Seating Arrangement - Beginner-Intermediate Level: adjacent seating BEGINNER-INTERMEDIATE

Comprehensive race against clock worksheet covering 20 beginner-intermediate-level seating arrangement problems. Worksheet 8 of 30 emphasizes adjacent seating. Master circular seating, linear arrangement, row seating through detailed explanations. Difficulty: building on fundamentals with moderate challenges. Tailored for developing preparation.

πŸ“ Worksheet 8 of 30 β€’ 20 questions β€’ ⏱️ Estimated time: 20 minutes β€’ 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Seating Arrangement
Worksheet 8 of 30 (26% complete)

Question 1

Eight persons are sitting in two concentric circles. Inner circle: C, D, A and B (4 persons) facing the center. Outer circle: P, R, Q and S (4 persons) facing the center (2 positions in outer circle are empty). Each inner person directly faces one outer seat (4 outer seats occupied, 2 empty). P faces C. D sits immediately to the right of C in the inner circle. B sits opposite to D in the inner circle. R sits second to the right of Q in the outer circle. S sits immediately to the left of an empty seat in the outer circle. Who sits opposite to D in the inner circle?
Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) β€” all occupied.
Outer circle: 6 positions O1–O6 clockwise β€” 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- D sits immediately to the right of C (inner circle, facing center: right=CW)
β†’ C and D are adjacent. Possible: C=I1, D=I2 or C=I2, D=I3, etc.
- B sits opposite to D:
If D=I2, then B=I4. Then C=I1 (left of I2), A=I3 (remaining).
All constraints consistent βœ“.

Inner: I1=C, I2=D, I3=A, I4=B

Step 4: Place outer circle persons
- P faces C(I1) β†’ P at O1 βœ“
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- R second to right of Q (outer, facing center: right=CW, step 2):
Remaining outer persons: R,Q,S at O2, O4, O5.
R=O2 β†’ Q=O4, S=O5 βœ“
R=O4 β†’ Q=O6(empty) βœ—
R=O5 β†’ Q=O1=P βœ—
∴ Q=O2, R=O4, S=O5 βœ“
- S(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(R) β€” NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) βœ“.

Step 5: Answer the question
D is at I2. Opposite of I2 = I4 = B.

Final Arrangements:
Inner (CW): I1=C, I2=D, I3=A, I4=B
Outer (CW): O1=P, O2=Q, O3=empty, O4=R, O5=S, O6=empty

Verification:
βœ“ P faces C (I1↔O1)
βœ“ D immediately right of C (I2 is CW from I1)
βœ“ B opposite D (I4 opposite I2)
βœ“ R second right of Q (O4 = O2 + 2 CW)
βœ“ S(O5) immediately left of empty O6

Answer: B sits opposite to D.

Question 2

Six persons O, P, M, K, N and L sit around a circular table facing outward. P sits second to the left of O. M sits opposite to P. K sits immediately to the right of M. N sits opposite to O. Who sits immediately to the left of P?
Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix O at position 1.
- P sits second to the LEFT of O: left(outward)=CW, so P is 2 CW from O.
pos[P] = 3
- M sits opposite P (pos 3): pos 6
- K sits immediately to the RIGHT of M (pos 6):
right(outward)=anti-CW β†’ pos 5
- N sits opposite O (pos 1): pos 4
- Remaining L fills pos 2.

Final Arrangement (clockwise):
pos1:O β†’ pos2:L β†’ pos3:P β†’ pos4:N β†’ pos5:K β†’ pos6:M
(All facing outward β†—)

Find immediate left of P (pos 3):
Left (outward) = clockwise β†’ pos 4 = N

Verification:
βœ“ P second to left of O (CW direction)
βœ“ M opposite P
βœ“ K immediately right (anti-CW) of M
βœ“ N opposite O

Answer: N sits immediately to the left of P.

