Venn Diagram CAT Questions (50+ Practice) with Answers & Solutions

Looking for Venn Diagram CAT Questions to practise DILR? This page covers 2-set and 3-set questions with simple solutions to help you understand the concepts and improve your accuracy. You can also download the CAT venn diagram question PDF for quick revision.

• CAT 2026 is a national-level MBA entrance exam accepted by the IIMs and several other management institutes.
• The exam tests students on areas such as Quantitative Ability, DILR, and VARC.
• Practising CAT venn diagram questions regularly can help you get familiar with different question types and improve your speed.

In this blog, we will discuss Venn Diagram CAT Questions in detail, covering their importance and solving strategies. Learn how to tackle these Venn diagram questions effectively for the CAT exam.

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What are Venn Diagram CAT Questions?

Venn Diagram CAT questions are all about understanding how different groups connect and overlap. They use circles to show what’s shared and what’s separate. You’ll often find them in the DILR section of the exam. Essentially, they test your logic and ability to make quick conclusions from the given data.

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Different Types of Venn Diagram CAT Questions 2026?

Venn diagrams are used in CAT to show how different groups or sets are related to each other. Most Venn diagram CAT questions are based on either two sets or three sets. Let’s look at both types.

1. Two-Set Venn Diagram

This is the simpler type and uses two circles, usually A and B. The common part of the circles shows the elements that are present in both sets.

• The part inside A but outside B represents A only.
• The part inside B but outside A represents B only.
• The overlapping part represents A ∩ B, or the elements common to both sets.

Explore: CAT Ratio and Proportion Questions

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2. Three-Set Venn Diagram

Here, three circles are used for sets A, B, and C. Since all three circles can overlap, there are more regions to keep track of.

• Some regions contain elements belonging to only one set.
• The areas where two circles overlap show the common elements of those two sets.
• The centre, where all three circles meet, represents A ∩ B ∩ C.

Before solving Venn diagram CAT questions, make sure you understand what each part of the diagram represents. This will make it easier to work through questions involving two or three sets.

CAT Venn Diagram Resources 

CAT Venn Diagram Resources	Action
CAT Venn Diagram Mock Test	Attempt Now
CAT Venn Diagram Preparation Video	Watch Free Video

Important Venn Diagram CAT Questions 2026 For Practise

Given below are some CAT Venn Diagram Questions And Answers For CAT exam that can help you in your CAT Preparation: 

1)  If the number of candidates who score at or above the 90th percentile overall and also at or above the 80th percentile in all three sections of the Common Entrance Test (CET) is a multiple of 5, then how many candidates were shortlisted for the Admission Entrance Test (AET) for the Academic Institute of Excellence (AIE)?

A. 170

B. 150

C. 130

D. 90

Answer: 170

2) If the number of candidates who score at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in the Common Entrance Test (CET) is divisible by 5, what is the count of candidates who score at or above the 90th percentile overall and at or above the 80th percentile in both Physics (P) and Mathematics (M) in CET? (TITA)

A. 20

B. 60

C. 80

D. 100

Answer: 60

3) What is the most accurate conclusion that can be drawn regarding the quantity of test takers for the BIE exam who scored at or above the 90th percentile in the CET?

A. 3 or 10

B. 10

C. 5

D. 7 or 10

Answer: 3 or 10

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4) If out of 200 students, 105 have a preference for pizza and 134 have a liking for burgers, what is the potential number of students who have a preference only for burgers?

A. 23

B. 96

C. 26

D. 93

Answer: 93

5) If the count of applicants who score at or above the 90th percentile overall and also score at or above the 80th percentile in P in CET exceeds 100, how many applicants had to take the separate BIE test?

A. 310

B. 321

C. 299

D. 330

Answer: 299

6) How many integers from 1 to 120 are not divisible by 2, 5, or 7?

A. 42

B. 41

C. 43

D. 40

Answer: 41

Explore: CAT Trigonometry Questions with Answers

7) In a group of 30 students, 15 participate in cricket and 20 participate in football. 5 students are involved in both cricket and football. What is the total number of students engaged in cricket, including those exclusively involved?

