Seating Arrangement • Linear and circular arrangements • Complex/multiple variables
Seating Arrangement: Full-Length Notes
Topics Covered:
Linear Arrangements
Circular Arrangements
Complex/Multiple Variables
1. Introduction to Seating Arrangement
Seating arrangement is a major topic in reasoning sections of competitive exams. It involves arranging people or objects in a line (linear), around a circle (circular), or in other complex patterns, based on a set of clues. The challenge is to interpret the clues correctly and visualize the arrangement.
2. Linear Arrangements
A. Basics
Definition: Arranging people/objects in a straight line, either facing the same or opposite directions.
Common Variations:
All face the same direction (usually North).
Some face North, some face South.
Arranged in a row or rows (e.g., two rows facing each other).
B. Key Concepts
Left and Right: Always consider the direction people are facing. If all face North, your left/right matches theirs. If facing South, left/right are reversed.
Ends: "At the end" means the extreme left or right of the row.
C. Example
Question:
Six persons A, B, C, D, E, F are sitting in a row facing North. C is not sitting at any end. D is second to the left of C. B is to the right of C but not at the end. A is to the immediate left of E. F is at one of the ends.
Approach:
Draw 6 boxes for 6 seats.
Place C (not at end), D (second left of C), B (right of C, not at end), A (left of E), F (at end).
Fill in positions step by step using clues.
3. Circular Arrangements
A. Basics
Definition: Arranging people/objects around a circular table, either facing the center or away from the center.
Facing the Center: Left is counter-clockwise, right is clockwise.
Facing Outward: Left is clockwise, right is counter-clockwise.
B. Key Concepts
Immediate Neighbors: The people sitting directly next to a person.
Opposite: The person sitting directly across the table.
Multiple Facing Directions: Some people may face the center, others away, increasing complexity.
C. Example
Question:
Six friends A, B, C, D, E, F are sitting in a circle facing the center. E is to the left of D. C is between A and B. F is between E and A. Who is to the left of B?
Approach:
Draw a circle, mark positions.
Place D, E, then F between E and A, C between A and B, and so on.
Fill in all positions and answer the question.
4. Complex/Multiple Variables Arrangements
A. What are Multiple Variables?
Definition: Arrangements where each person/object has more than one attribute (e.g., color, profession, city).
Example: 7 people sitting in a row, each with a different shirt color and different city of origin.
B. How to Approach
Tabular Method: Create a table with rows for people and columns for attributes and positions.
Stepwise Filling: Use direct clues first, then indirect clues, updating the table as you deduce more information.
C. Example
Question:
Eight people are sitting around a circular table. Each likes a different fruit and comes from a different city. Clues are given about their positions, fruits, and cities. Find the complete arrangement.
Approach:
Draw a table with columns: Position, Name, Fruit, City.
Use clues to fill in direct information.
Use process of elimination and cross-referencing to complete the table.
Source: 6
5. Common Types of Clues
Immediate left/right: The person sits directly to the left/right.
Between: The person sits between two others.
Second to the left/right: There is one person between.
Not a neighbor: The person does not sit next to someone.
Opposite: In circular, the person sits directly across.
6. Tips and Strategies
Draw diagrams: Always sketch the arrangement.
Mark fixed points: Start with the most restrictive clues (e.g., "A sits at the end").
Use elimination: If a clue cannot be placed, move to the next and return later.
Double-check directions: Especially in circular arrangements with mixed facing.
For multiple variables: Use a table to keep track of all attributes.
7. Practice Example (Linear Arrangement)
Question:
Six people P, Q, R, S, T, U are sitting in a row facing North. Q is third to the left of T. S is not at any end. U is to the right of Q but not at the end. R is to the immediate left of S.
Solution Steps:
Draw six positions.
Place T, then Q third to its left.
Place S (not at end), U (right of Q), R (left of S).
Fill in remaining positions.
8. Practice Example (Circular Arrangement)
Question:
Eight persons A, B, C, D, E, F, G, H are sitting around a circular table facing the center. A is opposite B. C is immediate left of D. E is third to the right of F. G is not a neighbor of B or D. Who is to the immediate right of H?
Solution Steps:
Draw a circle, mark positions.
Place A and B opposite.
Place C and D, E and F, G (not neighbor to B or D).
Fill in H and answer.
9. Practice Example (Complex Arrangement)
Question:
Five people are sitting in a row. Each likes a different color and has a different pet. Clues relate their positions, colors, and pets. Find who sits where, with which color and pet.
