Seating Arrangement – PGECET Study Notes
PGECET – Professional Graduate Engineering Common Entrance Test
Subject – Reasoning Ability
Topic – Seating Arrangement
1. Simple Explanation
Seating‑arrangement questions ask you to deduce the exact positions of people, objects or things in a row or a circle, based on a set of clues.
Think of each seat as a slot and each clue as a constraint on how those slots can be filled.
Typical elements you’ll encounter:
| Element | What It Means |
|---|---|
| Left/Right of | Seat immediately to the left/right |
| Opposite/Across from | Seat directly opposite in a circle or two‑row configuration |
| Between | Seat is exactly in the middle of two other seats |
| Seated at a fixed distance | A certain number of seats apart (e.g., 2 seats apart) |
| Adjacency | Sits next to |
| Order | “A is to the left of B” (not necessarily adjacent) |
Your job is to place everyone/objects in the correct order that satisfies all the clues simultaneously.
2. Key Points & Problem‑Solving Strategies
| # | Strategy | Why It Works |
|---|---|---|
| 1. Draw a Skeleton | Sketch the seats (row or circle) with labels (1,2,3… or A,B,C…). | Gives a physical framework to map clues. |
| 2. Identify Fixed Positions | Look for clues that pin a person/thing to a particular seat (e.g., “Mr. Patel sits in the 3rd seat”). | Removes uncertainty early. |
| 3. Use Relative Positioning | Translate “to the left/right of” into numerical differences. | Turns words into equations. |
| 4. Apply “Between” & “Opposite” | If X sits between Y & Z, Y and Z must be on opposite sides of X. | Helps narrow down placements. |
| 5. Leverage “Distance” Clues | “X sits 2 seats apart from Y” → | X |
| 6. Check for Contradictions | After each placement, verify all clues still hold. | Prevents later backtracking. |
| 7. Use Process of Elimination | If a seat can’t hold a particular person because of a conflict, rule it out. | Reduces options quickly. |
| 8. Keep a Record Sheet | Mark possibilities for each seat; update as you deduce. | Keeps track of deductions and prevents mistakes. |
| 9. Visualise with Tables | Especially useful when people have multiple attributes (e.g., gender, color). | Aids in spotting patterns. |
| 10. Double‑Check End Conditions | Make sure every clue is satisfied and every seat is filled. | Final verification step. |
3. Worked Example
Problem
Seven friends – A, B, C, D, E, F, G – are to sit in a straight row.
The following conditions apply:
- A sits to the left of C.
- B sits immediately to the right of F.
- D sits somewhere between B and E.
- G sits in the middle seat.
- C sits 2 seats to the right of D.
Determine the seating arrangement.
Step‑by‑Step Solution
| Step | What We Do | Why |
|---|---|---|
| 1. Draw the skeleton | Seats 1–7 labeled. | Visual structure. |
| 2. Fix G in the middle | Seat 4 = G. | Clue 4. |
| 3. Translate “A left of C” | A is somewhere left of C (no adjacency required). | Keeps relative relation. |
| 4. Translate “B right of F” | B = seat of F + 1. | Immediate adjacency. |
| 5. Translate “C 2 seats right of D” | Seat(C) = Seat(D) + 3. | Distance of 2 seats between them. |
| 6. Translate “D between B and E” | B < D < E or E < D < B (but B is immediately right of F). | D is somewhere between B & E. |
| 7. Try placing B & F | Since B is right of F, possibilities: (F=1,B=2), (F=2,B=3), (F=3,B=4), (F=4,B=5), (F=5,B=6), (F=6,B=7). | Enumerate. |
| 8. Check each possibility with G=4 | If B=4 → impossible (seat 4 already G). | Eliminate. |
| 9. Choose viable pair | Let’s try F=3, B=4 (but B=4 is G). No. | |
| > Try F=2, B=3. | Works. | |
| 10. Place B=3, F=2 | Seats: 1 ? , 2 = F, 3 = B, 4 = G. | Fill. |
| 11. Use “C 2 seats right of D” | D + 3 = C. | So possible pairs: (D=1,C=4) → C=4 is G → not allowed. |
(D=2,C=5) → D=F → not allowed.
(D=3,C=6) → D=B → not allowed.
(D