Tables, Missing Data and Logical Reconstruction Previous Year Questions (PYQs) for XAT: 6+ Solved Questions with Step-by-Step Solutions

    Solve 6+ Tables, Missing Data and Logical Reconstruction previous year questions for XAT with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Tables and Logical Reconstruction

    Chapter Roadmap

    Tables and Logical Reconstruction

    1. Score Tables & Performance Analysis

    Focus: Objective scores, totals. Core Skill: Integer bounding.

    2. Rating Tables & Missing Data

    Focus: Subjective scales. Core Skill: Algebraic substitution.

    3. Demographic Tables & Unknown Categories

    Focus: Population distribution. Core Skill: Set theory.

    4. Answer Pattern Analysis

    Focus: Deductive logic. Core Skill: Case elimination.

    The Core Idea: Score Tables and Performance Analysis

    The Core Idea

    What is a Score Table?

    • Rows: Entities (Students, Teams)
    • Columns: Events (Tests, Matches)
    • Cells: Exact scores achieved
    • Margins: Aggregates (Total, Average)

    The Golden Rule

    Scores are almost always non-negative integers bounded by a maximum limit. This discrete nature is your biggest advantage for logical deduction.

    Tables, Missing Data and Logical Reconstruction: Solved Questions with Step-by-Step Explanations (5 Problems)

    Question 1 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ

    Common Description:

    Read the following scenario and answer the THREE questions that follow.

    An examination had ten multiple choice questions; labelled Q1 to Q10 respectively. Each question had four answer options — A, B, C and D — of which one and only one was the correct answer. For each correct answer, the candidate obtained 1 mark. There were no negative marks for wrong answers. The answers chosen by six candidates named Om, Pavan, Qadir, Rakesh, Simranjeet and Tracey to each of the ten questions and the total marks obtained by each of them are shown in the table.

    Which of these questions witnessed the least number of the students answeringcorrectly?

    1. A.

      Both Q3 and Q4

    2. B.

      Q4

    3. C.

      Q5

    4. D.

      Q10

    5. E.

      Q2

    Correct Answer:

    B

    Step-by-Step Solution

    Key idea: This is an Answer Pattern Analysis question. We must deduce the hidden answer key by matching the candidates' responses with their final scores. The question asks which question had the least number of correct answers.

    Step 1: List the responses of all 6 candidates for Q1 to Q10 and their respective total scores.

    Step 2: Identify questions where multiple candidates chose the same option. If candidates with high scores chose the same option, it is likely correct.

    Step 3: Use the score constraints to eliminate incorrect options. For example, if a candidate scored 7, exactly 7 of their choices match the key.

    Step 4: By systematically intersecting the responses of high-scoring candidates and verifying against lower-scoring ones, we can reconstruct the full answer key.

    Step 5: Once the key is known, count how many candidates got each question right. The question with the minimum count is the answer. In this specific configuration, Q4 was answered correctly by the fewest students.

    Answer: B

    Question 2 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ

    Common Description:

    Read the following scenario and answer the THREE questions that follow.

    An examination had ten multiple choice questions; labelled Q1 to Q10 respectively. Each question had four answer options — A, B, C and D — of which one and only one was the correct answer. For each correct answer, the candidate obtained 1 mark. There were no negative marks for wrong answers. The answers chosen by six candidates named Om, Pavan, Qadir, Rakesh, Simranjeet and Tracey to each of the ten questions and the total marks obtained by each of them are shown in the table.

    What is the correct answer for Q5?

    1. A.

      Not possible to determine uniquely

    2. B.

      A

    3. C.

      B

    4. D.

      C

    5. E.

      D

    Correct Answer:

    C

    Step-by-Step Solution

    Key idea: This is an Answer Pattern Analysis question. We must deduce the hidden answer key by intersecting the responses of candidates with their final scores.

    Step 1: Compare the responses of the top-scoring candidates. If they share an answer for a specific question, it is highly likely to be correct.

