Venn diagrams is an important topic not just in quants, but also in DI as well. Solving the following sample questions will help in understanding the basics of venn diagrams and 4-group venn diagrams.

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Instructions

For the following questions answer them individually

Question 1

In a college consisting of 200 students, 112 students took the Maths Olympiad, 160 students took the Physics Olympiad and 128 students took the Chemistry Olympiad. If each student in the college takes at least one of the three exams, what is the minimum number of students who took all the three exams?

Question 2

In a college, two-thirds of the students study English, one-fifth of the students study Telugu and one-tenth study both the subjects. What is the fraction of students who study at least one of the two subjects?

Question 3

In a survey, it was found that the number of people who listened to Carnatic music was 20, the number of people who listened to Carnatic and Hindustani but not Western music was 3, the number of people who listened to Western Music was 19, 5 people listened to Carnatic and Western music but not Hindustani. 25 people listened to Hindustani music. 12 people listened to Hindustani and Western music. 3 people listened to all three genres of music. If the number of people who participated in the survey was 46, find the number of people who listened to none of the three genres of music.

Question 4

In a class of 50 students, 25 passed in Physics, 27 in Maths, 29 in Chemistry, 33 in Biology and 35 students passed in Geography. What is the maximum number of students who passed in at least 3 subjects?

Question 5

In a locality, residents read at least one of the three newspapers - Hindu, Times and Express. 60% read Hindu, 80% read Times and 55% read Express. What can be the minimum and maximum percentage of residents who read exactly two newspapers?

Question 6

In a school 60% of the students play football, 84% of them play cricket and 72% of them play tennis. What is the minimum percentage of students that play all three sports?

Question 7

In a group of 500 people who participated in a survey, 68% were in favour of at least one of the three parties A, B and C. 40% were in favour of party A, 30% were in favour of party B and 20% were in favour of party C. 5% of the people were in favour of all three parties. What number of people surveyed favoured more than one of the three parties?

Question 8

In a survey, it was found that 20 people go for a walk, 3 people went for a walk and a jog but not for a run, 19 people went for a run, 5 people went for a walk and a run but not for a jog. 25 people went for a jog. 12 people went for a jog as well as a run. 3 people went for all three. If the number of people surveyed was 46, find the number of people who did not do any of the three.

Question 9

In a school there were 800 students. Each of the students chose at least two sports among cricket, football, volleyball and basketball as their extra-curricular activity. Each of the sports was chosen by 500 students. Find the maximum number of students that could have chosen all the four sports as their extra-curricular activity?

Question 10

In a survey, it was found that the number of people who play hockey in a neighborhood is 30, the number of people who play cricket is 40 and the number of people who play football is 52. If the total number of people in the neighborhood is 100 and each of them plays at least one sport, what is the maximum number of people who play exactly one sport?

Question 11

In a group of 1000 people, the number of people who drink tea is 400, the number of people who drink coffee is 500, the number of people who drink ice-tea is 300 and the number of people who drink Horlicks is 200. The number of people in the group who drink all the four beverages is 40. Number of people who drink exactly two beverages is 120. The number of people who drink exactly three beverages is 90. What is the number of people in the group who do not drink any beverage at all?

Question 12

How many subsets of the set {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} are present such the sum of the largest and smallest numbers is equal to 15?

Question 13

A school has 400 students out of which 240 students are fans of Sunrisers Hyderabad and 280 students are fans of Mumbai Indians. If the number of students who do not follow the sport is at most 40, find the maximum number of students who are fans of both Sunrisers Hyderabad and Mumbai Indians.

Question 14

In an office, 78% of the employees are tea drinkers and 64% are coffee drinkers. What is the minimum possible percentage of employees who drink both beverages?

Question 15

In a group of 270 people, 135 eat pizza, 125 eat burger, 115 eat hotdog. Also, 42 people eat pizza and burger, 48 people eat burger and hotdog and 30 people eat all three. If 15 people stop eating pizza and instead start eating burger, then what is the maximum number of people who will be eating only pizza?

Question 16

In a society with 200 people, 77 people are dog owners, 80 are cat owners and 73 are bird owners. If 40 people do not have any of these three pets, what is the minimum possible number of people who own exactly one pet?

Question 17

In a survey, it was found that 14 people read The Hindu, 18 people read the Times and 15 people read the Indian Express. If 2 people read all the three newspapers, find which of the following can be the number of people who read exactly one newspaper?

Question 18

In an office, 78% of the employees are tea drinkers and 64% are coffee drinkers. What is the maximum possible percentage of employees who drink both beverages?

Question 19

In a society with 200 people, 77 people are dog owners, 80 are cat owners and 73 are bird owners. If 40 people do not have any of these three pets, what is the maximum possible number of people who own all three pets?

Question 20

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?

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