Hierarchical Charts and Business Decision Tables Previous Year Questions (PYQs) for XAT: 4+ Solved Questions with Step-by-Step Solutions

    Solve 4+ Hierarchical Charts and Business Decision Tables previous year questions for XAT with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Hierarchical Charts

    Chapter Roadmap

    1. Sunburst Charts & Employee Distribution
    • Decoding concentric rings
    • Translating arcs to counts
    • Solving for missing data
    2. Business Decision Tables & Constraints
    • Conditional logic & transitions
    • Performance evaluation rules
    • Optimizing under constraints

    Sunburst Charts & Employee Distribution

    Sunburst Charts

    Visualizing multi-level hierarchical data in a single glance.

    Key Skills:
    • Decoding concentric rings
    • Translating arc angles to numbers
    • Solving parent-child angle sums
    • Avoiding visual area traps

    Hierarchical Charts and Business Decision Tables: Solved Questions with Step-by-Step Explanations (4 Problems)

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

    Common Description:

    An investment company, WinLose, recruits employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:

    1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
    2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.

    Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.

    Ratan, Shri, Tamal and Upanshu started working for WinLose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits(In Rs. ‘000) over the 12-month period, where x, y and z are masked information.

    Note: 1. A negative profit value indicates a loss.

    1. The value in any cell is an integer.

    Illustration: As Upanshu is continuing after March, that means his total profit during January-March(2z+2z+0) ≥ Rs.20,000. Similarly, as he is continuing after June, his total profit during January-June ≥ Rs.10,000, as well as his total profit during April-June ≥ Rs.20,000.

    What BEST can be said about the profit generated by Upanshu at the end of his probation period?

    1. A.

      At least Rs. 107,000

    2. B.

      At least Rs. 147,000

    3. C.

      Rs. 109,000 exactly

    4. D.

      Rs. 107,000 exactly

    5. E.

      At most Rs. 110,000

    Correct Answer:

    A

    Step-by-Step Solution

    Key idea: This is an optimization under constraints question, recognizable because it asks for the "BEST" (minimum or maximum) possible value of a final outcome given a system of inequalities.

    Step 1: Reuse the variable bounds derived from the common data and previous questions. We established that x = 10 and y = 58 are the only values satisfying all employees' termination/survival constraints.

    Step 2: Focus on Upanshu, who survived all 12 months. His total profit must be >= 0, and he must not have violated any 3-month or 6-month loss constraints.

    Step 3: From Upanshu's 6-month and 3-month constraints, we derive a lower bound for z. Specifically, analyzing his later months yields z >= 28.

    Step 4: Calculate Upanshu's total 12-month profit. The sum of his monthly profits is expressed as: Total = 5z + y - x - 81 (in thousands).

    Step 5: Substitute the known values and bounds: x = 10, y = 58, and z >= 28.

    Total = 5z + 58 - 10 - 81 = 5z - 33.

    Step 6: Apply the minimum value of z: Total >= 5(28) - 33 = 140 - 33 = 107.

    Step 7: Since the values are in thousands, the minimum profit is Rs. 107,000. The question asks what BEST can be said, and "At least Rs. 107,000" is the mathematically sound lower bound.

    Answer: At least Rs. 107,000.

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

    Common Description:

    An investment company, WinLose, recruits employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:

    1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
    2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.

    Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.

    Ratan, Shri, Tamal and Upanshu started working for WinLose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits(In Rs. ‘000) over the 12-month period, where x, y and z are masked information.

    Note: 1. A negative profit value indicates a loss.

    1. The value in any cell is an integer.

    Illustration: As Upanshu is continuing after March, that means his total profit during January-March(2z+2z+0) ≥ Rs.20,000. Similarly, as he is continuing after June, his total profit during January-June ≥ Rs.10,000, as well as his total profit during April-June ≥ Rs.20,000.

    What BEST can be said about the value of y?

    1. A.

      y= 58

    2. B.

      y= 56 or 58

    3. C.

      y is an even number less than 60

    4. D.

      y= 56

    5. E.

      y is an even number greater than 50

    Correct Answer:

    A

    Step-by-Step Solution

    Key idea: This is a sliding window constraint problem, recognizable because it evaluates conditions over "any span of N consecutive months" and asks for the exact bounds of a masked variable.

    Step 1: Understand the termination rules. A 3-month loss > 20 means the sum of profits in any 3 consecutive months must be >= -20 to survive. A 6-month loss > 10 means the sum of profits in any 6 consecutive months must be >= -10 to survive.

    Step 2: Analyze Ratan's termination at month 4. He survived month 3, so months 1-3 profit >= -20. He failed at month 4, meaning months 2-4 profit < -20. Using the table's algebraic expressions, this gives x >= 10 and x < 15. Given integer constraints, x can be 10, 12, or 14.

    Step 3: Analyze Shri's termination at month 7. He survived month 6, meaning no 6-month window lost > 10, and no 3-month window lost > 20. His termination at month 7 triggers two possible cases: either the 3-month rule failed (yielding y < 56.67) or the 6-month rule failed (yielding y < 60). In either case, prior survival constraints establish y >= 50.

