Data Arrangement Worksheet 29 - Expert Level (comparative arrangement) | 20 Questions

Question 1

Six employees with distinct departments and roles form a reporting hierarchy. Use the clues to build the tree and answer: - Eshan and Zoya report to Qadir. - Hina and Sahil report to Eshan. - Gaurav reports to Zoya. - The Head is Qadir in Marketing department. Question: Who is the direct manager of Eshan?

Hierarchical Tree Construction
Draw a tree: place the Head at root. Connect direct reports according to clues.
Assign departments/roles after structure is stable.
Final tree edges (manager → report):
- Qadir → Eshan
- Qadir → Zoya
- Eshan → Hina
- Eshan → Sahil
- Zoya → Gaurav
Verification:
- All reporting relations satisfied.
- Unique direct manager per non-root node.
- Department/role association consistent with headship.

tree, hierarchy, manager, medium, organizational

Question 2

Study the following path and answer the question: A person starts from point X and walks 12 km North. He then turns left and walks 5 km. He then turns left and walks 8 km. He then turns right and walks 3 km. He then turns right and walks 4 km. Question: What is the shortest distance between the start point and the end point?

Direction Sense Strategy
Step 1: Track position on coordinate grid (East = +x, North = +y)
Start at (0,0) facing North
Step 1: Move +12 in y-direction → position updates
Step 2: Move -5 in x-direction
Step 3: Move -8 in y-direction
Step 4: Move +3 in x-direction
Step 5: Move +4 in y-direction → position updates

Final Position: (-2, 8)
Final Facing Direction: North

Answer to question: 8.2

direction, distance, displacement, medium, ssc, upsc

Question 3

Seven boxes of different colors are stacked on 7 different floors (Floor 7 is top, Floor 1 is bottom). Each box belongs to a different city and contains a different item. Clues: 1. The box on the top floor (7th floor) is White in color. 2. The box on the bottom floor (1st floor) is from Mumbai. 3. There are exactly 1 boxes between the Black box and the Brown box. 4. The box from Delhi is kept immediately below the box containing the Bottle. 5. The Green box is kept on an even-numbered floor but not on the 2nd floor. 6. The box containing Book is not kept on the topmost or bottommost floor. Question: How many boxes are kept between the Green and Blue boxes?

Multi-attribute Box Puzzle Strategy
Create a 7x4 table with Floors (7 top to 1 bottom) as rows.
Apply definite clues first (top floor color, bottom floor city).
Use spacing and adjacency clues to fix relative positions.
Use even/odd constraints to narrow down possibilities.

Final deduced arrangement (Top to Bottom):
Floor | Color | City | Item
--- | --- | --- | ---
7 | White | Hyderabad | Pen
6 | Brown | Kolkata | Laptop
5 | Red | Delhi | Bottle
4 | Black | Bengaluru | Book
3 | Pink | Chennai | Watch
2 | Green | Pune | Phone
1 | Blue | Mumbai | Charger

box-puzzle, multi-attribute, stacking, hard, cat, banking

Question 4

Five talks are scheduled on distinct days of a week (Mon–Sun). Use the clues: - Uma's talk is earlier than Sahil's. - Zoya's talk is neither first nor last. - Xavier's talk is before Eshan's. Question: Who gives the talk on Saturday?

Sequential Timeline
Order days as Monday→Sunday. Map constraints: 'earlier than', 'before', 'neither first nor last'.
Valid schedule: Tuesday:Uma, Wednesday:Xavier, Thursday:Zoya, Saturday:Eshan, Sunday:Sahil
Use inequalities to form partial orders and then linearize.
Verification:
- Uma's talk is earlier than Sahil's.
- Zoya's talk is neither first nor last.
- Xavier's talk is before Eshan's.

sequential, time, days, easy, before-after

Question 5

Nine distinct persons are arranged in a 3x3 matrix; each cell has exactly one person with a unique color. - The center cell is occupied by Gaurav who likes Orange. - Kaira sits opposite Bhavya on the grid edges. - Sahil is at a corner and does not like White. - Fatima is adjacent to Sahil. Question: In a 3x3 grid (rows and columns numbered 1 to 3), who occupies the cell at row 2, column 2?

Matrix/Spreadsheet Strategy
Label the grid with coordinates (r,c). Use definite placement clues (center, corners, opposites, adjacency) first.
Convert verbal relations to coordinate constraints and eliminate inconsistent options.
A consistent placement is:
C1 | C2 | C3
--- | --- | ---
Mira/Green | Cyrus/Yellow | Nihal/Blue
Kaira/Purple | Gaurav/Orange | Bhavya/White
Jatin/Pink | Fatima/Brown | Sahil/Black
Verification:
- Center, opposite, and corner constraints satisfied.
- Adjacency satisfied by orthogonal neighbors.
- Each person/color used exactly once.

matrix, 3x3, adjacency, opposite, hard, olympiad

Question 6

Six people are divided into two project groups of three each. Each person has a distinct primary skill (Frontend, Backend, Data, DevOps, QA, Design). Use the clues: - Rhea works with Xavier but not with Bhavya. - The DevOps person is in the same group as the Data person. - Uma is not in the same group as the Design person. - The Backend person is not with Vihaan. Question: Vihaan belongs to which project group?

