Data Arrangement Worksheet 24 - Advanced Level (logical sorting) | 20 Questions

Question 1

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 Delhi. 3. There are exactly 1 boxes between the Blue box and the Black box. 4. The box from Delhi is kept immediately below the box containing the Book. 5. The Blue box is kept on an even-numbered floor but not on the 2nd floor. 6. The box containing Charger is not kept on the topmost or bottommost floor. Question: How many boxes are kept between the White and Red 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 | Red | Mumbai | Phone
6 | Pink | Chennai | Laptop
5 | Yellow | Hyderabad | Pen
4 | Black | Pune | Charger
3 | Green | Bengaluru | Bottle
2 | Blue | Kolkata | Book
1 | White | Delhi | Watch

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

Question 2

Five talks are scheduled on distinct days of a week (Mon–Sun). Use the clues: - Priya's talk is earlier than Eshan's. - Tara's talk is neither first nor last. - Mira's talk is before Fatima's. Question: Who gives the talk on Wednesday?

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

sequential, time, days, easy, before-after

Question 3

Five talks are scheduled on distinct days of a week (Mon–Sun). Use the clues: - Cyrus's talk is earlier than Rhea's. - Tara's talk is neither first nor last. - Ira's talk is before Diya's. Question: Who gives the talk on Tuesday?

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

sequential, time, days, easy, before-after

Question 4

Six tasks T1–T6 have distinct priorities from 1 (highest) to 6 (lowest). Use the clues: - T3 has higher priority than T1. - T2 is the least urgent. - T4's priority is between T3 and T5. Question: Which task has the second-highest priority (just below the highest)?

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

sequential, priority, inequalities, medium, chain

Question 5

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

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

sequential, time, days, easy, before-after

Question 6

Nine persons are to be seated in a single row of 9 seats; one seat is vacant. The final arrangement is consistent with the given constraints. Answer the question: - A total of 8 persons are seated in 9 seats, with exactly one seat vacant. - The number of persons to the left of the vacant seat is one more than the number of persons to its right. - The person next to Priya is a fixed person (clue to force uniqueness). Question: In a row of 9 seats with one seat vacant, what occupies the seat exactly between Priya and Yash?

Incomplete Information Strategy: Fixed Vacancy
The constraint on the vacant seat's relative position fixes it immediately.
Final arrangement (Seats 1-9): 1: Empty; 2: Rhea; 3: Diya; 4: Priya; 5: Gaurav; 6: Kaira; 7: Omar; 8: Xavier; 9: Yash
The calculation for the question is done on the fixed layout.
Verification:
- Seat configuration: 5 persons left, 3 persons right of Empty (P5).
- Final positions of X and Y verified.

incomplete, vacancy, hard, upsc, validation

Question 7

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 Fatima and Rhea clockwise starting from Fatima?

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): Sahil -> Fatima -> Omar -> Tara -> Laksh -> Priya -> Rhea -> Eshan
Verification:
- Corners and middles alternate.
- Counting excludes the starting and ending persons.
- Computed count matches traversal.

rectangular, square-table, corners, middles, medium

Question 8

Ten family members sit around a circular table facing the center. Using the following information: Family Relationships: • Grandfather is the father of Father and Uncle. • Aarav is the son of Father. • Diya is the niece of Father. • Bhavya is the sister of Cyrus. • Mother is the daughter-in-law of Grandmother. • Aunt is the wife of Uncle. Seating Arrangement: • Grandfather sits opposite to Grandmother. • Father sits second to the right of Grandfather. • Aarav sits adjacent to his mother. • Diya sits third to the left of Uncle. • Bhavya does not sit adjacent to Cyrus. Question: How is Diya related to Uncle?

