By Planet E – Premier Coaching Institute for CAT & MBA Entrance Exams
Introduction
Venn Diagram questions are an integral part of the Logical Reasoning and Data Interpretation (LRDI) section of the CAT exam. These questions test your ability to understand relationships between different sets using diagrams. Mastering Venn diagrams can significantly boost your accuracy and speed in CAT LRDI.
This comprehensive guide by Planet E is designed to:
- Explain the fundamentals of Venn diagrams
- Cover two-set and three-set problems in detail
- Provide solved examples with diagrams
- Offer 15+ unique practice questions with answers and explanations
- Include a free PDF download for 50+ Venn Diagram CAT questions
What is a Venn Diagram?
A Venn diagram is a visual tool used to represent the relationships between sets. Each set is represented by a circle, and overlapping regions represent intersections of sets. These diagrams help in simplifying complex logical relationships.
Key Terminologies:
- Union (A ∪ B): Elements in either A, B, or both
- Intersection (A ∩ B): Elements common to both A and B
- Complement (~A): Elements not in set A
Types of Venn Diagrams in CAT
| Type | Description |
|---|---|
| Two-Set Venn Diagram | Involves two overlapping sets (e.g., Students who like Tea and Coffee) |
| Three-Set Venn Diagram | Involves three overlapping sets (e.g., Students who like Math, Physics, and Chemistry) |
Understanding Two-Set Venn Diagrams
Example 1:
In a class of 100 students:
- 60 like Tea
- 50 like Coffee
- 30 like both
Q: How many students like only Tea?
Solution: Only Tea = Total Tea – Both = 60 – 30 = 30
Diagram Explanation:
- Draw two overlapping circles
- Label one as Tea and the other as Coffee
- Place 30 in the overlapping region
- Remaining values go in their respective non-overlapping areas
Answer: 30
Understanding Three-Set Venn Diagrams
Three-set problems involve 7 regions:
- Only A
- Only B
- Only C
- A ∩ B only
- A ∩ C only
- B ∩ C only
- A ∩ B ∩ C
Example 2:
In a survey of 200 students:
- 100 like Math
- 90 like English
- 80 like Science
- 40 like both Math and English
- 30 like both Math and Science
- 25 like both English and Science
- 10 like all three
Q: How many students like only Math?
Solution: Only Math = Total Math – (Math ∩ English) – (Math ∩ Science) + All three = 100 – 40 – 30 + 10 = 40
Step-by-Step Approach to Solve Venn Diagram Questions
- Draw the Diagram: Always sketch it even if not asked
- Start from Common Area: Fill intersection of all three sets first
- Use the Given Data Logically: Fill values one by one
- Avoid Double Counting: Be careful with overlaps
- Apply Formulas When Needed:
- A ∪ B = A + B – A ∩ B
- Total = Sum of all 7 regions (in 3-set)
- Recheck the Total: Sum must match the given total
CAT-Level Venn Diagram Practice Questions (With Answers)
Q1. In a company of 100 employees:
- 60 are in HR
- 50 in Marketing
- 20 are in both
How many are only in HR?
- A. 20
- B. 40
- C. 60
- D. 80
Answer: B. 40
Q2. In a class:
- 40 students like History
- 50 like Geography
- 30 like both
How many like neither subject if the class has 70 students?
- A. 10
- B. 20
- C. 5
- D. 15
Solution: History only = 10, Geography only = 20, Both = 30. Total liking either = 60. So, neither = 70 – 60 = 10
Answer: A. 10
Q3. In a town of 500 people:
- 300 read Newspapers
- 200 read Magazines
- 100 read both
How many read either Newspapers or Magazines?
- A. 400
- B. 300
- C. 200
- D. 250
Solution: 300 + 200 – 100 = 400
Answer: A. 400
Download PDF of 50+ Practice Questions
For more practice, download Planet E’s exclusive 50+ Venn Diagram Questions for CAT 2025 PDF with answers and explanations.
[Download Here] (link to be added)
Bonus: Tips from Planet E CAT Experts
- Use diagrams even when not explicitly needed
- Start from the most restrictive data (usually the intersection of three)
- Keep calculations clean to avoid overcounting
- Practice similar DI sets from past CAT papers
- Learn to solve 3-set problems mentally with pattern recognition
Conclusion
Mastering Venn diagram questions can significantly improve your LRDI performance in CAT. With the right strategy, clear visualization, and consistent practice using Planet E’s expert-curated questions, you can develop strong problem-solving skills and improve your accuracy.
For structured coaching, enroll in Planet E’s comprehensive CAT 2025 preparation program, available both offline (Mumbai) and online (PAN India).
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