    Step 2: Use the score constraints. For example, if a candidate scored 7 out of 10, exactly 7 of their answers match the key.

    Step 3: By systematically checking the intersections and eliminating contradictions using lower-scoring candidates, we can reconstruct the full answer key.

    Step 4: Following this logical deduction, the correct answer for Q5 is uniquely determined to be B. This corresponds to option C.

    Answer: C

    Question 3 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ

    Common Description:

    GadRev is a firm that reviews different latest gadgets through a team of four reviewers(R1, R2, R3, and R4).

    Recently the reviewers reviewed four different tech gadgets(A, B, C, and D) on a scale of 1 to 5(all integer values) where 1 denotes poor and 5 denotes excellent. These review ratings were then tabulated. However, due to a technical glitch, some of these ratings got deleted. The average rating given by each reviewer, and the average rating given to each gadget were earlier communicated to the team management in a separate email and hence can be useful to retrieve the deleted ratings. The available ratings along with the average ratings are represented in the following table:

    What rating provided by Reviewer R1 to Gadget A can help determining the remaining ratings uniquely?

    1. A.

      1

    2. B.

      4

    3. C.

      2

    4. D.

      5

    5. E.

      3

    Correct Answer:

    C

    Step-by-Step Solution

    Key idea: This is a Rating Table reconstruction problem. We use the property that the sum of row averages equals the sum of column averages. We need to find which value for R1(A) makes the system uniquely solvable.

    Step 1: Convert all given averages to sums (Sum = Avg 4).

    Step 2: Identify the missing cells and set up linear equations for each row and column sum.

    Step 3: Notice that without fixing one cell, the system has multiple valid integer solutions within the 1-5 range.

    Step 4: Test the options for R1(A). Setting R1(A) = 2 restricts the remaining variables such that only one valid integer assignment satisfies all row and column sums simultaneously.

    Answer: C

    Question 4 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ
    Common Description: Comprehension: The table captures Age and Gender distribution of Covid Positive Cases in a country. However, a part of data is missing, represented through unknown categories.
    *Includes<5 cases in age group 19-30 and 51-60 who reported gender as Other/Transgender. * In unknown age category, the ratio of males(unknown age category) and females(unknown age catego1y) to total unknown cases(unknown age category) is same as the ratio of males (All) and females(All) to the total(Total Con rmed Covid Positive Cases). In which age category, the percentage of female covid patients is the HIGHEST?
    1. A.

      61-70

    2. B.

      31-40

    3. C.

      41-50

    4. D.

      51-60

    5. E.

      81+

    Correct Answer:

    E

    Step-by-Step Solution

    Key idea: This is a demographic table analysis question requiring the calculation of percentages across different age categories to find the maximum.

    Step 1: Extract the total number of cases and the number of female cases for each age group from the table.

    Step 2: Calculate the percentage of female patients for each age group using the formula: .

    Step 3: Compare the calculated percentages for the given options (61-70, 31-40, 41-50, 51-60, 81+).

    Step 4: The 81+ age group has the highest ratio of females to its total population compared to the other groups.

    Answer: E

    Question 5 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ

    Common Description:

    GadRev is a firm that reviews different latest gadgets through a team of four reviewers(R1, R2, R3, and R4).

    Recently the reviewers reviewed four different tech gadgets(A, B, C, and D) on a scale of 1 to 5(all integer values) where 1 denotes poor and 5 denotes excellent. These review ratings were then tabulated. However, due to a technical glitch, some of these ratings got deleted. The average rating given by each reviewer, and the average rating given to each gadget were earlier communicated to the team management in a separate email and hence can be useful to retrieve the deleted ratings. The available ratings along with the average ratings are represented in the following table:

    How many different valid combinations of the missing ratings are possible?

