The Venn diagram is also one of the important topics that aspirants must consider practising to get a good score in CAT. 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. 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.
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Year | Weightage |
2022 | 1 |
2021 | 0 |
2020 | 1 |
2019 | 1 |
2018 | 4 |
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.
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
correct answer:-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
correct answer:-3
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
correct answer:-4
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
correct answer:-7
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
correct answer:-52
If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be
correct answer:-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?
correct answer:-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)?
correct answer:-2
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:
correct answer:-3
Which of the following additional information would enable to find the exact number of volunteers involved in various projects?
correct answer:-1
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?
correct answer:-2
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?
correct answer:-1
What is the number of projects in which Gyani alone is involved?
correct answer:-4
What is the number of projects in which Medha alone is involved?
correct answer:-2
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?
correct answer:-3
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?
correct answer:-2
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.
correct answer:-3
What is the maximum percentage of people who can watch all the three channels?
correct answer:-2
If 5% of people watched DD and CNN, 10% watched DD and BBC, then what percentage of people watched BBC and CNN only?
correct answer:-1
Referring to the previous question, what percentage of people watched all the three channels?
correct answer:-4
In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having atleast one among cable -TV and VCR?
correct answer:-4
Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?
correct answer:-3
There are 3 clubs A, B & C in a town with 40, 50 & 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?
correct answer:-2
How many schools had none of the three viz., laboratory, library or play - ground?
correct answer:-4
What was the ratio of schools having laboratory those having library?
correct answer:-2