Grouping Strategy
Represent two groups: Project A and Project B. Apply co-membership and exclusion conditions.
Correct grouping:
- Project A: Rhea, Vihaan, Xavier
- Project B: Bhavya, Uma, Yash
Verification:
- Co-working constraints satisfied.
- Role-based co-locations respected.
- Exclusions enforced without conflicts.

grouping, classification, medium, teams, co-membership

Question 7

Nine distinct persons are arranged in a 3x3 matrix; each cell has exactly one person with a unique color. - The center cell is occupied by Hina who likes White. - Gaurav sits opposite Yash on the grid edges. - Zoya is at a corner and does not like Brown. - Gaurav is adjacent to Bhavya. Question: In a 3x3 grid (rows and columns numbered 1 to 3), who occupies the cell at row 3, column 2?

Matrix/Spreadsheet Strategy
Label the grid with coordinates (r,c). Use definite placement clues (center, corners, opposites, adjacency) first.
Convert verbal relations to coordinate constraints and eliminate inconsistent options.
A consistent placement is:
C1 | C2 | C3
--- | --- | ---
Eshan/Black | Diya/Yellow | Zoya/Red
Gaurav/Pink | Hina/White | Yash/Brown
Bhavya/Purple | Tara/Orange | Qadir/Green
Verification:
- Center, opposite, and corner constraints satisfied.
- Adjacency satisfied by orthogonal neighbors.
- Each person/color used exactly once.

matrix, 3x3, adjacency, opposite, hard, olympiad

Question 8

Seven persons sit in a row facing north. Use the conditions: - Yash sits at the leftmost end. - Diya sits at the rightmost end. - If Yash sits to the left of Kaira, then Vihaan must be at an extreme end. - If Priya is adjacent to Eshan, then Tara does not sit at position 4. - Diya sits third from the left. Question: Who sits at position 4 from the left?

If-Then Conditional Strategy
Start with fixed endpoints and fixed position (third from left).
The first conditional is true and is consistent with the setup.
The second conditional helps constrain the positions of D, E, and F, leading to a unique solution.
Validated arrangement: Position 1: Yash; Position 2: Kaira; Position 3: Vihaan; Position 4: Priya; Position 5: Eshan; Position 6: Tara; Position 7: Diya
Efficiency tip: Prefer constraints that fix absolute positions early; defer conditional branches until necessary.
Verification:
- Leftmost and rightmost fixed.
- Third-from-left fixed.
- Conditionals do not contradict final layout.

linear, conditional, if-then, hard, branching

Question 9

Five talks are scheduled on distinct days of a week (Mon–Sun). Use the clues: - Nihal's talk is earlier than Bhavya's. - Fatima's talk is neither first nor last. - Qadir's talk is before Wafa's. Question: Who gives the talk on Saturday?

Sequential Timeline
Order days as Monday→Sunday. Map constraints: 'earlier than', 'before', 'neither first nor last'.
Valid schedule: Monday:Nihal, Tuesday:Qadir, Wednesday:Fatima, Thursday:Wafa, Saturday:Bhavya
Use inequalities to form partial orders and then linearize.
Verification:
- Nihal's talk is earlier than Bhavya's.
- Fatima's talk is neither first nor last.
- Qadir's talk is before Wafa's.

sequential, time, days, easy, before-after

Question 10

Seven boxes of different colors are stacked on 7 different floors (Floor 7 is top, Floor 1 is bottom). Each box belongs to a different city and contains a different item. Clues: 1. The box on the top floor (7th floor) is Red in color. 2. The box on the bottom floor (1st floor) is from Bengaluru. 3. There are exactly 1 boxes between the Black box and the Pink box. 4. The Black box is kept immediately above the box from Mumbai. 5. The Blue box is kept on an even-numbered floor but not on the 2nd floor. 6. The box containing Laptop is not kept on the topmost or bottommost floor. Question: What item does the Green box contain?

Multi-attribute Box Puzzle Strategy
Create a 7x4 table with Floors (7 top to 1 bottom) as rows.
Apply definite clues first (top floor color, bottom floor city).
Use spacing and adjacency clues to fix relative positions.
Use even/odd constraints to narrow down possibilities.

