CAT DI Venn Diagrams Questions & Solutions

A sample of real CAT DI Venn Diagrams past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 48 DI Venn Diagrams questions in all — sign up free to practise them timed.

1. Passage

   There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.

   Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.

   The following facts are also known:

   1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
   2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
   3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
   4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
   5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.

   Q1.CAT 2022

   How many boys are there in the class?

   Answer: 50

2. Q2.CAT 2022

   How many female dancers are interested in attending a 2-day event?

   • 2

   • 1

   • 0

   • Cannot be determined

3. Passage

   A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU.

   The following facts are also known:

   1. There were equal numbers of domestic and foreign products.
   2. Half of the domestic products were FDA approved cosmetic products.
   3. None of the foreign products had both the approvals, while 60 domestic products had both the approvals.
   4. There were 140 nutrition products, half of them were foreign products.
   5. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.

   Q3.CAT 2022

   If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?

   • 50

   • 30

   • 10

   • 20

4. Passage

   1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.
   
   a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
   b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only.
   c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only.
   d. 100 patients were treated with exactly three types of medicines.
   e. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type B.
   f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.

   Q4.CAT 2020

   How many patients were treated with medicine types B and D only?

   Answer: 150

5. Passage

   Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.
   
   The following facts are known about these ten musicians.

   1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla.
   2. D is an expert in both tabla and ghatam.
   3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam.
   4. Neither I nor J is an expert in tabla.
   5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

   Q5.CAT 2020

   Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam?

   • F and G

   • C and E

   • A and B

   • C and F

6. Passage

   A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied.

   F1: Own software for OTLP
   F2: Trained teachers for OTLP
   F3: Training materials for OTLP
   F4: All students having Laptops

   The following observations were summarized from the survey.

   1. 80 schools did not have any of the four facilities - F1, F2, F3, F4.
   2. 40 schools had all four facilities.
   3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.
   4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.
   5. 313 schools had F2.
   6. 26 schools had only F2 and F3 (but neither F1 nor F4).
   7. Among the schools having F4, 24 had only F3, and 45 had only F2.
   8. 162 schools had both F1 and F2.
   9. The number of schools having F1 was the same as the number of schools having F4.

   Q6.CAT 2020

   What was the number of schools having only facilities F1 and F3?

   Answer: 42

7. Passage

   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.

   Q7.CAT 2019

   What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?

   • 40

   • 25

   • 20

   • 50

8. Passage

   1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. The following facts are known about the satellites:

   1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
   2. The number of satellites serving all three of B, C, and S is 100.
   3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
   4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B.

   Q8.CAT 2018

   If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?

   • At most 475

   • Exactly 475

   • No conclusion is possible based on the given information

   • At least 475

9. Passage

   Fun Sports (FS) provides training in three sports - Gilli-danda (G), Kho-Kho (K), and Ludo (L). Currently it has an enrollment of 39 students each of whom is enrolled in at least one of the three sports. The following details are known:

   1. The number of students enrolled only in L is double the number of students enrolled in all the three sports.
   2. There are a total of 17 students enrolled in G.
   3. The number of students enrolled only in G is one less than the number of students enrolled only in L.
   4. The number of students enrolled only in K is equal to the number of students who are enrolled in both K and L.
   5. The maximum student enrollment is in L.
   6. Ten students enrolled in G are also enrolled in at least one more sport.

   Q9.CAT 2018

   Due to academic pressure, students who were enrolled in all three sports were asked to withdraw from one of the three sports. After the withdrawal, the number of students enrolled in G was six less than the number of students enrolled in L, while the number of students enrolled in K went down by one. After the withdrawal, how many students were enrolled in both G and K?

   Answer: 2

10. Passage

    Applicants for the doctoral programmes of Ambi Institute of Engineering (AIE) and Bambi Institute of Engineering (BIE) have to appear for a Common Entrance Test (CET). The test has three sections: Physics (P), Chemistry (C), and Maths (M). Among those appearing for CET, those at or above the 80th percentile in at least two sections, and at or above the 90th percentile overall, are selected for Advanced Entrance Test (AET) conducted by AIE. AET is used by AIE for final selection.

    For the 200 candidates who are at or above the 90th percentile overall based on CET, the following are known about their performance in CET:

    1. No one is below the 80th percentile in all 3 sections.
    2. 150 are at or above the 80th percentile in exactly two sections.
    3. The number of candidates at or above the 80th percentile only in P is the same as the number of candidates at or above the 80th percentile only in C. The same is the number of candidates at or above the 80th percentile only in M.
    4. Number of candidates below 80th percentile in P: Number of candidates below 80th percentile in C: Number of candidates below 80th percentile in M = 4:2:1.

       BIE uses a different process for selection. If any candidate is appearing in the AET by AIE, BIE considers their AET score for final selection provided the candidate is at or above the 80th percentile in P. Any other candidate at or above the 80th percentile in P in CET, but who is not eligible for the AET, is required to appear in a separate test to be conducted by BIE for being considered for final selection. Altogether, there are 400 candidates this year who are at or above the 80th percentile in P.

    Q10.CAT 2017

    If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, then how many candidates were shortlisted for the AET for AIE?

    Answer: 170

11. Q11.CAT 1990

    Choose the set in which the statements are most logically related.
    A. All candid men are persons who acknowledge merit in a rival.
    B. Some learned men are very candid.
    C. Some learned men are not persons who acknowledge merit in a rival.
    D. Some learned men are persons who are very candid.
    E. Some learned men are not candid.
    F. Some persons who recognize merit in a rival are learned.

    • ABE

    • ACF

    • ADE

    • BAF

12. Q12.CAT 1990

    Choose the set in which the statements are most logically related.
    A. Some mammals are carnivores.
    B. All whales are mammals.
    C. All whales are aquatic animals.
    D. All whales are carnivores.
    E. Some aquatic animals are mammals.
    F. Some mammals are whales.

    • ADF

    • ABC

    • AEF

    • BCE

CAT DI Venn Diagrams previous year questions with solutions — AthenaPrep