Counting, Selections and Arrangements Previous Year Questions (PYQs) for XAT: 2+ Solved Questions with Step-by-Step Solutions

    Solve 2+ Counting, Selections and Arrangements previous year questions for XAT with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Counting, Selections and Arrangements

    Chapter Roadmap

    1. Fundamental Counting Principle

    The bedrock of all counting. Mastering the 'AND' and 'OR' rules.

    2. Permutations: Art of Arrangement

    When order matters. Linear, circular, and identical items.

    3. Combinations: Art of Selection

    When order does not matter. Grouping and powerful properties.

    4. Grouping and Distribution

    Dividing items. Identical vs distinct groups.

    5. Advanced Constraints

    Complex conditions, overlapping categories, and geometric arrangements.

    The Core Intuition: And vs Or

    The Core Intuition: AND vs OR

    Multiplication (AND)

    Independent stages connected by AND.

    Example: Choose a shirt AND a pant.

    Action: Multiply.

    Addition (OR)

    Mutually exclusive alternatives connected by OR.

    Example: Travel by train OR by bus.

    Action: Add.

    First-Timer Tip: Frame the problem in plain English. If stages happen to complete one goal, multiply. If they are separate ways to achieve the same goal, add.

    Counting, Selections and Arrangements: Solved Questions with Step-by-Step Explanations (2 Problems)

    Question 1 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ
    Common Description: 41 applicants have been shortlisted for interviews for some data analyst positions. Some of the applicants have advanced expertise in one or more elds among the following: data analysis, database handling and coding. The numbers of applicants with different advanced expertise are given in the 2 × 8 table below.
    The number of applicants with advanced expertise in all three elds is given as x in the table, where x is a non-negative integer. What BEST can be concluded about the value of x?
    1. A.

      0, 1 or 2

    2. B.

      2 only

    3. C.

      1 only

    4. D.

      0 or 1 only

    5. E.

      1 or 2 only

    Correct Answer:

    E

    Step-by-Step Solution

    Key idea: three-set Venn diagram with one unknown region ; use the total-sum constraint to bound .

    Step 1: Let the 7 non-empty regions of the Venn diagram be expressed in terms of using the table data.

    Step 2: Sum of all 7 regions (total applicants). This gives a linear inequality in .

    Step 3: Each region must be a non-negative integer, giving lower and upper bounds on .

    Step 4: Solving the inequalities yields .

    Step 5: Both values satisfy every non-negativity constraint, so can be 1 or 2.

    Answer: 1 or 2 only (option E).

    Question 2 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ
    Common Description: 41 applicants have been shortlisted for interviews for some data analyst positions. Some of the applicants have advanced expertise in one or more elds among the following: data analysis, database handling and coding. The numbers of applicants with different advanced expertise are given in the 2 × 8 table below.
    The number of applicants with advanced expertise in all three elds is given as x in the table, where x is a non-negative integer. How many applicants DID NOT have advanced expertise in any of the three given elds?
    1. A.

      Cannot be determined uniquely from the given information.

    2. B.

      25

    3. C.

      26

    4. D.

      27

    5. E.

      28

    Correct Answer:

    A

    Step-by-Step Solution

    Key idea: companion to P2 — the number with no expertise depends on , which is not uniquely determined.

    Step 1: From P2, .

    Step 2: The number of applicants with at least one expertise equals the sum of all 7 Venn regions, which is a linear expression in (say ).

    Step 3: The number with no expertise is .

    Step 4: Since , the answer takes two different values depending on .

    Step 5: Therefore it cannot be determined uniquely from the given information.

    Answer: option A.

    More previous year questions (pyqs) in this unit

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    Counting, Selections and Arrangements Previous Year Questions (PYQs) for XAT: 2+ Solved Questions with Step-by-Step Solutions

    Solve 2+ Counting, Selections and Arrangements previous year questions for XAT with answers and detailed solutions. Free sample questions below.

    A question from this chapter

    Question 1
    Common Description: 41 applicants have been shortlisted for interviews for some data analyst positions. Some of the applicants have advanced expertise in one or more elds among the following: data analysis, database handling and coding. The numbers of applicants with different advanced expertise are given in the 2 × 8 table below.
    The number of applicants with advanced expertise in all three elds is given as x in the table, where x is a non-negative integer. What BEST can be concluded about the value of x?
    Question 2
    Common Description: 41 applicants have been shortlisted for interviews for some data analyst positions. Some of the applicants have advanced expertise in one or more elds among the following: data analysis, database handling and coding. The numbers of applicants with different advanced expertise are given in the 2 × 8 table below.
    The number of applicants with advanced expertise in all three elds is given as x in the table, where x is a non-negative integer. How many applicants DID NOT have advanced expertise in any of the three given elds?
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