Top 25 CAT Quant Venn Diagrams Questions With Video Solutions

The Venn diagram is also one of the important topics that aspirants must consider practising to get a good score in CAT. Venn Diagrams is one of the important topics in the CAT Quant/LRDI section. The questions from this topic come under modern maths. On this page, you can find all the Venn diagram questions from previous CAT question papers and the detailed video solutions explaining the CAT toppers. These are a good source of practice for CAT preparation; One can also download these questions in a PDF format or can take them in a test format. Click on the below link to download all the Venn diagram questions from CAT's previous papers with the detailed video solutions and also check out the free CAT mocks to understand the latest CAT exam pattern and understand the types of questions that are likely to appear on the exam.

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CAT Quant - Venn Diagrams Questions Weightage Over Past 5 Years

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CAT Quant - Venn Diagram Formulas PDF

CAT Venn diagrams are among the important topics in the quantitative aptitude section, and it is vital to understand the formulas related to them clearly. To help the aspirants to ace this topic, we have made a PDF containing a comprehensive list of formulas, tips, and tricks that you can use to solve Venn diagram questions with ease and speed. Click on the below link to download the CAT Venn diagram formulas PDF.

VennDiagram1

Consider three intersecting sets A, B and C. A represents all the elements in set A and A’ represents all the elements not in A. The image shows the different areas in a venn diagram and the meaning of each area.* $$ n(A \cup B)$$ = $$n(A)+n(B)-n(A \cap B)$$

$$n(A \cup B \cup C)$$ = $$n(A)+n(B)+n(C)$$-$$n(A \cap B)$$ - $$n(B \cap C)$$ - $$n(A \cap C)$$ + $$n(A \cap B \cap C)$$

Only A can be translated as A and not B and not C

Similarly, A’ and B’ and C’  = Universal set – (A or B or C)

CAT 2022 Venn Diagrams questions

Question 1

In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is

CAT 2020 Venn Diagrams questions

Question 1

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

CAT 2019 Venn Diagrams questions

Question 1

A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

CAT 2018 Venn Diagrams questions

Question 1

For two sets A and B, let AΔB denote the set of elements which belong to A or B but not both. If P = {1,2,3,4}, Q = {2,3,5,6,}, R = {1,3,7,8,9}, S = {2,4,9,10}, then the number of elements in (PΔQ)Δ(RΔS) is


Question 2

Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is


Question 3

If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be


Question 4

If A = {$$6^{2n} -35n - 1$$}, where $$n$$ = 1,2,3,... and B = {35($$n$$-1)}, where $$n$$ = 1,2,3,... then which of the following is true?

CAT 2006 Venn Diagrams questions

Question 1

A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:

Only September: 18;

September but not August: 23;

September and July: 8;

September:28;

July: 48;

July and August: 10;

none of the three months: 24

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?

Show Answer Explanation

CAT 2005 Venn Diagrams questions

Instruction for set 1:

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

  • A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
  • The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
  • 17 volunteers are involved in the TR project.
  • The number of volunteers involved in the TR project alone is one less than the number ofvolunteers involved in ER project alone.

  • Ten volunteers involved in the TR project are also involved in at least one more project.

Question 1

Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:

Show Answer Explanation

Instruction for set 1:

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

  • A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
  • The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
  • 17 volunteers are involved in the TR project.
  • The number of volunteers involved in the TR project alone is one less than the number ofvolunteers involved in ER project alone.

  • Ten volunteers involved in the TR project are also involved in at least one more project.

Question 2

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?

Show Answer Explanation

Instruction for set 1:

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

  • A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
  • The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
  • 17 volunteers are involved in the TR project.
  • The number of volunteers involved in the TR project alone is one less than the number ofvolunteers involved in ER project alone.

  • Ten volunteers involved in the TR project are also involved in at least one more project.

Question 3

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?

Show Answer Explanation

Instruction for set 1:

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

  • A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
  • The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
  • 17 volunteers are involved in the TR project.
  • The number of volunteers involved in the TR project alone is one less than the number ofvolunteers involved in ER project alone.

  • Ten volunteers involved in the TR project are also involved in at least one more project.

Question 4

After the withdrawal of volunteers, as indicated in the previous question, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?

Show Answer Explanation

CAT 2003 Venn Diagrams questions

Instruction for set 1:

DIRECTIONS for the following two questions: Answer the questions on the basis of the information given below.

New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.

Question 1

What is the number of projects in which Gyani alone is involved?

Show Answer Explanation

Instruction for set 1:

DIRECTIONS for the following two questions: Answer the questions on the basis of the information given below.

New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.

Question 2

What is the number of projects in which Medha alone is involved?

Show Answer Explanation

CAT 2002 Venn Diagrams questions

Question 1

Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e. either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?

CAT 2001 Venn Diagrams questions

Question 1

On her walk through the park, Hamsa collected 50 coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following:

The number of red oak leaves with spots is even and positive.

The number of red oak leaves without any spot equals the number of red maple leaves without spots.

All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves.

There are no spotted maple leaves that are not red.

There are exactly 6 red spotted maple leaves.

There are exactly 22 maple leaves that are neither spotted nor red.

How many oak leaves did she collect?

Show Answer Explanation

CAT 1999 Venn Diagrams questions

Question 1

In a survey of political preference, 78% of those asked were in favor of at least one of the proposals: I, II and III. 50% of those asked favored proposal I, 30% favored proposal II, and 20% favored proposal III. If 5% of those asked favored all three of the proposals, what percentage of those asked favored more than one of the 3 proposals.

Show Answer Explanation

CAT 1997 Venn Diagrams questions

Instruction for set 1: A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

Question 1

What is the maximum percentage of people who can watch all the three channels?


Instruction for set 1: A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

Question 2

If 5% of people watched DD and CNN, 10% watched DD and BBC, then what percentage of people watched BBC and CNN only?


Instruction for set 1: A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

Question 3

Referring to the previous question, what percentage of people watched all the three channels?

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