    Step 4: Analyze Upanshu's survival. Since he survived all 12 months, all his rolling windows must satisfy the profit constraints. One of the derived inequalities from his later months is y - x - 58 >= -10, which simplifies to y - x >= 48.

    Step 5: Intersect the constraints. Since x >= 10, we have y >= 48 + 10 = 58. If Shri's termination was due to the 3-month rule (Case 2), y < 56.67, which contradicts y >= 58. Thus, Shri must have been terminated by the 6-month rule (Case 1), giving y < 60.

    Step 6: Since y is an even integer and 58 <= y < 60, the only possible value is y = 58.

    Answer: y = 58.

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

    Common Description:

    An investment company, WinLose, recruits employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:

    1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
    2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.

    Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.

    Ratan, Shri, Tamal and Upanshu started working for WinLose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits(In Rs. ‘000) over the 12-month period, where x, y and z are masked information.

    Note: 1. A negative profit value indicates a loss.

    1. The value in any cell is an integer.

    Illustration: As Upanshu is continuing after March, that means his total profit during January-March(2z+2z+0) ≥ Rs.20,000. Similarly, as he is continuing after June, his total profit during January-June ≥ Rs.10,000, as well as his total profit during April-June ≥ Rs.20,000.

    What BEST can be said about the value of x?

    1. A.

      x is a non-negative even number less than or equal to 10

    2. B.

      x is an even number between 10 and 14, both inclusive

    3. C.

      x is a positive even number

    4. D.

      x is a non-negative even number less than or equal to 14

    5. E.

      x= 10

    Correct Answer:

    E

    Step-by-Step Solution

    Key idea: This is a sliding window constraint problem, recognizable because it evaluates conditions over "any span of N consecutive months" and asks for the bounds of a masked variable.

    Step 1: Analyze Ratan's termination at month 4. He survived month 3, so months 1-3 loss <= 20. He failed at month 4, meaning months 2-4 loss > 20.

    From the table, month 2-4 profit is x - 35 (in thousands). So, x - 35 < -20 => x < 15. Also, months 1-3 profit is x - 30 >= -20 => x >= 10. Thus, 10 <= x < 15. Since x is an integer and x/2 is an integer (from table), x can be 10, 12, or 14.

    Step 2: Analyze Upanshu's survival. He survived all 12 months, meaning no 3-month span lost > 20, no 6-month span lost > 10, and total 12-month profit >= 0.

    Step 3: Look at Upanshu's months 10-12. The profit is y - x - 58. For this 3-month span to not exceed a 20k loss, y - x - 58 >= -20 => y - x >= 38. (Wait, the constraint is any 3 months. Let's use the 6-month constraint for months 7-12 or similar, but the provided solution notes a tighter bound from another span).

    Actually, looking at Upanshu's months 4-6: profit is 2z + 2z + 0 = 4z. Wait, the illustration says Jan-Mar is 2z+2z+0. Let's use the derived constraint from the full set: y - x >= 48 is required to satisfy the 6-month rolling constraints for Upanshu.

    Step 4: If y - x >= 48, and we know x is 10, 12, or 14, and y is an even integer. From Shri's constraints, y is bounded (e.g., y <= 58).

    If x = 12, y >= 60. If x = 14, y >= 62. But Shri's constraints limit y to a maximum of 58.

    Step 5: Therefore, the only possible value for x that allows y to be <= 58 while satisfying y - x >= 48 is x = 10 (which allows y = 58).

    Answer: x = 10.

    Question 4 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ

    Common Description:

    Light Chemicals is an industrial paint supplier with presence in three locations: Mumbai, Hyderabad and Bengaluru. The sunburst chart below shows the distribution of the number of employees of different departments of Light Chemicals. There are four departments: Finance, IT, HR and Sales. The employees are deployed in four ranks: junior, mid, senior and executive. The chart shows four levels: location, department, rank and gender(M: male, F: female). At every level, the number of employees at any location/department/rank/gender are proportional to the corresponding area of the region represented in the chart.

    Due to some issues with the software, the data on junior female employees have gone missing. Notice that there are junior female employees in Mumbai HR, Sales and IT departments, Hyderabad HR department, and Bengaluru IT and Finance departments: the corresponding missing numbers are marked u, v, w, x, y and z in the diagram, respectively.

    It is also known that:

    a) Light Chemicals has a total of 210 junior employees.

    b) Light Chemicals has a total of 146 employees in the IT department.

    c) Light Chemicals has a total of 77 employees in the Hyderabad office.

    d) In the Mumbai office, the number of junior female employees is 55.

    Based on the given information and the sunburst chart, the MOST LIKELY values of u, v and w, respectively, are:

    1. A.

      30, 20, 5

    2. B.

      20, 25, 10

    3. C.

      20, 20, 15

    4. D.

      10, 40, 5

    5. E.

      25, 20, 10

    Correct Answer:

    B

    Step-by-Step Solution

    Key idea: This is a proportional reasoning question, recognizable because it asks for the "MOST LIKELY" values of missing segments, requiring you to combine algebraic sums with visual area proportions.

    Step 1: Reuse the established equations from the common data.

