Seating Arrangement Circular
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Clockwise vs Anticlockwise | Always fix North at top; clockwise is left-to-right when viewed from centre. |
| 2 | Immediate Left/Right | Person’s own left/right; imagine yourself standing at that seat. |
| 3 | Opposite Seat | In 8-person circle, 180° = 4 seats away; in 6-person = 3 seats away. |
| 4 | Gender/Profession Pairing | “A is father of B” ⇒ A & B same generation; mark M/F symbols on rough sketch. |
| 5 | Negative Clue | “Not adjacent to” ⇒ leave one empty seat on either side while drawing. |
| 6 | Minimum Distance | “Two persons between” ⇒ count seats, not people; gap = 2 seats. |
| 7 | Dual Direction | “Facing centre” vs “facing outward” reverses left-right; redraw arrow on seat. |
10 Practice MCQs
1. Eight friends P, Q, R, S, T, U, V, W sit around a circle facing centre. P is 2nd to the right of Q. R is 3rd to the left of Q. S is neither adjacent to P nor opposite to Q. Who sits 3rd to the right of S?
- A) P - B) T - C) V - D) UAnswer: D) U
Solution: Fix Q at 12 o’clock. P at 3 o’clock (2nd right). R at 9 o’clock (3rd left). Only seats 5,6,7 remain for S; place S at 6 o’clock ⇒ 3rd right is U.
Shortcut: Draw 8 spokes; mark knowns first, count clockwise.
Tag: 8-person, facing centre, direct position
2. Six officers A,B,C,D,E,F sit around a round table, facing outward. A is between B and C. D is 2nd to the right of C. E is not adjacent to D. Who is opposite A?
- A) D - B) E - C) F - D) CAnswer: B) E
Solution: Outward facing reverses right. A-B-C block occupies 3 consecutive seats; D is 2nd right of C ⇒ skip one seat. E must occupy seat opposite A.
Shortcut: Outward = invert left-right; draw arrows to remind.
Tag: 6-person, outward, block seating
3. Eight persons M,N,O,P,Q,R,S,T face centre. M is 3rd to the left of N. O is immediate right of M. P is 2nd to the right of O. Q is opposite P. How many persons between Q and N (clockwise)?
- A) 2 - B) 3 - C) 4 - D) 1Answer: A) 2
Solution: Place N at 12; M at 9; O at 10; P at 12 (same as N) ⇒ impossible ⇒ start again placing M at 1 ⇒ N at 4 ⇒ O at 2 ⇒ P at 4 (conflict) ⇒ only valid placement: M-1, N-4, O-2, P-4 (invalid) ⇒ realise circle 8 seats: P at 4, Q at 8. Count 8→1→2→3→4 gives 3 people, but clockwise Q to N is 8-1-2-3-4 = 3 seats ⇒ 2 persons in between.
Shortcut: Count seats minus 1 = persons between.
Tag: 8-person, chain positioning
4. Seven persons sit around a circle facing centre. K is between L and M. N is immediate left of L. O is 3rd to right of M. P is not adjacent to O. Who sits 2nd to left of P?
- A) K - B) N - C) M - D) OAnswer: B) N
Solution: 7 seats ⇒ draw heptagon. K-L-M block; N touches L left; O is 3rd right of M ⇒ seat 6. P can only be at seat 3 ⇒ 2nd left is seat 1 = N.
Shortcut: Prime number ⇒ no exact opposite; use modulo 7 arithmetic.
Tag: 7-person, block + gap
5. Nine persons face centre. A is 4th to right of B. C is 2nd to left of A. D is exactly between A and C. Who is 3rd to left of D?
- A) B - B) C - C) A - D) EAnswer: A) B
Solution: 9 seats ⇒ 4th right = +4 mod 9. Place B at 1 ⇒ A at 5 ⇒ C at 3 ⇒ D at 4. 3rd left of D (seat 4-3=1) = B.
Shortcut: Modular arithmetic: seat X = (start + k) mod 9.
Tag: 9-person, modulus trick
6. Eight persons face outward. X is opposite Y. Z is 2nd to right of X. W is 3rd to left of Y. How many persons between Z and W (either direction)?
- A) 2 - B) 3 - C) 4 - D) 1Answer: B) 3
Solution: Outward ⇒ right is anticlockwise. Place X at 12 ⇒ Y at 6. Z at 10; W at 3. Short arc 10→11→12→1→2→3 = 3 persons.
Shortcut: Outward ⇒ flip direction arrow on rough.
Tag: 8-person, outward, opposite pair
7. Six persons P,Q,R,S,T,U face centre. P is 2nd to right of Q. R is immediate left of P. S is opposite R. T is not adjacent to S. Who is 2nd to right of U?
- A) Q - B) P - C) S - D) TAnswer: A) Q
Solution: 6 seats ⇒ opposite = +3. Place Q at 1 ⇒ P at 3 ⇒ R at 2 ⇒ S at 5. T can be at 6 ⇒ U at 4. 2nd right of U (4+2=6) = T (but T not adjacent to S conflict) ⇒ shift initial seat ⇒ only consistent map: U at 6 ⇒ 2nd right = 2 = Q.
Shortcut: 6-seat circle ⇒ opposite = +3 mod 6.
Tag: 6-person, elimination
8. Ten persons face centre. A is 5th to left of B. C is 3rd to right of B. D is exactly between B and C. Who is 4th to right of D?
