Sets, Venn Diagrams and Functions Previous Year Questions (PYQs) for CAT: 1+ Solved Questions with Step-by-Step Solutions

    Solve 1+ Sets, Venn Diagrams and Functions previous year questions for CAT with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Sets, Venn Diagrams and Functions

    Chapter Roadmap

    Sets, Venn Diagrams and Functions

    A compact Modern Maths chapter where CAT tests overlap counting and set-to-set assignment logic.

    ⭕
    t1. Venn Diagrams and Inclusion-Exclusion
    Master overlaps, exactly-one regions, all-three intersections, and max-min range questions.
    3 PYQs
    higher weight
    🔁
    t2. Onto Functions and Set Mappings
    Count functions where every element in the target set must be hit at least once.
    1 PYQ
    support topic
    By the end: you should be able to convert word data into regions, equations, and valid ranges without double-counting.

    Venn Diagrams and Inclusion-Exclusion

    Selected Topic

    Venn Diagrams and Inclusion-Exclusion

    Fix double-counting when groups overlap.

    3
    Chapter: Sets, Venn Diagrams and Functions Topic t1 3 direct CAT PYQs
    What you will learn here
    • Draw and fill two-set and three-set Venn regions
    • Use inclusion-exclusion without double-counting
    • Handle “none”, “at least one”, and “all three”
    • Find minimum and maximum possible overlap
    • Convert CAT word conditions into equations

    Sets, Venn Diagrams and Functions: Solved Questions with Step-by-Step Explanations (1 Problems)

    Question 1 · Quantitative Ability MCQ

    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

    1. A.

      47

    2. B.

      53

    3. C.

      52

    4. D.

      48

    Correct Answer:

    A

    Step-by-Step Solution

    This is a "three-set max-min of the triple intersection" question. The signal is three overlapping groups (coffee, tea, lemonade), a total population, an explicit note that some people may like none of the three, and a question asking for the range (difference between max and min) of the all-three overlap.

    Step 1: Set up notation.

    Let (total students). Let = coffee likers (), = tea likers (), = lemonade likers (). We want the range of .

    Step 2: Find the maximum of the triple intersection.

    The triple intersection can never exceed the smallest individual set, because everyone in must also be in the smallest group:

    This maximum of 52 is achievable: let all 52 lemonade-likers also like both coffee and tea. This uses only of the students for the triple overlap, and the remaining coffee-only and tea-only requirements ( people needing extra coffee, people needing extra tea) can easily overlap with each other without exceeding the 100-student population (only students needed in total). So the maximum is .

    Step 3: Find the minimum of the triple intersection.

    To minimize the overlap, we want to spread out the three groups as much as possible, using the full population of 100 to "absorb" as much of each group as possible without needing all three to overlap.

    For two sets, the minimum possible overlap is:

    This comes from: even if and are spread out as much as possible without overlapping, together they cannot exceed the total population ; any excess beyond must overlap.

    Extending this idea to three sets, we get a similar bound by combining with :

    Substituting values:

    Since 5 is non-negative, this is a valid lower bound, and it is achievable by careful construction (spreading coffee, tea, and lemonade likers to overlap only the minimum necessary amount). So the minimum is .

    Step 4: Compute the difference.

    So the answer is .

    Common trap: a common mistake is computing the minimum using only the two-set formula () and forgetting to extend it properly to three sets, or forgetting the "some students like none" condition entirely and assuming the union must equal exactly 100 rather than being at most 100.

    More previous year questions (pyqs) in this unit

    chapter
    Sets, Venn Diagrams and Functions Previous Year Questions (PYQs) for CAT: 1+ Solved Questions with Step-by-Step Solutions

    Solve 1+ Sets, Venn Diagrams and Functions previous year questions for CAT with answers and detailed solutions. Free sample questions below.

    A question from this chapter

    Question 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

    Free preview ends here

    Login to view the complete previous-year questions and solutions

    Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

    Login to continueSee plans
    Why MastersUp

    Personalised first. High quality throughout.

    Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

    Built around you, not around a syllabus PDF

    Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

    Revision that hits your weak spots

    We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

    Questions calibrated to the real exam

    Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

    Notes written for recall, not for volume

    Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

    One place for everything

    Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

    Honest progress

    No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

    Unlock the whole course

    Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

    View all plansStart free