9 Set Theory PYQ (Solutions)
Master Set Theory for CAT 2026 with practice questions and detailed explanations
Set Theory questions in QA typically involve Venn diagrams or the Principle of Inclusion–Exclusion (PIE). While sets appear more often in DILR as puzzles, QA occasionally includes formula-based questions such as finding the number of elements in unions/intersections.
- CAT 2017–2019: No major focus on pure set theory within QA.
- CAT 2020: Slot-2 included 1 question on a 3-set Venn diagram.
- CAT 2022: Slot-1 also had 1 set theory question in QA.
Expected Weightage:
Across 2017–2024, QA usually had 0 or 1 question from set theory/Venn diagrams. It is not a core QA topic, but CAT sometimes inserts a numerical inclusion–exclusion question to test basic counting concepts.
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Weightage Over Past Years
| Year | Q.NONumber of questions | Difficulty Level |
|---|---|---|
| 2024 | 1 | Hard |
| 2022 | 1 | Hard |
| 2020 | 2 | Medium |
| 2019 | 1 | Hard |
| 2018 | 4 | Medium |
CAT 2024 Set Theory questions
Question 1
Slot-3
In a group of 250 students, the percentage of girls was at
least 44% and at most 60%. The rest of the students were boys. Each student opted for either
swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while
70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible
number of students who opted for both swimming and running, are
In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
CAT 2022 Set Theory questions
Question 1
Slot-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
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 Set Theory questions
Question 1
Slot-1
Among 100 students, x₁ have birthdays in January, x₂ have birthdays in February, and so on. If x₀ = max(x₁, x₂, ..., x₁₂), then the smallest possible value of x₀ is
Among 100 students, x₁ have birthdays in January, x₂ have birthdays in February, and so on. If x₀ = max(x₁, x₂, ..., x₁₂), then the smallest possible value of x₀ is
Question 2
Slot-2
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
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 Set Theory questions
Question 1
Slot-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
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 Set Theory questions
Question 1
Slot-1
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?
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 2
Slot-1
If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be
If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be
Question 3
Slot-2
For two sets A and B, let A △ B 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 (P △ Q) △ (R △ S) is
For two sets A and B, let A △ B 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 (P △ Q) △ (R △ S) is
Question 4
Slot-2
If A = {6²n - 35n - 1 : n = 1, 2, 3, ...} and B = {35(n - 1) : n = 1, 2, 3, ...} then which of the following is true?
If A = {6²n - 35n - 1 : n = 1, 2, 3, ...} and B = {35(n - 1) : n = 1, 2, 3, ...} then which of the following is true?
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