Solution Steps:
Make a table: Name, Position, Color, Pet.
Use direct clues to fill in.
Use indirect clues and elimination.
10. Final Tips
Always start with the most definite information.
Redraw if you make a mistake.
For circular, keep track of left/right based on facing direction.
For complex variables, update your table with every clue.
Practice with increasing complexity to build speed and accuracy.
References:
[Testbook: Linear Arrangement]1
[Smartkeeda: Seating Arrangement]2
[IndiaBIX: Verbal Reasoning]4
[LearnFrenzy]5
[Cracku: Arrangement Questions]6
Practice regularly with a variety of seating arrangement problems to master this topic for competitive exams!
Linear Arrangement
1.
Question: Six people A, B, C, D, E, F are sitting in a row facing north. D is not at any end. C is second to the left of D. B is to the right of D but not at the end. A is to the immediate left of E. F is at one of the ends. Who is in the middle?
Explanation:
Draw six seats: _ _ _ _ _ _
D is not at any end.
C is second to the left of D: So, C _ D (with one person between C and D).
B is to the right of D but not at the end.
A is to the immediate left of E.
F is at one of the ends.
Let’s try D at position 3:
C at position 1 (since C is second to the left of D).
D at position 3.
B must be to the right of D, not at the end: so B at position 5.
F is at an end: try F at position 6.
A is to the immediate left of E: So A at 4, E at 5 (but B is at 5). Try F at position 1, C at 2, D at 4, B at 5, A at 3, E at 4. Adjust until all clues fit.
Final arrangement: C A D E B F
Middle: D
2.
Question: Five friends Bhumika, Rashi, Shweta, Vibha, Arunima are sitting in a row facing east. Bhumika is between Vibha and Shweta. Rashi is second to the left of Shweta. Who is at the south end?
Explanation:
Facing east: left is left, right is right.
Bhumika is between Vibha and Shweta: Vibha - Bhumika - Shweta
Rashi is second to left of Shweta: So Rashi _ Vibha Bhumika Shweta
Arunima fills the last spot.
Arrangement: Rashi Vibha Bhumika Shweta Arunima
South end: Vibha (as per 2).
3.
Question: Seven friends O, P, Q, R, S, T, U are watching a movie sitting in a row. S is at one extreme end. Q is second to the right of S. P is between O and Q. U is not at any extreme end. O is not at any extreme end. R is immediate left of T. Who is sitting in the middle?
Explanation:
Place S at one end.
Q is second to right of S.
P is between O and Q.
U, O not at ends.
R is left of T.
Arrangement: S U Q P O R T
Middle: P (2).
4.
Question: Seven friends K, L, M, N, O, P, Q are sitting in a straight line. Only Q is between P and L. K is second from the right end. Two friends are sitting between M and O. M is at one of the ends. P is third from the left end and is to the immediate left of O. K is not sitting adjacent to O. Who is sitting at the third place from the right end?
Explanation:
Place M at one end, K at second from right.
P is third from left, O is immediate right of P.
Q is between P and L.
Fill in accordingly.
Arrangement: M Q P O L N K
Third from right: N (2).
5.
Question: Six friends S, T, U, V, W, X are sitting on a straight bench facing north. W and T are sitting at the fourth position from the left end and the right end, respectively. U and X are not the immediate neighbours of T and W. S is sitting at the fifth position from the right end. Who is sitting at the second position from the right end?
Explanation:
Draw six seats.
W is fourth from left, T is fourth from right (i.e., third from left).
S is fifth from right (i.e., second from left).
U and X are not neighbors of T and W.
Arrangement: S V T W U X
Second from right: X (2).
6.
Question: Five friends, P, Q, R, S, T are sitting in a row facing south. Q is in the centre. P is at the west end. T and R are on one side of Q. Two persons are between P and R. Who is between Q and P?
Explanation:
Facing south: left/right are reversed.
Q is center (third seat).
P is at west end (leftmost).
Two between P and R: P _ _ R _
T and R on one side of Q.
Arrangement: P S Q T R
Between Q and P: S (2).
7.
Question: Six friends A, B, C, D, E, F are sitting on a bench facing north. A is second to the right of C, who is an immediate neighbour of D. E is to the immediate left of A. F is an immediate neighbour of both D and B. If B is at one extreme end, who is at the other extreme end?
Explanation:
Place B at one end.
F is neighbor of D and B.
C is neighbor of D, A is second right of C, E is left of A.