Blood Relations + Circular Seating Strategy
Step 1: Draw the family tree from relationship clues:
Grandfather (M) + Grandmother (F)
├── Father (M) + Mother (F)
│ ├── Aarav (M)
│ ├── Bhavya (F)
│ └── Cyrus (M)
└── Uncle (M) + Aunt (F)
└── Diya (F)

Step 2: Apply seating clues to arrange 10 persons around a circle:
Clockwise arrangement: Grandfather -> Grandmother -> Father -> Mother -> Aarav -> Bhavya -> Cyrus -> Diya -> Uncle -> Aunt

Step 3: Verify all constraints:
✓ Grandfather is the father of Father and Uncle.
✓ Aarav is the son of Father.
✓ Diya is the niece of Father.
✓ Bhavya is the sister of Cyrus.
✓ Mother is the daughter-in-law of Grandmother.
✓ Aunt is the wife of Uncle.
✓ Grandfather sits opposite to Grandmother.
✓ Father sits second to the right of Grandfather.
✓ Aarav sits adjacent to his mother.
✓ Diya sits third to the left of Uncle.
✓ Bhavya does not sit adjacent to Cyrus.

blood-relations, circular, family-tree, hard, ssc, banking

Question 9

Five persons have distinct heights. Use the clues to determine their relative heights: - Uma is taller than Tara. - Rhea is shorter than Mira but taller than Cyrus. - Tara is not the tallest. Question: Who is the tallest among them?

Ordering by Comparative Statements
Heights ascending: Cyrus(157cm) < Rhea(161cm) < Mira(162cm) < Tara(167cm) < Uma(183cm)
Place by pairwise comparisons; confirm unique top and bottom.
Verification:
- Uma is taller than Tara.
- Rhea is shorter than Mira but taller than Cyrus.
- Tara is not the tallest.

ordering, size, heights, easy, comparatives

Question 10

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: - Hina works with Jatin but not with Omar. - The DevOps person is in the same group as the Data person. - Laksh is not in the same group as the Design person. - The Backend person is not with Wafa. Question: Uma 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: Hina, Jatin, Wafa
- Project B: Laksh, Omar, Uma
Verification:
- Co-working constraints satisfied.
- Role-based co-locations respected.
- Exclusions enforced without conflicts.

grouping, classification, medium, teams, co-membership

Question 11

Nine persons are to be seated in a single row of 9 seats; one seat is vacant. The final arrangement is consistent with the given constraints. Answer the question: - A total of 8 persons are seated in 9 seats, with exactly one seat vacant. - The number of persons to the left of the vacant seat is one more than the number of persons to its right. - The person next to Sahil is a fixed person (clue to force uniqueness). Question: In a row of 9 seats with one seat vacant, how many persons/seats are between Sahil and Mira?

Incomplete Information Strategy: Fixed Vacancy
The constraint on the vacant seat's relative position fixes it immediately.
Final arrangement (Seats 1-9): 1: Wafa; 2: Laksh; 3: Sahil; 4: Aarav; 5: Mira; 6: Kaira; 7: Tara; 8: Gaurav; 9: Empty
The calculation for the question is done on the fixed layout.
Verification:
- Seat configuration: 5 persons left, 3 persons right of Empty (P5).
- Final positions of X and Y verified.

incomplete, vacancy, hard, upsc, validation

Question 12

Five students attempted a test and received distinct ranks (1 best to 5 worst), took distinct times, and attempted distinct subjects. Use the clues: - The student ranked 1 finished earlier than the one who attempted English. - Jatin did not take 74 minutes and is not ranked 4. - The fastest finisher attempted History. - The one ranked 3 took more time than Gaurav. Question: Who secured Rank 1?

