CAT Set theory & Venn diagrams Questions

Set theory organises overlapping categories. Venn diagrams help distinguish 'only', 'at least' and 'exactly' conditions and avoid counting the same member more than once.

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Key concepts

Union, intersection and complement
Inclusion–exclusion
Exactly one, exactly two and all categories

CAT set theory & venn diagrams practice questions

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Practise Free Tests on InsideIIM

Common mistakes

Treating an inclusive intersection as an 'only' region.
Forgetting members outside every listed set.

Practical solving approaches

Fill the deepest overlaps first, then move outward.
Check that all disjoint regions add to the stated total, including the outside region.

Set theory & Venn diagrams FAQs

Does A intersect B include members of a third set?: Yes. Unless the problem says 'A and B only', the intersection includes members who also belong to other sets.

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CAT set theory & venn diagrams practice questions

Question 1Type in the answerEASY

Type in your answer in the input box provided below the question.

Refer to the data below and answer the questions that follow.

If survey also indicates that 20% of the people watch Mony and Moon, and 16% watch XEE and Moon, then what percentage of the people watch only XEE?

Question 2Type in the answerMEDIUM

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Answer the questions independently of each other.

Of the 2 lakh students who appeared for the 5 national management entrance tests last year, 70% appeared for JMET, 75% for ATMA, 80% for MAT, 85% for XAT and 90% for CAT. What is the minimum number of students who appeared for all the 5 tests?

Question 3Type in the answerMEDIUM

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Answer the questions independently of each other.

Out of 260 students, 190 passed in English, 60 passed in Maths and 75 passed in Science. For every student who failed only in English, there were 2 students who failed only in Science, and 3 who failed in Maths alone. The number of students who passed in exactly 2 subjects was 5 more than the number of students who passed in all the three subjects. Also, those who passed in English along with only 1 other subject were equal in number to those who passed in all 3 subjects. Find the number of students who failed in all the three subjects.

Question 4Multiple choiceMEDIUM

Select the correct alternative from the given choices.

In a tournament, there are n teams T₁ ,T₂, ..., T_n, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common:
T₁ & T₂, T₂ & T₃, ..., T_n–1 & T_n, and T_n & T₁. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?

Question 5Multiple choiceMEDIUM

Select the correct alternative from the given choices.

In an examination, 35% of students failed in quants and 42% of students failed in verbal while 14% failed in both the topics. If 222 students passed in both the topics, how many students appeared to write the examination?

Question 6Type in the answerMEDIUM

How many preferred only fruit juice?

A survey was conducted among 95 students who visited the college canteen everyday. The number of students
who preferred tea, coffee or a fruit juice in the break was as follows: coffee : 28; tea and fruit juice : 6; only tea :
35; all three : 4; coffee and fruit juice : 10; tea and coffee : 7; none : 7.

CAT Set theory & Venn diagrams Questions

Set theory organises overlapping categories. Venn diagrams help distinguish 'only', 'at least' and 'exactly' conditions and avoid counting the same member more than once.

Loading question count…

Key concepts

Union, intersection and complement
Inclusion–exclusion
Exactly one, exactly two and all categories

CAT set theory & venn diagrams practice questions

Loading questions…

Practise Free Tests on InsideIIM

Common mistakes

Treating an inclusive intersection as an 'only' region.
Forgetting members outside every listed set.

Practical solving approaches

Fill the deepest overlaps first, then move outward.
Check that all disjoint regions add to the stated total, including the outside region.

Set theory & Venn diagrams FAQs

Does A intersect B include members of a third set?: Yes. Unless the problem says 'A and B only', the intersection includes members who also belong to other sets.

Loading practice data…

CAT set theory & venn diagrams practice questions

Question 1Type in the answerEASY

Type in your answer in the input box provided below the question.

Refer to the data below and answer the questions that follow.

If survey also indicates that 20% of the people watch Mony and Moon, and 16% watch XEE and Moon, then what percentage of the people watch only XEE?

Question 2Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Question 3Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Question 4Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 5Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 6Type in the answerMEDIUM

How many preferred only fruit juice?

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CAT Set theory & Venn diagrams Questions

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CAT set theory & venn diagrams practice questions

Common mistakes

Practical solving approaches

Set theory & Venn diagrams FAQs

CAT Set theory & Venn diagrams Questions

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CAT set theory & venn diagrams practice questions

Common mistakes

Practical solving approaches

Set theory & Venn diagrams FAQs

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CAT Set theory & Venn diagrams Questions

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CAT set theory & venn diagrams practice questions

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Set theory & Venn diagrams FAQs

CAT Set theory & Venn diagrams Questions

Key concepts

CAT set theory & venn diagrams practice questions

Common mistakes

Practical solving approaches

Set theory & Venn diagrams FAQs

More Modern Maths practice