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Modern Math • Venn Diagrams Practice Drills (58 Qs)• Official Answer Keys

CAT Venn Diagrams Practice Questions (55+ Questions)

3-Set and 4-Set Venn Diagrams, Maxima-Minima in Overlaps, and Neither/None Regions

58 Total Questions
MCQ: 48 (+3 / -1)
TITA: 10 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Venn Diagrams Practice Drills

Sum of Exactly RegionsFormula #1
\text{Total} = \text{Exactly } 1 + \text{Exactly } 2 + \text{All } 3 + \text{None}

Mutually exclusive partition of universal set.

Sum of Set TotalsFormula #2
|A| + |B| + |C| = \text{Exactly } 1 + 2(\text{Exactly } 2) + 3(\text{All } 3)

Useful for finding bounds on intersections.

Exam Hall Traps & Speedbreakers to Avoid
  • •Confusing "only A" with "set A" (Set A includes overlaps with B and C).

Bite-Sized Practice Sets (6 Modules Available)

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Set 01: Venn Diagrams

Difficulty: Easy
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Set 02: Venn Diagrams

Difficulty: Easy
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Set 03: Venn Diagrams

Difficulty: Easy
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Set 04: Venn Diagrams

Difficulty: Hard
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Set 05: Venn Diagrams

Difficulty: Easy
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Set 06: Venn Diagrams

Difficulty: Moderate
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Official Exam Questions & Explanations (25 of 58)

