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Practice Question - 15 (Venn Diagram) | 100 DILR Questions for CAT Preparation PDF Download

Students in a college are discussing two proposals -
A: a proposal by the authorities to introduce dress code on campus, and
B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.
A student does not necessarily support either of the two proposals.
In an upcoming election for student union president, there are two candidates in fray:
Sunita and Ragini. Every student prefers one of the two candidates.
A survey was conducted among the students by picking a sample of 500 students. The following information was noted from this survey.
1. 250 students supported proposal A and 250 students supported proposal B.
2. Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
3. Among those who preferred Ragini, 30% supported proposal A.
4. 20% of those who supported proposal B preferred Sunita.
5. 40% of those who did not support proposal B preferred Ragini.
6. Every student who preferred Sunita and supported proposal B also supported proposal A.
7. Among those who preferred Ragini, 20% did not support any of the proposals.

Q1: Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?

Practice Question - 15 (Venn Diagram) | 100 DILR Questions for CAT Preparation

View Answer

Ans: 64
Total number of students surveyed = 500
Every student prefers one of the two candidates. Ragini(R) and Sunita(S).
Thus, R+S=500.
According to statement 2, "Among the 200 students who preferred Sunita as student union president, 80% supported proposal A."
The number of students who support Sunita(S)=200
The number of students who supported Ragini(R)=300

According to statements 2 and 3, 160 students who supported Sunita also supported the proposal A & 90 students who supported Ragini also supported proposal A.

According to statements 4 and 6, we can make the following Venn diagram for Sunita.

According to statement 5 and 7, we can make the following Venn diagram.

The number of students who preferred Sunita and the proposal A=160
=160/250= 64%

Q2: What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?

View Answer

Ans: 84
Total number of students surveyed= 500
Every student prefers one of the two candidates. Ragini(R) and Sunita(S).
Thus, R+S=500.
According to statement 2, "Among the 200 students who preferred Sunita as student union president, 80% supported proposal A."
The number of students who support Sunita(S)=200
The number of students who supported Ragini(R)=300

According to statements 2 and 3, 160 students who supported Sunita also supported the proposal A & 90 students who supported Ragini also supported proposal A.

According to statements 4 and 6, we can make the following Venn diagram for Sunita.

According to statement 5 and 7, we can make the following Venn diagram.

The percentage of the students surveyed who did not support proposal A preferred Ragini as student union president = 210/250 = 84%
Answer 84

Q3: What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
(a) 40
(b) 25
(c) 20
(d) 50

View Answer

Ans: (d)
Total number of students surveyed= 500
Every student prefers one of the two candidates. Ragini(R) and Sunita(S).
Thus, R + S = 500.
According to statement 2, "Among the 200 students who preferred Sunita as student union president, 80% supported proposal A."
The number of students who support Sunita(S)=200
The number of students who supported Ragini(R)=300

According to statements 2 and 3, 160 students who supported Sunita also supported the proposal A & 90 students who supported Ragini also supported proposal A.
According to statements 4 and 6, we can make the following Venn diagram for Sunita.

According to statement 5 and 7, we can make the following Venn diagram.

According to the Venn diagram, the students surveyed who supported both proposals A and B preferred Sunita as student union president Practice Question - 15 (Venn Diagram) | 100 DILR Questions for CAT Preparation

Q4: How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
(a) 150
(b) 210
(c) 200
(d) 40

View Answer

Ans: (a)
Total number of students surveyed= 500
Every student prefers one of the two candidates. Ragini(R) and Sunita(S).
Thus, R + S = 500.
According to statement 2, "Among the 200 students who preferred Sunita as student union president, 80% supported proposal A."
The number of students who support Sunita(S)=200
The number of students who supported Ragini(R)=300

According to statement 5 and 7, we can make the following Venn diagram.

From the diagram, we can understand that option (a) is correct.

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FAQs on Practice Question - 15 (Venn Diagram) - 100 DILR Questions for CAT Preparation

1. What is a Venn diagram and how is it used in problem-solving?

Ans. A Venn diagram is a visual representation of the relationships between different sets. It consists of overlapping circles that each represent a set, with the overlapping areas showing the common elements. Venn diagrams are commonly used in problem-solving to illustrate logical relationships, analyze data, and simplify complex problems by visually organizing information.

2. What types of questions can be solved using Venn diagrams in exams?

Ans. Venn diagrams can be used to solve a variety of questions in exams, particularly those related to set theory. Common types of questions include determining the number of elements in union and intersection of sets, finding the total number of elements in different categories, and solving problems that involve multiple groups or classifications. They are particularly useful in questions that require comparisons between the groups.

3. How can I effectively interpret Venn diagrams during exams?

Ans. To effectively interpret Venn diagrams during exams, first, identify the sets represented by each circle. Pay attention to the areas where circles overlap, as these represent common elements. Carefully read the question to understand what is being asked, focusing on the specific areas of the diagram relevant to the problem. Practice with various diagrams to become familiar with different configurations and their implications.

4. What are some common mistakes to avoid when using Venn diagrams?

Ans. Common mistakes when using Venn diagrams include miscounting elements in the overlapping areas, misunderstanding the relationships between sets, and not clearly labeling the sets. It is also important to ensure that all possible elements are accounted for, including those that do not belong to any set. Taking time to double-check your work can help avoid these errors.

5. Can Venn diagrams be applied to real-life situations outside of exams?

Ans. Yes, Venn diagrams can be applied to a variety of real-life situations. They are useful in fields such as statistics, logic, and decision-making, helping to visualize relationships and overlaps between different groups or categories. For example, they can be used in business to analyze market segments, in education to categorize student performance, or in research to compare different studies.

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Sep 26, 2025 Last updated

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