Final deduced arrangement (Top to Bottom):
Floor | Color | City | Item
--- | --- | --- | ---
7 | Red | Delhi | Laptop
6 | Pink | Kolkata | Watch
5 | Orange | Pune | Charger
4 | Black | Chennai | Pen
3 | Green | Mumbai | Bottle
2 | Blue | Hyderabad | Phone
1 | Yellow | Bengaluru | Book

box-puzzle, multi-attribute, stacking, hard, cat, banking

Question 11

Six tasks T1–T6 have distinct priorities from 1 (highest) to 6 (lowest). Use the clues: - T6 has higher priority than T4. - T2 is the least urgent. - T1's priority is between T6 and T5. Question: Which task has the second-highest priority (just below the highest)?

Symbolic Reasoning with Inequalities
Priority chain (lower number = higher priority): T6(prio=1) > T1(prio=2) > T4(prio=3) > T5(prio=4) > T3(prio=5) > T2(prio=6)
From clues, derive inequalities and place tasks accordingly.
Verification:
- T6 has higher priority than T4.
- T2 is the least urgent.
- T1's priority is between T6 and T5.

sequential, priority, inequalities, medium, chain

Question 12

Eight persons sit around a square table facing the center; four at corners and four at middle of sides. How many middle-seated persons are there between Diya and Ira clockwise starting from Diya?

Square Seating Strategy
Label positions in clockwise order as C1, M1, C2, M2, C3, M3, C4, M4. Corners are even-indexed if starting at C1=0.
Traverse clockwise from X to Y and count middle positions encountered.
One valid order (clockwise): Ira -> Omar -> Mira -> Bhavya -> Eshan -> Gaurav -> Diya -> Cyrus
Verification:
- Corners and middles alternate.
- Counting excludes the starting and ending persons.
- Computed count matches traversal.

rectangular, square-table, corners, middles, medium

Question 13

Six employees with distinct departments and roles form a reporting hierarchy. Use the clues to build the tree and answer: - Eshan and Xavier report to Jatin. - Diya and Zoya report to Eshan. - Sahil reports to Xavier. - The Head is Jatin in Sales department. Question: Who is the direct manager of Zoya?

Hierarchical Tree Construction
Draw a tree: place the Head at root. Connect direct reports according to clues.
Assign departments/roles after structure is stable.
Final tree edges (manager → report):
- Jatin → Eshan
- Jatin → Xavier
- Eshan → Diya
- Eshan → Zoya
- Xavier → Sahil
Verification:
- All reporting relations satisfied.
- Unique direct manager per non-root node.
- Department/role association consistent with headship.

tree, hierarchy, manager, medium, organizational

Question 14

Eight persons sit around a square table facing the center; four at corners and four at middle of sides. How many middle-seated persons are there between Rhea and Zoya clockwise starting from Rhea?

Square Seating Strategy
Label positions in clockwise order as C1, M1, C2, M2, C3, M3, C4, M4. Corners are even-indexed if starting at C1=0.
Traverse clockwise from X to Y and count middle positions encountered.
One valid order (clockwise): Gaurav -> Zoya -> Rhea -> Laksh -> Tara -> Eshan -> Wafa -> Diya
Verification:
- Corners and middles alternate.
- Counting excludes the starting and ending persons.
- Computed count matches traversal.

rectangular, square-table, corners, middles, medium

Question 15

Eight persons sit around a square table facing the center; four at corners and four at middle of sides. How many middle-seated persons are there between Cyrus and Hina clockwise starting from Cyrus?

Square Seating Strategy
Label positions in clockwise order as C1, M1, C2, M2, C3, M3, C4, M4. Corners are even-indexed if starting at C1=0.
Traverse clockwise from X to Y and count middle positions encountered.
One valid order (clockwise): Mira -> Aarav -> Laksh -> Xavier -> Uma -> Diya -> Hina -> Cyrus
Verification:
- Corners and middles alternate.
- Counting excludes the starting and ending persons.
- Computed count matches traversal.

rectangular, square-table, corners, middles, medium

Question 16

Seven persons sit in a row facing north. Use the conditions: - Gaurav sits at the leftmost end. - Omar sits at the rightmost end. - If Gaurav sits to the left of Ira, then Priya must be at an extreme end. - If Diya is adjacent to Yash, then Fatima does not sit at position 4. - Omar sits third from the left. Question: Who sits at position 4 from the left?