Multi-Parameter Optimization
Set up a table: Student x (Rank, Time, Subject). Use rank-time inequalities and subject anchors (fastest subject).
Student | Rank | Time(min) | Subject
--- | --- | --- | ---
Laksh | 1 | 77 | Geography
Sahil | 2 | 64 | English
Jatin | 3 | 74 | Science
Ira | 4 | 80 | History
Gaurav | 5 | 68 | Music
Integrate constraints across dimensions and validate uniqueness.
Verification:
- The student ranked 1 finished earlier than the one who attempted English.
- Jatin did not take 74 minutes and is not ranked 4.
- The fastest finisher attempted History.
- The one ranked 3 took more time than Gaurav.

integration, rank, time, subject, hard, olympiad

Question 13

Eight boxes are stacked on 8 different floors (Floor 8 is the top). Conditions: - Box White is kept on the topmost floor (8). - There are exactly four boxes between Box Yellow and Box Purple. - Box Pink is kept immediately below Box Purple. - Box Brown is kept on an odd-numbered floor, but not floor 1. - Box Black is not kept on an even-numbered floor. Question: How many boxes are placed between Box Brown and Box Pink?

Floor Puzzle Strategy: Vertical Stack
Floors are 8 (Top) to 1 (Bottom). Start with definite positions: Box A on F8.
Use the 'four boxes between' clue to fix positions of B and F.
Use the adjacent clue (Box G immediately below Box F) to fix the remaining positions.
The final arrangement (Floor: Box) is:
8: White; 7: Yellow; 6: Brown; 5: Green; 4: Orange; 3: Purple; 2: Pink; 1: Black
Verification: Box Brown is on F6 and Box Pink is on F2. The boxes between are on F5, F4, F3 (3 boxes).

categorical, stacking, floor-puzzle, banking, ssc

Question 14

Ten family members sit around a circular table facing the center. Using the following information: Family Relationships: • Grandfather is the father of Father and Uncle. • Aarav is the son of Father. • Diya is the niece of Father. • Bhavya is the sister of Cyrus. • Mother is the daughter-in-law of Grandmother. • Aunt is the wife of Uncle. Seating Arrangement: • Grandfather sits opposite to Grandmother. • Father sits second to the right of Grandfather. • Aarav sits adjacent to his mother. • Diya sits third to the left of Uncle. • Bhavya does not sit adjacent to Cyrus. Question: How is Bhavya related to Mother?

Blood Relations + Circular Seating Strategy
Step 1: Draw the family tree from relationship clues:
Grandfather (M) + Grandmother (F)
├── Father (M) + Mother (F)
│ ├── Aarav (M)
│ ├── Bhavya (F)
│ └── Cyrus (M)
└── Uncle (M) + Aunt (F)
└── Diya (F)

Step 2: Apply seating clues to arrange 10 persons around a circle:
Clockwise arrangement: Grandfather -> Grandmother -> Father -> Mother -> Aarav -> Bhavya -> Cyrus -> Diya -> Uncle -> Aunt

Step 3: Verify all constraints:
✓ Grandfather is the father of Father and Uncle.
✓ Aarav is the son of Father.
✓ Diya is the niece of Father.
✓ Bhavya is the sister of Cyrus.
✓ Mother is the daughter-in-law of Grandmother.
✓ Aunt is the wife of Uncle.
✓ Grandfather sits opposite to Grandmother.
✓ Father sits second to the right of Grandfather.
✓ Aarav sits adjacent to his mother.
✓ Diya sits third to the left of Uncle.
✓ Bhavya does not sit adjacent to Cyrus.

blood-relations, circular, family-tree, hard, ssc, banking

Question 15

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 Green in color. 2. The box on the bottom floor (1st floor) is from Mumbai. 3. There are exactly 2 boxes between the Pink box and the Black box. 4. The Purple box is kept immediately above the box from Kolkata. 5. The Pink box is kept on an even-numbered floor but not on the 2nd floor. 6. The box containing Phone is not kept on the topmost or bottommost floor. Question: The Black box belongs to which city?

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 | Green | Delhi | Bottle
6 | Red | Chennai | Pen
5 | Black | Hyderabad | Charger
4 | Purple | Pune | Phone
3 | White | Kolkata | Book
2 | Pink | Bengaluru | Watch
1 | Brown | Mumbai | Laptop

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

Question 16

Six persons have distinct preferences across Brand, Sport, and Vehicle. Using the clues, determine the complete mapping and answer: - Omar does not prefer Gamma or Tennis. - The one who prefers Iota drives Truck. - Yash plays Chess, and the one who drives Ship prefers Kappa. - Neither Fatima nor Eshan prefers Alpha. - The Table Tennis player does not drive Bus. - If someone prefers Theta, then they do not play Badminton. Question: Who plays Football?