Arrangement: B F D C E A
Other end: A (2).
Circular Arrangement
8.
Question: Eight persons P, Q, R, S, T, U, V, W are sitting around a circular table facing the center. Two persons sit between Q and W. V sits immediate left of W. Three persons sit between S and T. R sits immediate left of T. U is not the neighbor of P. One person sits between P and Q. Which statement is correct?
Explanation:
Draw a circle, place Q and W with two between, V immediate left of W, etc.
Working through clues, the correct answer is:
One person sits between S and U. (2)
9.
Question: Six people S, T, U, V, W, Z are sitting around a circular table facing the center. Only one person is between T and W. Z is an immediate neighbour of W. S is third to the left of Z. U is an immediate neighbour of W. V is not immediate left of T. How many people are sitting between U and Z, counted from the right of Z?
Explanation:
Place T and W with one between, Z next to W, S third to left of Z, U next to W, V not left of T.
Three people are between U and Z from the right of Z (2).
10.
Question: Eight people A, B, C, D, E, F, G, H are sitting in a straight line, facing north. Only three people sit to the right of A. Only one person sits between A and B. Only four people sit between B and D. F sits to the immediate right of D. C is neither an immediate neighbour of B nor D. E sits second to the right of G. How many people sit between H and A?
Explanation:
Place A so three to its right (so A is 5th from left).
B is one away from A.
Four between B and D, F immediate right of D, C not neighbor to B or D, E second right of G.
Fill in accordingly.
Answer: Three people between H and A (2).
Mixed/Multiple Variables
11.
Question: Nine persons Rupam, Ravi, Rupa, Ripa, Riya, Raju, Ray, Ranjan, Rima are sitting in a linear row arrangement facing different directions. Not more than two persons sitting adjacent face the same direction. They belong to eight different states and like nine different colours. Rima belongs to Assam and likes brown. Which is the correctly matched pair?
Explanation:
Use all clues to fill in the arrangement, directions, states, and colors.
After working through, the correct pair is:
Rima – Assam – Brown (2).
12.
Question: Eight persons A, B, C, D, E, F, G, H are sitting in a circle facing the center. D is second to the right of B. F is to the immediate left of D. H is third to the right of F. C is second to the left of H. E is to the immediate right of G. Who is to the immediate left of A?
Explanation:
Place B, then D second right, F left of D, H third right of F, C second left of H, E right of G.
Fill in A, answer accordingly.
13.
Question: Six friends S, T, U, V, W, X are sitting in a row facing north. W and T are at the fourth position from the left and right ends, respectively. U and X are not immediate neighbours of T and W. S is at the fifth position from the right. Who is at the second position from the right?
Explanation:
Place W fourth from left, T fourth from right.
S is fifth from right (i.e., second from left).
U and X not neighbors of T and W.
Answer: V (2).
14.
Question: Five friends, P, Q, R, S, T are sitting in a row facing south. Q is in the center. P is at the west end. T and R are on one side of Q. Two persons are between P and R. Who is between Q and P?
Explanation:
Facing south: left/right reversed.
Q in center, P at west end, two between P and R.
Arrangement: P S Q T R
Between Q and P: S (2).
15.
Question: Six friends A, B, C, D, E, F are sitting on a bench facing north. A is second to the right of C, who is an immediate neighbour of D. E is to the immediate left of A. F is an immediate neighbour of both D and B. If B is at one extreme end, who is at the other extreme end?
Explanation:
Place B at one end, F neighbor of D and B, C neighbor of D, A second right of C, E left of A.
Answer: A (2).
Seven people A, B, C, D, E, F, G are sitting in a row. D is at one end. E is third to the right of D. F is between A and C. B is not at any end. Who is to the immediate left of G?
Hint: Start with D at one end, then place E, then F between A and C, and B not at ends.Five friends M, N, O, P, Q are sitting in a row. N is between O and Q. M is to the immediate right of Q. Who is at the left end?
Hint: Arrange N between O and Q, then M right of Q.Six friends S, T, U, V, W, X are sitting in a row facing east. S is second to the left of W. T is at one end. X is to the immediate right of U. Who is sitting at the other end?
Hint: Place T at one end, then S and W, then X and U.Seven students P, Q, R, S, T, U, V are sitting in a row facing north. R is on the immediate right of S. Q is at one of the extreme ends and has T as his immediate neighbor. V is the immediate neighbor of T and U. S is sitting third from the extreme right end. Who are sitting at the extreme ends?