Question 3

Six persons U, Q, P, T, S and R are sitting in a row. Some are facing North and some are facing South. U sits third from the left end facing North. Q sits second to the right of U and faces opposite direction. P sits at the left extreme end facing South. T sits immediately to the left of Q facing North. R sits at the right extreme end. Who sits between P and U?
Solution Approach:

Step 1: Mark directions
↑ = North facing, ↓ = South facing

Step 2: Apply position-based conditions
- U sits third from the left end facing North (↑) β†’ Position 3
- P sits at the left extreme end facing South (↓) β†’ Position 1

Position: P(↓) _ U(↑) _ _ _

Step 3: Apply relative positioning
- Q sits second to the right of U (pos 3) β†’ Position 5
- Q faces opposite direction to U (North) β†’ Q faces South (↓)
- T sits immediately to the left of Q (pos 5) facing North (↑) β†’ Position 4

Position: P(↓) _ U(↑) T(↑) Q(↓) _

Step 4: Fill remaining positions
Remaining persons: S, R
Position 2 gets S, Position 6 gets R

Final Arrangement:
Pos: P(↓) S(↑) U(↑) T(↑) Q(↓) R(↑)

Verification:
βœ“ U at pos 3, facing North
βœ“ Q at pos 5 (second right of U), facing South (opposite of U)
βœ“ P at pos 1 (left extreme), facing South
βœ“ T at pos 4 (immediately left of Q), facing North

Person between P (pos 1) and U (pos 3): pos 2 = S

Answer: S sits between P and U.

Question 4

Eight persons C, H, D, F, G, B, E and A are sitting around a square table. Four persons sit at corners and four at the middle of sides, all facing the center. C sits at a corner. H sits second to the right of C. D sits at the middle of a side and is not adjacent to C. F sits opposite to C. G sits at a corner immediately to the right of D. B sits immediately to the left of H. E is not adjacent to F. How many persons sit between C and F when counted from the left of C?
Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) β†’ M1(2) β†’ C2(3) β†’ M2(4) β†’ C3(5) β†’ M3(6) β†’ C4(7) β†’ M4(8) β†’ back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7

Step 2: Place persons systematically
- C sits at a corner β†’ pos 1
- H sits second to the RIGHT of C: right(center-facing)=CW
2 CW from pos 1 β†’ pos 3 βœ“ (corner)
- F sits OPPOSITE C (pos 1) β†’ pos 5 βœ“
- D at midpoint, NOT adjacent to C(pos 1):
Adjacent to pos 1: pos 8 and pos 2
D β†’ pos 6 (midpoint, not adjacent) βœ“
- G sits at corner immediately to the RIGHT of D(pos 6):
1 CW from pos 6 β†’ pos 7 (corner) βœ“

Step 3: Remaining persons
Remaining: B, E, A
Fill remaining seats: pos2=B, pos8=E, pos4=A

Final Arrangement (clockwise):
pos1:C β†’ pos2:B β†’ pos3:H β†’ pos4:A β†’ pos5:F β†’ pos6:D β†’ pos7:G β†’ pos8:E

Step 4: Count from LEFT of C to F
Left = anti-clockwise direction from C(pos 1):
pos1(C) β†’ pos8(E) β†’ pos7(G) β†’ pos6(D) β†’ pos5(F)
Persons between (excluding C and F): pos8(E), pos7(G), pos6(D)
Count = 3 person(s)

Answer: Three person(s) sit between C and F.

Question 5

Two parallel rows of chairs. Row 1 has D, E, A, C and B facing South. Row 2 has Q, P, R, T and S facing North. Each person in one row faces exactly one person from the other row. A sits fourth from the left end of Row 1. Q faces A. D sits at an extreme end of Row 1. E sits second to the right of D. P sits second to the left of Q. R sits at an extreme end of Row 2. S is not adjacent to Q in Row 2. Who faces E?
Solution Approach:

Step 1: Draw the double row setup
Row 1 faces South (↓), Row 2 faces North (↑)
Person at position i in Row 1 faces person at position i in Row 2.

Position: 1 2 3 4 5
Row 1 (↓): _ _ _ _ _
Row 2 (↑): _ _ _ _ _

Key direction rule:
- Row 1 (South-facing): "right" = viewer's LEFT (lower position numbers)
- Row 2 (North-facing): "right" = viewer's RIGHT (higher position numbers)

Step 2: Place Row 1 persons
- A sits 4th from the left end of Row 1 β†’ Row 1, pos 4
- D sits at an extreme end: pos 1 or pos 5
- E sits second to the RIGHT of D (south-facing β†’ lower position):
pos[E] = pos[D] - 2
If D at pos 1 β†’ pos[E] = -1 (invalid βœ—)
If D at pos 5 β†’ pos[E] = 3 βœ“ (pos 3 is free)
∴ D at pos 5, E at pos 3 βœ“

Row 1: _ _ E A D
Remaining C,B at pos 1 and 2 (either order β€” pinned next).