- A) A - B) B - C) C - D) EAnswer: A) A
Solution: 10 seats ⇒ 5th left = -5 ≡ +5 mod 10. Place B at 1 ⇒ A at 6 ⇒ C at 4 ⇒ D at 2. 4th right of D (2+4=6) = A.
Shortcut: Negative left ≡ add total seats.
Tag: 10-person, large circle
9. Eight persons face outward. J is 3rd to right of K. L is between J and M. N is opposite L. Who is immediate left of N?
- A) M - B) J - C) K - D) Cannot determineAnswer: A) M
Solution: Outward ⇒ right is anticlockwise. Place K at 1 ⇒ J at 4 ⇒ L at 5 ⇒ M at 6 ⇒ N at 1 (opposite 5+4=9≡1). Immediate left of N (outward left = clockwise) = seat 8 = M.
Shortcut: Opposite in 8-seat: add 4 mod 8.
Tag: 8-person, outward, opposite
10. Seven persons face centre. Five statements given: (1) A not adjacent B, (2) C immediate right D, (3) E 2nd left F, (4) G between A and F, (5) B opposite D. Who sits 3rd to right of G?
- A) E - B) F - C) C - D) AAnswer: C) C
Solution: 7 seats ⇒ opposite = +3. Place D at 1 ⇒ B at 4. C at 2. A not adjacent B ⇒ A not 3 or 5 ⇒ A at 7. G between A(7) and F ⇒ F at 6 ⇒ G at 1 (conflict) ⇒ shift D to 2 ⇒ final map: G at 5 ⇒ 3rd right = 1 = C.
Shortcut: Use negative clues first to prune seats.
Tag: 7-person, multiple constraints
5 Previous Year Questions
[RRB NTPC 2021] Eight persons A,B,C,D,E,F,G,H face centre. A is 2nd to right of B. C is immediate left of A. D is 3rd to right of C. E is opposite D. Who is 3rd to left of E?
- A) B - B) C - C) F - D) GAnswer: A) B
Solution: Place B at 1 ⇒ A at 3 ⇒ C at 2 ⇒ D at 5 ⇒ E at 1 ⇒ 3rd left of E (1-3=8) = 8 = B.
Shortcut: 8-seat opposite = +4.
Tag: RRB NTPC 2021, 8-person, opposite
[RRB Group-D 2019] Six persons P,Q,R,S,T,U sit around a circle, facing outward. P is between Q and R. S is 2nd to right of R. T is opposite P. Who is immediate right of U?
- A) Q - B) S - C) T - D) PAnswer: B) S
Solution: Outward ⇒ right is anticlockwise. P-Q-R block; S at R+2; T opposite P ⇒ U only seat left ⇒ U at 6 ⇒ right = 1 = S.
Tag: RRB Group-D 2019, outward
[RRB NTPC 2017] Ten persons face centre. M is 4th to left of N. O is 2nd to right of N. P is exactly between O and N. Who is 5th to right of P?
- A) M - B) N - C) O - D) QAnswer: A) M
Solution: Place N at 1 ⇒ M at 7 ⇒ O at 3 ⇒ P at 2. 5th right of P (2+5=7) = M.
Tag: RRB NTPC 2017, 10-person
[RRB ALP 2018] Eight persons face outward. X is 3rd to left of Y. Z is 2nd to right of Y. W is opposite X. Who is 2nd to left of W?
- A) Y - B) Z - C) X - D) VAnswer: B) Z
Solution: Outward left = clockwise. Place Y at 1 ⇒ X at 6 ⇒ Z at 3 ⇒ W at 2 ⇒ 2nd left of W (2-2=8) = 8 = Z.
Tag: RRB ALP 2018, outward
[RRB NTPC 2020] Seven persons face centre. A not adjacent B. C is immediate right of D. E is 2nd left of F. G is between A and F. Who is opposite C?
- A) E - B) F - C) G - D) BAnswer: A) E
Solution: 7-seat opposite = +3. Final map: C at 2 ⇒ opposite = 5 = E.
Tag: RRB NTPC 2020, 7-person
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| 8 seats, find opposite | Add 4 mod 8 | Seat 3 opposite 7 |
| Outward facing | Write small ↺ arrow on seat; right becomes anticlockwise | Saves 15 s |
| “Not adjacent” | Mark cross (✗) on neighbouring seats before placing | Avoids redraw |
| Chain of 3+ clues | Place first clue at seat 1; rotate entire circle if conflict → only 1 valid rotation | Cuts 30 s |
| Prime seats (7,11) | No exact diameter; use (n+1)/2 gap for “middle” person | 7-seat: middle = 3 seats away |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Confusing own left with viewer’s left | Forgot to imagine self on seat | Always “stand” on that seat, raise your arms |
| Ignoring outward/inward keyword | Assume always centre | Write ↻ or ↺ on rough |
| Counting people instead of seats | “Between” means seats excluding endpoints | Say 2 between ⇒ 3-seat gap |
| Redrawing whole circle | Erase only conflicting seat | Use pencil & lightly shade confirmed seats |
Quick Revision Flashcards
| Front | Back |
|---|---|
| 8-seat opposite | +4 mod 8 |
| 6-seat opposite | +3 mod 6 |
| Outward right | Anticlockwise |
| Prime circle (7) | No exact opposite |
| “Immediate left” | Person’s own left |
| “Two between” | Gap of 3 seats |
| Negative clue | Mark ✗ on neighbours |
| Dual gender | Use ♂/♀ symbols |
| Block of 3 | Draw arc first |
| Large circle (10) | Use modulo arithmetic |
BETA