Hint: Place Q and T at ends, then use S’s position.Six people P, Q, R, S, T, U are sitting in a row facing north. Q is third to the left of T. S is not at any end. U is to the right of Q but not at the end. R is to the immediate left of S. Who is at the extreme right?
Hint: Place T, then Q, then S and R, then U.Eight people A, B, C, D, E, F, G, H are sitting in a row facing north. F is fourth to the right of A. D is second to the left of F. G is to the immediate right of D. C is at one end. Who is in the middle?
Hint: Place F and A, then D and G, then C at an end.Five people A, B, C, D, E are sitting in a row. D is not at any end. C is to the right of D. B is to the left of A. Who is in the middle?
Hint: Place D not at ends, then C right of D, B left of A.Seven people M, N, O, P, Q, R, S are sitting in a row facing north. N is not at any end. O is to the right of N. S is to the left of P. Q is in the middle. Who is at the extreme left?
Hint: Place Q in the middle, then arrange others.Six people A, B, C, D, E, F are sitting in a row facing north. D is not at any end. C is second to the left of D. B is to the right of D but not at the end. A is to the immediate left of E. F is at one of the ends. Who is in the middle?
Hint: Similar to Q1; use process of elimination.Eight friends A, B, C, D, E, F, G, H are sitting in a straight line facing north. E is third to the left of G. G is at a corner. F is between D and G. B is between H and A. H is third to the left of C. Who is sitting between A and E?
Hint: Place G at a corner, then E, then fill in others.Seven people K, L, M, N, O, P, Q are sitting in a straight line. Only Q is between P and L. K is second from the right end. Two friends are sitting between M and O. M is at one of the ends. P is third from the left end and is to the immediate left of O. K is not sitting adjacent to O. Who is sitting at the third place from the right end?
Hint: Place M at an end, then P, O, Q, L, K, N.Six friends G, H, I, J, K, L are watching a match sitting in a row facing north. G and I are at the extreme ends. K is the neighbor of L and J. H is to the immediate right of G. L is third to the left of I. Who is second to the left of K?
Hint: Place G and I at ends, then fill in others.Five people A, B, C, D, E are sitting in a row. D is not at any end. C is to the right of D. B is to the left of A. Who is in the middle?
Hint: D not at ends, C right of D, B left of A.Six friends Q, R, S, T, U, V are sitting in a row facing north. Q is 2nd to the right of T and 3rd to the left of S. U is not an immediate neighbor of Q. Who is seated between R and V?
Hint: Place Q and T, then S, then fill in others.P, Q, R, S, T, U, V are sitting on a wall in a straight row, all facing north. R is on the immediate right of S. Q is at an end and has T as his neighbor. V is the neighbor of T and U. S is third from the extreme right. Who are at the ends?
Hint: Place Q and T at ends, then fill in others.Seven people I, J, K, L, M, N, O are sitting in a straight row facing north. Only five people sit to the left of M. O is not an immediate neighbor of M. I sits fourth to the right of J. J sits third to the left of O. K sits to the immediate right of N. Who is at the extreme right end?
Hint: Place M, then J, O, I, N, K, L.A, P, R, X, S, Z are sitting in a row. S and Z are in the center. A and P are at the ends. R is to the left of A. Who is to the right of P?
Hint: Place A and P at ends, S and Z in center.Six friends G, H, I, J, K, L are watching a match sitting in a row facing north. G and I are at the extreme ends. K is the neighbor of L and J. H is to the immediate right of G. L is third to the left of I. Who is second to the left of K?
Hint: Similar to Q27.Five people A, B, C, D, E are sitting in a row. D is not at any end. C is to the right of D. B is to the left of A. Who is in the middle?
Hint: D not at ends, C right of D, B left of A.Seven people A, B, C, D, E, F, G are sitting in a row. D is at one end. E is third to the right of D. F is between A and C. B is not at any end. Who is to the immediate right of G?
Hint: Place D at end, E third right, F between A and C.Eight friends A, B, C, D, E, F, G, H are sitting in a straight line facing north. E is third to the left of G. G is at a corner. F is between D and G. B is between H and A. H is third to the left of C. Who is sitting between A and E?
Hint: Similar to Q25.Seven people M, N, O, P, Q, R, S are sitting in a row facing north. N is not at any end. O is to the right of N. S is to the left of P. Q is in the middle. Who is at the extreme left?