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.
- Omar does not prefer Gamma or Tennis.
- The one who prefers Iota drives Truck.
- Yash plays Chess, and the one who drives Ship prefers Kappa.
- Neither Fatima nor Eshan prefers Alpha.
- The Table Tennis player does not drive Bus.
- If someone prefers Theta, then they do not play Badminton.
Continue elimination until each row has a unique triplet.
Verified final mapping:
Person | Brand | Sport | Vehicle
--- | --- | --- | ---
Omar | Iota | Table Tennis | Metro
Zoya | Gamma | Badminton | Ship
Yash | Alpha | Tennis | Bus
Fatima | Theta | Football | Truck
Eshan | Zeta | Chess | Car
Rhea | Kappa | Cricket | Cycle
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

Question 17

Five students attempted a test and received distinct ranks (1 best to 5 worst), took distinct times, and attempted distinct subjects. Use the clues: - The student ranked 1 finished earlier than the one who attempted Science. - Yash did not take 56 minutes and is not ranked 4. - The fastest finisher attempted Physics. - The one ranked 3 took more time than Rhea. Question: Who secured Rank 1?

Multi-Parameter Optimization
Set up a table: Student x (Rank, Time, Subject). Use rank-time inequalities and subject anchors (fastest subject).
Student | Rank | Time(min) | Subject
--- | --- | --- | ---
Aarav | 1 | 46 | Art
Bhavya | 2 | 34 | Science
Yash | 3 | 56 | Math
Fatima | 4 | 39 | Physics
Rhea | 5 | 71 | Chemistry
Integrate constraints across dimensions and validate uniqueness.
Verification:
- The student ranked 1 finished earlier than the one who attempted Science.
- Yash did not take 56 minutes and is not ranked 4.
- The fastest finisher attempted Physics.
- The one ranked 3 took more time than Rhea.

integration, rank, time, subject, hard, olympiad

Question 18

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

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: Fatima, Kaira, Nihal, Jatin, Wafa, Eshan
- Case 2: Fatima, Nihal, Kaira, Jatin, Wafa, Eshan
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

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 Xavier who likes Orange. - Eshan sits opposite Tara on the grid edges. - Vihaan is at a corner and does not like Blue. - Tara is adjacent to Xavier. Question: In a 3x3 grid (rows and columns numbered 1 to 3), who occupies the cell at row 3, column 1?

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
--- | --- | ---
Qadir/Purple | Tara/Blue | Vihaan/White
Sahil/Brown | Xavier/Orange | Uma/Black
Aarav/Green | Eshan/Pink | Priya/Red
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 20

Consider the following five database-like records with unique fields (ID, Name, City, Score). Using the clues, determine relationships and answer: - The record with ID 633 has a higher score than the record from Hyderabad. - Priya's score is not the lowest. - The person from Bengaluru has an ID greater than 633. Question: Which city corresponds to the highest score?

Relational Reasoning (DB-style)
Think in terms of unique-key constraints across fields (ID, Name, City, Score).
ID | Name | City | Score
--- | --- | --- | ---
184 | Ira | Chennai | 84
579 | Xavier | Hyderabad | 83
340 | Priya | Delhi | 79
367 | Omar | Bengaluru | 70
633 | Qadir | Mumbai | 85
Use comparative score clues and ID inequalities to identify maxima/minima.
Verification:
- The record with ID 633 has a higher score than the record from Hyderabad.
- Priya's score is not the lowest.
- The person from Bengaluru has an ID greater than 633.

database, records, constraints, hard, keys

Data Arrangement - Advanced Level: logical sorting ADVANCED

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