CAT · Data Interpretation & Logical Reasoning
2-set and 3-set Venn problems — overlaps, exclusive regions.
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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?