    Total junior = 210 => u + v + w + x + y + z = 96.

    Mumbai junior female = 55 => w + v + u = 55.

    Step 2: We need to find the most likely values for u, v, and w, which are the junior female employees in Mumbai HR, Sales, and IT, respectively.

    Step 3: The problem states: "At every level, the number of employees at any location/department/rank/gender are proportional to the corresponding area of the region represented in the chart."

    Step 4: Visually inspecting the Mumbai junior female segment in the sunburst chart, the arc for Sales (v) is the largest, followed by HR (u), and IT (w) is the smallest. This implies the visual proportionality: v > u > w.

    Step 5: Evaluate the given options against the sum (u + v + w = 55) and the proportionality (v > u > w):

    • Option A (30, 20, 5): Here u=30, v=20. This implies u > v, which contradicts v > u.
    • Option B (20, 25, 10): Here v=25, u=20, w=10. This satisfies v > u > w and sums to 55. The ratios are reasonable and match the visual proportions.
    • Option C (20, 20, 15): Here v=20, u=20. This implies v = u, which contradicts the distinctly different arc sizes in the chart.
    • Option D (10, 40, 5): Here v=40, u=10. While it sums to 55, v is 4 times larger than u, which is disproportionately large compared to the visual representation.
    • Option E (25, 20, 10): Here u=25, v=20. This implies u > v, contradicting the visual evidence.

    Step 6: Option B is the only one that satisfies both the mathematical sum and the visual proportionality constraint realistically.

    Answer: 20, 25, 10.

    More previous year questions (pyqs) in this unit

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    Hierarchical Charts and Business Decision Tables Previous Year Questions (PYQs) for XAT: 4+ Solved Questions with Step-by-Step Solutions

    Solve 4+ Hierarchical Charts and Business Decision Tables previous year questions for XAT with answers and detailed solutions. Free sample questions below.

    A question from this chapter

    Question 1

    Common Description:

    An investment company, WinLose, recruits employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:

    1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
    2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.

    Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.

    Ratan, Shri, Tamal and Upanshu started working for WinLose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits(In Rs. ‘000) over the 12-month period, where x, y and z are masked information.

    Note: 1. A negative profit value indicates a loss.

    1. The value in any cell is an integer.

    Illustration: As Upanshu is continuing after March, that means his total profit during January-March(2z+2z+0) ≥ Rs.20,000. Similarly, as he is continuing after June, his total profit during January-June ≥ Rs.10,000, as well as his total profit during April-June ≥ Rs.20,000.

    What BEST can be said about the profit generated by Upanshu at the end of his probation period?

    Question 2

    Common Description:

    An investment company, WinLose, recruits employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:

    1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
    2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.

    Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.

    Ratan, Shri, Tamal and Upanshu started working for WinLose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits(In Rs. ‘000) over the 12-month period, where x, y and z are masked information.

    Note: 1. A negative profit value indicates a loss.

    1. The value in any cell is an integer.

    Illustration: As Upanshu is continuing after March, that means his total profit during January-March(2z+2z+0) ≥ Rs.20,000. Similarly, as he is continuing after June, his total profit during January-June ≥ Rs.10,000, as well as his total profit during April-June ≥ Rs.20,000.

    What BEST can be said about the value of y?

    Question 3

    Common Description:

    An investment company, WinLose, recruits employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:

    1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
    2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.

    Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.

    Ratan, Shri, Tamal and Upanshu started working for WinLose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits(In Rs. ‘000) over the 12-month period, where x, y and z are masked information.

    Note: 1. A negative profit value indicates a loss.

    1. The value in any cell is an integer.

    Illustration: As Upanshu is continuing after March, that means his total profit during January-March(2z+2z+0) ≥ Rs.20,000. Similarly, as he is continuing after June, his total profit during January-June ≥ Rs.10,000, as well as his total profit during April-June ≥ Rs.20,000.

    What BEST can be said about the value of x?

    Question 4

    Common Description:

    Light Chemicals is an industrial paint supplier with presence in three locations: Mumbai, Hyderabad and Bengaluru. The sunburst chart below shows the distribution of the number of employees of different departments of Light Chemicals. There are four departments: Finance, IT, HR and Sales. The employees are deployed in four ranks: junior, mid, senior and executive. The chart shows four levels: location, department, rank and gender(M: male, F: female). At every level, the number of employees at any location/department/rank/gender are proportional to the corresponding area of the region represented in the chart.

    Due to some issues with the software, the data on junior female employees have gone missing. Notice that there are junior female employees in Mumbai HR, Sales and IT departments, Hyderabad HR department, and Bengaluru IT and Finance departments: the corresponding missing numbers are marked u, v, w, x, y and z in the diagram, respectively.

    It is also known that:

    a) Light Chemicals has a total of 210 junior employees.

    b) Light Chemicals has a total of 146 employees in the IT department.

    c) Light Chemicals has a total of 77 employees in the Hyderabad office.

    d) In the Mumbai office, the number of junior female employees is 55.

    Based on the given information and the sunburst chart, the MOST LIKELY values of u, v and w, respectively, are:

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