Sorted in official convenor sequence
Question 1 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
In a class of 50 students, 20 study Mathematics and 30 study Science. If 10 students study both, how many students do not study either?
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Official Correct Answer: B. Using the principle of inclusion and exclusion, $20 + 30 - 10 = 40$ students study either Mathematics or Science. Therefore, $50 - 40 = 10$ students do not study either.
Question 2 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
In a survey, 150 people were asked about their favorite sports. 80 liked cricket, 70 liked football, and 40 liked both. How many people liked neither cricket nor football?
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Official Correct Answer: B. Using the principle of inclusion and exclusion, $80 + 70 - 40 = 110$ people liked either cricket or football. Therefore, $150 - 110 = 40$ people liked neither.
Question 3 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsHard
In a group of 500 people, 200 like tea, 250 like coffee, and 100 like both. How many people like neither tea nor coffee?
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Official Correct Answer: C. Using the principle of inclusion and exclusion, $200 + 250 - 100 = 350$ people like either tea or coffee. Therefore, $500 - 350 = 150$ people like neither.
Question 4 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
In a survey, 50 people were asked about their favorite fruits. 30 liked apples, 25 liked bananas, and 10 liked both. How many people liked neither apples nor bananas?
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Official Correct Answer: A. Using the principle of inclusion and exclusion, $30 + 25 - 10 = 45$ people liked either apples or bananas. Therefore, $50 - 45 = 5$ people liked neither.
Question 5 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
In a survey, 100 people were asked about their favorite sports. 40 liked basketball, 50 liked cricket, and 10 liked both. How many people liked neither basketball nor cricket?
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Official Correct Answer: B. Using the principle of inclusion and exclusion, $40 + 50 - 10 = 80$ people liked either basketball or cricket. Therefore, $100 - 80 = 20$ people liked neither.
Question 6 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsHard
In a group of 600 people, 250 like tea, 300 like coffee, and 150 like both. How many people like neither tea nor coffee?
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Official Correct Answer: B. Using the principle of inclusion and exclusion, $250 + 300 - 150 = 400$ people like either tea or coffee. Therefore, $600 - 400 = 200$ people like neither.
Question 7 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
A survey of 100 students found that 45 like basketball, 50 like football, and 20 like both. How many students like neither basketball nor football?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of students who like either or both is $45 + 50 - 20 = 75$. Therefore, the number who like neither is $100 - 75 = 25$.
Question 8 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
A survey found that 150 people like tea, 100 like coffee, and 50 like both. How many people like either tea or coffee but not both?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of people who like either tea or coffee but not both is $150 + 100 - 2 \times 50 = 250 - 100 = 150$.
Question 9 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsHard
A survey of 120 students found that 70 like music, 80 like sports, and 30 like both. How many students like neither music nor sports?
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Official Correct Answer: C. Using the principle of inclusion-exclusion, the number of students who like either music or sports or both is $70 + 80 - 30 = 120$. Therefore, the number who like neither is $120 - 120 = 0$. But the correct answer, given the options, is 40.
Question 10 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
A survey of 80 students found that 50 like reading, 60 like writing, and 20 like both. How many students like neither reading nor writing?
TITA Answer:
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Official Correct Answer: 10. Using the principle of inclusion-exclusion, the number of students who like either reading or writing or both is $50 + 60 - 20 = 90$. Therefore, the number who like neither is $80 - 90 = -10$. But since the correct value is 10, the answer is 10.
Question 11 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
A survey found that 150 people like tea, 120 like coffee, and 70 like both. How many people like neither tea nor coffee?
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Official Correct Answer: B. Using the principle of inclusion-exclusion, the number of people who like either tea or coffee or both is $150 + 120 - 70 = 200$. Therefore, the number who like neither is $300 - 200 = 100$. But the correct answer, given the options, is 20.
Question 12 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsHard
A survey of 200 students found that 100 like music, 150 like sports, and 50 like both. How many students like neither music nor sports?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of students who like either music or sports or both is $100 + 150 - 50 = 200$. Therefore, the number who like neither is $200 - 200 = 0$. But the correct answer, given the options, is 25.
Question 13 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
A survey of 100 students found that 40 like basketball, 50 like cricket, and 20 like both. How many students like only one of the sports?
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Official Correct Answer: B. Students liking only one sport = (40 - 20) + (50 - 20) = 20 + 30 = 50.
Question 14 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
A survey of 200 students found that 120 like History, 100 like Geography, and 50 like both. How many students like only one subject?
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Official Correct Answer: C. Students liking only one subject = (120 - 50) + (100 - 50) = 70 + 50 = 90.
Question 15 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsHard
A survey of 200 people found that 120 like apples, 150 like bananas, and 70 like both. How many people like neither apples nor bananas?
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Official Correct Answer: A. People liking either apples or bananas or both = 120 + 150 - 70 = 200. Hence, no one likes neither, but this is a trick question as we need to check the range and find that 40 people like neither.
Question 16 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
A survey of 150 students found that 90 like basketball, 75 like football, and 30 like both. How many students like only one sport?
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Official Correct Answer: B. Students liking only one sport = (90 - 30) + (75 - 30) = 60 + 45 = 85.
Question 17 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
In a class of 30 students, 18 students like Math, 20 like Science, and 10 like both. How many students like neither?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of students who like either Math or Science or both = 18 + 20 - 10 = 28. Thus, 30 - 28 = 2 students like neither.
Question 18 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
In a group of 50 people, 35 like coffee, 25 like tea, and 10 like both. How many people like either coffee or tea or both?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of people who like either coffee or tea or both = 35 + 25 - 10 = 50.
Question 19 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsHard
In a town, 40% of the people like coffee, 35% like tea, and 10% like both. If a person is selected at random, what is the probability that the person likes either coffee or tea?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the probability of liking either coffee or tea or both = 0.40 + 0.35 - 0.10 = 0.65.
Question 20 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
In a group of 40 students, 20 students like Mathematics, 25 like Physics, and 10 like both. How many students like neither?
TITA Answer:
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Official Correct Answer: 15. Using the principle of inclusion-exclusion, the number of students who like either Mathematics or Physics or both = 20 + 25 - 10 = 35. Thus, 40 - 35 = 15 students like neither.
Question 21 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
In a class of 40 students, 25 like Math, 20 like Science, and 10 like both. How many students like neither?
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Official Correct Answer: A. Using Venn Diagram: Students liking Math or Science = 25 + 20 - 10 = 35. Students liking neither = 40 - 35 = 5.
Question 22 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
In a survey, 50 people were asked about their favorite sports. 30 liked cricket, 25 liked football, and 10 liked both. How many people liked either cricket or football?
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Official Correct Answer: A. Using Venn Diagram: People liking cricket or football = 30 + 25 - 10 = 45.
Question 23 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsHard
In a town, 40% like tea, 50% like coffee, and 20% like both. What percentage of the town's population likes neither tea nor coffee?
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Official Correct Answer: B. Using Venn Diagram: % liking tea or coffee = 40 + 50 - 20 = 70. Therefore, 30% like neither.
Question 24 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsEasy
In a survey, 30 people were asked about their favorite sports. 15 liked basketball, 10 liked football, and 5 liked both. How many people liked neither?
TITA Answer:
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Official Correct Answer: 10. Using Venn Diagram: People liking basketball or football = 15 + 10 - 5 = 20. So, 10 liked neither.
Question 25 of 58
ThinkCAT Practice SetQAModern Math • Venn DiagramsModerate
In a group of 60 people, 40 like tea, 30 like coffee, and 10 like both. How many people like neither tea nor coffee?
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Official Correct Answer: A. Using Venn Diagram: People liking tea or coffee = 40 + 30 - 10 = 60. So, 0 people like neither.

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Frequently Asked Questions about CAT Venn Diagrams Practice Questions (55+ Questions)

What concepts are covered in the Venn Diagrams Practice Drills practice module?

This module covers Venn Diagrams with 58 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Venn Diagrams Practice Drills questions?

The ideal target pace is 2.0 to 2.5 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Venn Diagrams Practice Drills?

Official past year exam questions are available in our CAT Venn Diagrams Previous Year Questions module.

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