If-Then Conditional Strategy
Start with fixed endpoints and fixed position (third from left).
The first conditional is true and is consistent with the setup.
The second conditional helps constrain the positions of D, E, and F, leading to a unique solution.
Validated arrangement: Position 1: Gaurav; Position 2: Ira; Position 3: Priya; Position 4: Diya; Position 5: Yash; Position 6: Fatima; Position 7: Omar
Efficiency tip: Prefer constraints that fix absolute positions early; defer conditional branches until necessary.
Verification:
- Leftmost and rightmost fixed.
- Third-from-left fixed.
- Conditionals do not contradict final layout.

linear, conditional, if-then, hard, branching

Question 17

Eight people sit in two rows of four each. Row-1 faces south and Row-2 faces north. Opposite seats align by index. - Nihal sits opposite Xavier. - Wafa sits second from one end. - Bhavya sits at an extreme end. - The person opposite Kaira is not at an extreme end. Question: Who sits directly opposite Xavier?

Table Method: Row-1 (top, South-facing) and Row-2 (bottom, North-facing) are parallel.
Fixed: Nihal opposite Xavier. Use the end constraints on Bhavya and the non-end constraint for the person opposite Kaira.
One valid arrangement:
Row-1 (South, L→R): Nihal, Wafa, Fatima, Hina
Row-2 (North, L→R): Xavier, Rhea, Bhavya, Kaira
Verification:
- Nihal sits opposite Xavier.
- Wafa sits second from one end.
- Bhavya sits at an extreme end.
- The person opposite Kaira is not at an extreme end.

double-row, facing, opposites, easy, ssc

Question 18

Six people sit in a row facing North. Conditions: - Vihaan sits at the extreme right end (Position 6). - There are three people sitting between Rhea and Omar. - Qadir sits third to the right of Omar. - Neither Ira nor Wafa sits at any extreme end. Question: Who is sitting at the immediate right of Qadir?

Ambiguity Strategy: Proving Non-Unique Solution
Step 1: Fix D (P6). Use the 'three between' clue (Clue 2) to determine the positions of F (P5) and B (P1).
Step 2: Use E's position (Clue 3) to fix E (P4).
The arrangement is fixed at: B, P2, P3, E, F, D.
Step 3: The remaining people are A and C for positions P2 and P3. Clue 4 prevents them from being at the ends, leaving two cases:
- Case 1: Omar, Ira, Wafa, Qadir, Rhea, Vihaan
- Case 2: Omar, Wafa, Ira, Qadir, Rhea, Vihaan
The person immediately right of E is F in both valid cases, so the answer is uniquely determined.

linear, ambiguity, cannot-be-determined, gmat, cat

Question 19

Eight persons sit around a square table facing the center; four at corners and four at middle of sides. How many middle-seated persons are there between Kaira and Priya clockwise starting from Kaira?

Square Seating Strategy
Label positions in clockwise order as C1, M1, C2, M2, C3, M3, C4, M4. Corners are even-indexed if starting at C1=0.
Traverse clockwise from X to Y and count middle positions encountered.
One valid order (clockwise): Aarav -> Kaira -> Yash -> Nihal -> Priya -> Rhea -> Zoya -> Wafa
Verification:
- Corners and middles alternate.
- Counting excludes the starting and ending persons.
- Computed count matches traversal.

rectangular, square-table, corners, middles, medium

Question 20

Six persons have distinct preferences across Brand, Sport, and Vehicle. Using the clues, determine the complete mapping and answer: - Tara does not prefer Zeta or Volleyball. - The one who prefers Beta drives Train. - Jatin plays Football, and the one who drives Cycle prefers Kappa. - Neither Cyrus nor Laksh prefers Eta. - The Cricket player does not drive Van. - If someone prefers Alpha, then they do not play Athletics. Question: Who plays Tennis?

CAT/GMAT-Style Multi-Parameter Table
Create a 6x4 table (Person x Brand x Sport x Vehicle).
Apply constraints in layers: negative exclusions first, then direct mappings, then conditional implications.
- Tara does not prefer Zeta or Volleyball.
- The one who prefers Beta drives Train.
- Jatin plays Football, and the one who drives Cycle prefers Kappa.
- Neither Cyrus nor Laksh prefers Eta.
- The Cricket player does not drive Van.
- If someone prefers Alpha, then they do not play Athletics.
Continue elimination until each row has a unique triplet.
Verified final mapping:
Person | Brand | Sport | Vehicle
--- | --- | --- | ---
Tara | Beta | Cricket | Ship
Eshan | Zeta | Athletics | Cycle
Jatin | Eta | Volleyball | Van
Cyrus | Alpha | Tennis | Train
Laksh | Delta | Football | Car
Vihaan | Kappa | Chess | Metro
Efficiency tip: Track constraints per attribute as sets; propagate implications ('If A then not B').
Verification:
- Each attribute used exactly once across persons.
- All conditional and negative clues hold.
- No contradictions; unique solution obtained.

multi-parameter, conditional, hard, cat, gmat, table

Data Arrangement - Expert Level: comparative arrangement EXPERT

What you'll learn in this worksheet:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20