A. 10

B. 15

C. 20

D. 26

Answer: 20

8) Out of 50 employees in a company, 25 are in the sales department, and 30 are in the marketing department, with 15 employees working in both departments. How many employees work exclusively in the sales department?

A. 10

B. 15

C. 20

D. 21

Answer: 15

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9) In a group of 50 employees, 25 work in sales, 30 in marketing, and 15 in both departments. How many employees work solely in the sales department?

A. 100

B. 250

C. 150

D. 200

Answer: 200

10) In a park, there are a total of 100 individuals. 60 of them are enjoying the swings, while 40 are having fun on the slides. Additionally, 20 people are enjoying both the swings and slides. How many people are exclusively using the swings?

A. 10

B. 60

C. 20

D. 70

Answer: 60

Check: Algebra Topics for CAT 2026

11) There are 300 books in a library, with 150 in Hindi and 200 in English. Additionally, 50 books are in both languages. Ultimately, I need to figure out how many books are exclusively in English.

A. 150

B. 155

C. 159

D. 160

Answer: 150

Read the passage and answer the following:-

There were a total of 100 schools in the town. Out of these, 30 schools had a playground but did not have a library or a laboratory. The number of schools with only a laboratory was twice the number of schools with only a library. The number of schools with both a laboratory and a library was one-fourth the number of schools with only a laboratory. In total, 35 schools had either a library, a laboratory, or both.

12) How many schools do not have any of the three facilities: laboratory, library, and playground?

A. 25

B. 69

C. 35

D. 49

Answer: 35

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13) What was the proportion of schools with a laboratory compared to those with a library?

A. 2:1

B. 1:1`

C. 5:3

D. 4:5

Answer: 5:3

Read more: VARC Syllabus for CAT

14) There are three clubs A, B, and C with 40, 50, and 60 members, respectively. 10 people are members of all three clubs, and 70 are members of only one club. How many people belong to exactly two clubs?

A. 15

B. 25

C. 35

D. 45

Answer: 25

15) Out of the 100 families in the neighborhood, 45 possess radios, 75 own televisions, and 25 own VCRs. Additionally, only 10 families possess all three electronics, and every VCR owner also possesses a television. Moreover, 25 families possess only a radio. How many families possess only a television?

A. 30

B. 40

C. 60

D. 50

Answer: 40

Read more: CAT Reasoning Syllabus 2026

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CAT DILR - Venn Diagram Questions Weightage Over the Past 5 Years

The number of Venn diagram questions can vary from one CAT paper to another. The table below shows the number of questions asked in DILR over the past five years:

CAT Year	Venn Diagram Questions
2025	0
2024	0
2023	0
2022	10
2021	0
2020	4

How To Solve Venn Diagram Questions 2026

• Understand Venn Diagram CAT Questions set theory concepts such as union, intersection, and complements before attempting CAT Venn diagram questions.
• Clearly define the sets represented by the circles in the Venn diagram questions for CAT.
• Redraw the diagram neatly to organize your thoughts, even if a diagram is provided.
• Mark each section of the Venn diagram with its corresponding set representation.
• Convert the given information set into numerical values representing elements in those regions.
• Focus on understanding the logic and plugging in the given values rather than memorizing formulas.
• Pay attention to the area where circles overlap, as it often represents elements belonging to both sets.
• Directly label specific sections of the Venn diagram with numbers based on the information provided.
• Use the total number of elements to calculate values for specific sections based on the information.
• Analyze the relationships between sets to deduce values for overlapping regions.
• Familiarize yourself with the question format and difficulty level expected in the CAT exam by practising with CAT previous year question papers.
• Focus on getting the answer right rather than rushing through questions.
• If a question seems difficult or is taking too long, skip it and come back to it later.
• Check: CAT Exam Shift Timings 2026

Conclusion

This post has provided you with an Venn diagram CAT questions  to solve those CAT logical reasoning questions. By grasping the fundamental idea and working on various question types, you'll be on your way to mastering the CAT exam. Keep in mind that the key is to recognize the connections between the information sets presented and represent them visually in the Venn diagram.

Now, try a few Venn diagram questions on your own. Regular practice will help you understand the concepts better and solve CAT DILR questions with more confidence.