Venn Diagrams

Q1 · Venn Diagrams · EASY

A Venn diagram shows the number of students studying three languages: Hindi (H), English (E), and French (F). n(H only)=30, n(E only)=25, n(F only)=20, n(H∩E only)=15, n(E∩F only)=10, n(H∩F only)=12, n(H∩E∩F)=8. How many students study at least two languages?

Q2 · Venn Diagrams · MEDIUM

In a survey of 180 professionals, 85 read Business Weekly, 95 read Finance Today, and 72 read Market Digest. 38 read both Business Weekly and Finance Today, 30 read both Finance Today and Market Digest, and 25 read both Business Weekly and Market Digest. If 15 professionals read all three publications, how many professionals read exactly one publication?

Q3 · Venn Diagrams · HARD

In a college, 320 students enrolled for at least one of three courses: Data Science, AI, and Cloud Computing. 140 enrolled for Data Science, 160 for AI, and 180 for Cloud Computing. 50 students enrolled for both Data Science and AI but not Cloud Computing. 60 enrolled for both AI and Cloud Computing but not Data Science. 40 enrolled for both Data Science and Cloud Computing but not AI. How many students enrolled for all three courses?

Q4 · Venn Diagrams · EASY

In a survey of 200 students, 120 students play cricket, 90 play football, and 50 play both cricket and football. How many students play neither cricket nor football?

Q5 · Venn Diagrams · EASY

In a business school batch of 120 students, 70 students enrolled in the Finance elective, 65 students enrolled in Marketing, and 50 students enrolled in Operations. Additionally, 30 students enrolled in both Finance and Marketing, 25 students enrolled in both Marketing and Operations, and 20 students enrolled in both Finance and Operations. Exactly 10 students enrolled in all three electives. How many students did NOT enroll in any of these three electives?