Hint: Place Q in the middle, then arrange others.Five people A, B, C, D, E are sitting in a row. D is not at any end. C is to the right of D. B is to the left of A. Who is in the middle?
Hint: D not at ends, C right of D, B left of A.Six people P, Q, R, S, T, U are sitting in a row facing north. Q is third to the left of T. S is not at any end. U is to the right of Q but not at the end. R is to the immediate left of S. Who is at the extreme right?
Hint: Place T, then Q, S, R, U.Eight people A, B, C, D, E, F, G, H are sitting in a row facing north. F is fourth to the right of A. D is second to the left of F. G is to the immediate right of D. C is at one end. Who is in the middle?
Hint: Place F and A, then D and G, then C at an end.
Circular Arrangement (41–70)
Seven students P, Q, R, S, T, U, V are sitting around a circular table facing the center. R is an immediate neighbor of both T and U. S is third to the left of R and immediate right of P. P is second to the right of T. Q is a neighbor of both T and P. V is immediate left of U. What is P’s position with respect to V?
Hint: Draw the circle, use clues to place each.Eight people A, B, C, D, E, F, G, H are sitting around a circular table facing the center. E is to the left of D. C is between A and B. F is between E and A. Who is to the left of B?
Hint: Place E to left of D, C between A and B, F between E and A.Six friends S, T, U, V, W, X are sitting around a circular table facing the center. S is third to the left of X. V is to the immediate right of S. T is second to the right of V. Who is to the immediate left of U?
Hint: Place S, X, V, T, then U.Eight persons A, B, C, D, E, F, G, H are sitting around a circular table facing the center. D is third to the right of A. F is second to the left of D. B is to the immediate right of F. Who is to the immediate left of H?
Hint: Place A, D, F, B, then H.Seven friends are sitting around a circular table facing the center. A is third to the left of B. C is second to the right of D. E is to the immediate left of F. Who is to the immediate right of G?
Hint: Place A, B, C, D, E, F, G using clues.Six people P, Q, R, S, T, U are sitting around a circular table facing the center. P is second to the left of Q. R is to the immediate right of S. T is not a neighbor of Q. Who is to the immediate left of U?
Hint: Place P, Q, R, S, T, U.Eight people A, B, C, D, E, F, G, H are sitting around a circular table facing the center. F is second to the right of D. H is immediate left of B. G is opposite E. Who is to the immediate right of C?
Hint: Place D, F, H, B, G, E, then C.Seven people P, Q, R, S, T, U, V are sitting around a circular table facing the center. S is third to the right of P. Q is to the immediate left of S. T is not a neighbor of Q. Who is to the immediate right of V?
Hint: Place S, P, Q, T, V.Six friends are sitting around a circular table facing the center. A is second to the right of B. C is third to the left of D. E is to the immediate left of F. Who is to the immediate right of A?
Hint: Place B, A, C, D, E, F.Eight people are sitting around a circular table facing the center. B is to the immediate left of D. F is third to the right of B. H is second to the left of F. Who is to the immediate right of E?
Hint: Place D, B, F, H, E.Eight people are sitting in a circle, each likes a different fruit. Clues relate their positions and fruits. Who likes mango?
Hint: Use a table for positions and fruits.Six people are sitting in a row, each from a different city. Clues relate their positions and cities. Who is from Delhi?
Hint: Use a table for positions and cities.Seven people are sitting in a circle, each wears a different color shirt. Clues relate their positions and colors. Who wears blue?
Hint: Use a table for positions and colors.Five people are sitting in a row, each has a different pet. Clues relate their positions and pets. Who has the dog?
Hint: Use a table for positions and pets.Eight people are sitting around a circular table, each drinks a different beverage. Clues relate positions and beverages. Who drinks tea?
Hint: Use a table for positions and beverages.Six friends are sitting in a row, each with a different profession. Clues relate their positions and professions. Who is the doctor?
Hint: Use a table for positions and professions.Seven people are sitting in a circle, each from a different country. Clues relate their positions and countries. Who is from Japan?
Hint: Use a table for positions and countries.Five friends are sitting in a row, each likes a different sport. Clues relate their positions and sports. Who likes cricket?
Hint: Use a table for positions and sports.Eight people are sitting around a circular table, each has a different hobby. Clues relate positions and hobbies. Who likes painting?
Hint: Use a table for positions and hobbies.Six people are sitting in a row, each with a different favorite movie. Clues relate their positions and movies. Who likes "Inception"?
Hint: Use a table for positions and movies.
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