What's new in our website? People who study quantitative aptitude to get prepared for competitive exams are stumbling to solve set theory word problems. The reason for their stumbling is, they do not know the basic stuff to solve venn diagram word problems with 3 circles. Let us consider the following example, to have better understanding of the above stuff explained using venn diagram. Example: In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Let F, H and C represent the set of students who play foot ball, hockey and cricket respectively. Venn diagram related to the above situation: From the venn diagram, we can have the following details. Find how many had taken one course only. Problem 2 : In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group. Assume that each student in the group plays at least one game. Solution : Step 1 : Let F, H and C represent the set of students who play foot ball, hockey and cricket respectively. Problem 3 : In a class of 60 students, 40 students like math, 36 like science, 24 like both the subjects. Find the number of students who like i Math only, ii Science only iii Either Math or Science iv Neither Math nor science Solution : Step 1 : Let M and S represent the set of students who like math and science respectively. Problem 4 : At a certain conference of 100 people there are 29 Indian women and 23 Indian men. Out of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. Find the number of women doctors attending the conference. Solution : Step 1 : Let M and D represent the set of Indian men and Doctors respectively. And the remaining 1 is Indian women doctor. Problem 5 : In a college, 60 students enrolled in chemistry,40 in physics, 30 in biology, 15 in chemistry and physics,10 in physics and biology, 5 in biology and chemistry. No one enrolled in all the three. Find how many are enrolled in at least one of the subjects. Solution : Let A,B and C are the sets enrolled in the subjects Chemistry,Physics and Biology respectively. Problem 6: In a town 85 % of the people speak Tamil,40 % speak English and 20 % speak Hindi. Also 32% speak English and Tamil, 13 % speak Tamil and Hindi and 10 % speak English and Hindi, find the percentage of people who can speak all the three languages. Solution: Let A,B and C are the people who speak Tamil, English and Hindi respectively. Problem 7 : An advertising agency finds that, of its 170 clients,115 use Television,110 use Radio and 130 use Magazines. Also 85 use Television and Magazines,75 use Television and Radio,95 use Radio and Magazines,70 use all the three. Draw Venn diagram to represent these data. Find i how many use only Radio? Solution: Let A,B and C are the people who speak Television, Radio and Magazines respectively. And also we hope that the word problems on sets and venn diagrams explained above would be much useful for the students who struggle to solve venn diagram word problems with 3 circles.