# Set Theory: Practice Problems

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Q.1. A survey was conducted, it was found that the number of people who prefer only Burger, only Pizza, both Burger and Pizza and neither of them are 40, 45, 18 & 22 respectively. Find the number of people surveyed.
A. 69
B. 79
C. 82
D. 89
Q.2. In a college of 350 students, every student needs to choose among the three subjects (i.e. Economics, Accounts & Taxation) offered along with the main course. The students who chose each of these subjects are 120, 80 & 95. The number of students who chose more than one of the three is 28 more than the number of students who chose all the three subjects. If there are no students who chose none of the three subjects, how many students study all the three subjects?
A. 83
B. 25
C. 67
D. 42
Q.3. In a group of 120 people, 54 like Coca Cola and 84 like Pepsi and each person likes at least one of the two beverages. How many like both Coca Cola & Pepsi?
A. 24
B. 18
C. 32
D. 12
Q.4. After sports day in a college, college awarded medals in different categories. 72 medals in Athletics, 24 medals in weightlifting and 36 medals in swimming. If these medals went to a total of 90 persons and only 8 persons got medals in all the three sports, how many received medals in exactly two of these sports?
A. 6
B. 8
C. 10
D. 12
Q.5. In a group of 300 students, 216 students study Hindi and 129 study Punjabi. How many study Hindi only? How many study Punjabi only and how many study both Hindi & Punjabi?
A. Rs. 75
B. Rs. 100
C. Rs. 72
D. Rs. 77.5
Q.6. In a class of 212 students, each student studies at least one of the three subjects Mandarin, French and Spanish. 96 of them study Mandarin, 102 studies French and 106 Spanish. 32 studies Mandarin and French, 34 study Mandarin and Spanish and 36 study French and Spanish. How many students study all the three subjects?
A. 12
B. 10
C. 8
D. 6
Q.7. A survey was conducted among certain people, it was found that the number of people who like only Chocolate, only Vanilla, both Chocolate and Vanilla and neither of them are 120, 135, 54 & 66 respectively. Find the number of people surveyed.
A. Rs. 207
B. Rs. 234
C. Rs. 246
D. Rs. 267
Q8. In a class of 120 students, 36 enrolled for both Quant and Verbal. 66 enrolled for Verbal. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only Quant and not Verbal?
A. 90
B. 30
C. 54
D. 84
Q9. In a party with 600 guests, 180 guests ate Vanilla as well as Chocolate Ice cream. 330 ate Chocolate Ice Cream. If all the guests at the party ate at least one of the two ice creams, then how many guests ate only Vanilla and not Chocolate?
A. 450
B. 150
C. 270
D. 420
Q10. In a sports club of 530 members, each member plays at least one of the three sports Cricket, Football and Squash. 240 of them play Cricket, 255 play Football and 265 Squash. 80 play Cricket and Football, 85 play Cricket and Squash and 90 play Football and Squash. How many members play all the three sports?
A. 30
B. 25
C. 20
D. 15
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