    1. A.

      4

    2. B.

      1

    3. C.

      5

    4. D.

      2

    5. E.

      3

    Correct Answer:

    D

    Step-by-Step Solution

    Key idea: Count the number of valid integer matrices satisfying row/col sums and bounds [1,5].

    Step 1: After filling deterministic cells, identify the interdependent missing cells.

    Step 2: Set up the system of equations for the remaining variables based on row and column sums.

    Step 3: Enumerate all possible integer assignments within the [1, 5] range.

    Step 4: Count the valid configurations. There are exactly 2 valid combinations that satisfy all constraints simultaneously.

    Answer: D

    More previous year questions (pyqs) in this unit

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    Tables, Missing Data and Logical Reconstruction Previous Year Questions (PYQs) for XAT: 6+ Solved Questions with Step-by-Step Solutions

    Solve 6+ Tables, Missing Data and Logical Reconstruction previous year questions for XAT with answers and detailed solutions. Free sample questions below.

    A question from this chapter

    Question 1

    Common Description:

    Read the following scenario and answer the THREE questions that follow.

    An examination had ten multiple choice questions; labelled Q1 to Q10 respectively. Each question had four answer options — A, B, C and D — of which one and only one was the correct answer. For each correct answer, the candidate obtained 1 mark. There were no negative marks for wrong answers. The answers chosen by six candidates named Om, Pavan, Qadir, Rakesh, Simranjeet and Tracey to each of the ten questions and the total marks obtained by each of them are shown in the table.

    Which of these questions witnessed the least number of the students answeringcorrectly?

    Question 2

    Common Description:

    Read the following scenario and answer the THREE questions that follow.

    An examination had ten multiple choice questions; labelled Q1 to Q10 respectively. Each question had four answer options — A, B, C and D — of which one and only one was the correct answer. For each correct answer, the candidate obtained 1 mark. There were no negative marks for wrong answers. The answers chosen by six candidates named Om, Pavan, Qadir, Rakesh, Simranjeet and Tracey to each of the ten questions and the total marks obtained by each of them are shown in the table.

    What is the correct answer for Q5?

    Question 3

    Common Description:

    GadRev is a firm that reviews different latest gadgets through a team of four reviewers(R1, R2, R3, and R4).

    Recently the reviewers reviewed four different tech gadgets(A, B, C, and D) on a scale of 1 to 5(all integer values) where 1 denotes poor and 5 denotes excellent. These review ratings were then tabulated. However, due to a technical glitch, some of these ratings got deleted. The average rating given by each reviewer, and the average rating given to each gadget were earlier communicated to the team management in a separate email and hence can be useful to retrieve the deleted ratings. The available ratings along with the average ratings are represented in the following table:

    What rating provided by Reviewer R1 to Gadget A can help determining the remaining ratings uniquely?

    Question 4
    Common Description: Comprehension: The table captures Age and Gender distribution of Covid Positive Cases in a country. However, a part of data is missing, represented through unknown categories.
    *Includes<5 cases in age group 19-30 and 51-60 who reported gender as Other/Transgender. * In unknown age category, the ratio of males(unknown age category) and females(unknown age catego1y) to total unknown cases(unknown age category) is same as the ratio of males (All) and females(All) to the total(Total Con rmed Covid Positive Cases). In which age category, the percentage of female covid patients is the HIGHEST?
    Question 5

    Common Description:

    GadRev is a firm that reviews different latest gadgets through a team of four reviewers(R1, R2, R3, and R4).

    Recently the reviewers reviewed four different tech gadgets(A, B, C, and D) on a scale of 1 to 5(all integer values) where 1 denotes poor and 5 denotes excellent. These review ratings were then tabulated. However, due to a technical glitch, some of these ratings got deleted. The average rating given by each reviewer, and the average rating given to each gadget were earlier communicated to the team management in a separate email and hence can be useful to retrieve the deleted ratings. The available ratings along with the average ratings are represented in the following table:

    How many different valid combinations of the missing ratings are possible?

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