who took only one ride.
Only one ride = a + b + c = 20. Hence (c).
Number of students who took atleast one ride = 20 + 25 + 35 = 80
Then the number of students who did not took any ride = g = 110 – 80 = 30

9) 110 students went to theme park where they could ride on the roller coaster,
Centrox and Cable car. It was known that 35 of them took all the rides, and 60 of them took at least two
Of the three rides. Each ride costs Rs.2, and the total receipts were of the theme park were Rs.350
What is the cost for atleast two of the three rides?

Show Solution
Cost for atleast two rides = 100 + 210 = Rs.310. Hence (d).

10) 110 students went to theme park where they could ride on the roller coaster,
Centrox and Cable car. It was known that 35 of them took all the rides, and 60 of them took at least two
Of the three rides. Each ride costs Rs.2, and the total receipts were of the theme park were Rs.350
How many students did not try any of the rides?

Show Solution
Number of students who took atleast one ride = 20 + 25 + 35 = 80
Then the number of students who did not took any ride = g = 110 – 80 = 30. Hence (a).

11) In a factory 2750 employees are working. They use different vehicles such as
Cab, Bike and Train as their mode of transportation. Among them 160 employees use only Cab and
Train. 100 employees use only Bike. 300 employees use Cab and Bike.470 employees use only Bike and
Train.180 employees use only Cab and Bike. 510 employees use only Cab. And number of employees
who uses only one vehicle are 1460.
How many employeesare use all the three vehicles?

Show Solution
 
Number of employees who use all the three vehicles = 180 + x = 300 → x = 120. Hence (d).

12) In a factory 2750 employees are working. They use different vehicles such as
Cab, Bike and Train as their mode of transportation. Among them 160 employees use only Cab and
Train. 100 employees use only Bike. 300 employees use Cab and Bike.470 employees use only Bike and
Train.180 employees use only Cab and Bike. 510 employees use only Cab. And number of employees
who uses only one vehicle are 1460.
Find the number of employees who use only Train.

Show Solution
Number of employees who uses only one vehicle = 1460
Only Cab + only Bike + only Train = 1460
510 + 100 + only Train = 1460 = 850 Hence (c).

13) In a factory 2750 employees are working. They use different vehicles such as
Cab, Bike and Train as their mode of transportation. Among them 160 employees use only Cab and
Train. 100 employees use only Bike. 300 employees use Cab and Bike.470 employees use only Bike and
Train.180 employees use only Cab and Bike. 510 employees use only Cab. And number of employees
who uses only one vehicle are 1460.
How many employees do not use any of the three vehicles?

Show Solution
Total employees = only 1 vehicle + only 2 vehicles + only 3 vehicles + none
2750 = 1460 + 810 + 120 + none
2750 = 2390 + none
Employees do not use any of the three vehicles = 360.Hence (a).

14) In a factory 2750 employees are working. They use different vehicles such as
Cab, Bike and Train as their mode of transportation. Among them 160 employees use only Cab and
Train. 100 employees use only Bike. 300 employees use Cab and Bike.470 employees use only Bike and
Train.180 employees use only Cab and Bike. 510 employees use only Cab. And number of employees
who uses only one vehicle are 1460.
How many employees use the Bike?

Show Solution
Employees who use Bike = 100 + 180 + 120 + 470 = 870. Hence (b).

15) In a factory 2750 employees are working. They use different vehicles such as
Cab, Bike and Train as their mode of transportation. Among them 160 employees use only Cab and
Train. 100 employees use only Bike. 300 employees use Cab and Bike.470 employees use only Bike and
Train.180 employees use only Cab and Bike. 510 employees use only Cab. And number of employees
who uses only one vehicle are 1460.
How many employees are use atleast two of the three vehicles?

Show Solution
Employees use at least two of the three vehicles = 180 + 160 + 470 + 120 = 930. Hence (d).