Step 3: Place Row 2 persons
- Q faces A (pos 4) β†’ Q at Row 2, pos 4
- P sits second to the LEFT of Q (north-facing β†’ lower position):
pos[P] = pos[Q] - 2 = 2 β†’ P at Row 2 pos 2 βœ“
- R sits at extreme end of Row 2: pos 1 or pos 5
- S is NOT adjacent to Q (pos 4): adjacent = pos 3 and pos 5
So S β‰  pos 3 and S β‰  pos 5
Remaining positions for R,T,S: pos 1, pos 3, pos 5
S not at pos 3 or pos 5 β†’ S at pos 1
R at extreme β†’ pos 5 (since pos 1 is S) βœ“
T fills pos 3 βœ“

Row 2: S P T Q R

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): C/B C/B E A D
Row 2 (↑): S P T Q R

Find who faces E:
E is at Row 1, position 3.
Person at Row 2, position 3 = T

Answer: T faces E.

Question 6

Six persons Eshaan, Divya, Amit, Bina, Chetan and Falguni are sitting in a row facing North. Each has a different profession: Teacher, Doctor, Lawyer, Banker, Engineer and Architect. Eshaan is a Teacher and sits third from the left. The Doctor sits second from the left. Divya sits second to the right of the Doctor. The Engineer sits immediately to the right of Eshaan. Chetan is a Lawyer and is not adjacent to Eshaan. The Banker sits at the right extreme end. Falguni sits at an extreme end. Bina is not at an extreme end. What is the profession of Bina?
Solution Approach:

Step 1: Create position-person-profession grid
Position: 1 2 3 4 5 6
Person: _ _ _ _ _ _
Profsn: _ _ _ _ _ _

Step 2: Apply direct conditions
- Eshaan is Teacher, sits at position 3
- The Doctor sits second from the left β†’ position 2
(Which person is the Doctor? Must be Amit, the only one unassigned here β€” verified below.)
- Divya sits second to the right of the Doctor (pos 2): 2+2 = pos 4 β†’ Divya at position 4

Position: _ [Doctor] Eshaan Divya _ _
Profsn: _ Doctor Teacher _ _ _

Step 3: Apply adjacency and profession constraints
- The Engineer sits immediately to the RIGHT of Eshaan(pos 3) β†’ pos 4 = Divya
∴ Divya is the Engineer βœ“
- The Banker sits at right extreme β†’ position 6

Position: _ [Doctor] Eshaan Divya _ [law]
Profsn: _ Doctor Teacher Engineer _ Banker

Step 4: Identify the Engineer
Persons left for pos1,2,5,6: Amit, Bina, Chetan, Falguni
The Doctor is at pos2. Which person?
Not Eshaan(pos3), not Divya(pos4). Try each remaining:
Amit at pos2 β†’ Amit=Doctor βœ“ (no other constraint violated)

Position: _ Amit Eshaan Divya _ _
Profsn: _ Doctor Teacher Engineer _ _

Step 5: Place E, D, F
Remaining persons: Chetan,Bina,Falguni β†’ positions 1, 5, 6.
- Chetan is Lawyer and NOT adjacent to Eshaan(pos3): adjacent = pos2,pos4.
Chetan not at pos2(taken) or pos4(taken). Remaining: pos1, pos5, pos6. All satisfy adjacency βœ“.
- Falguni sits at an extreme end: pos1 or pos6.
- Bina is NOT at an extreme end: Bina not at pos1 or pos6 β†’ Bina at pos5.
- Falguni at extreme: pos1 or pos6.
- Banker at pos6. If F=Banker, F at pos6. Otherwise F at pos1.
After placing D=pos5: remaining Chetan and Falguni at pos1 and pos6.
F at extreme β†’ F at pos1 or pos6 (both extreme).
Who is the Banker (pos6)? Not Eshaan(doc), Divya(ban), Amit(eng), Bina(remaining profsn), Chetan(tea).
Banker must be Falguni. So Falguni at pos6 = Banker. Chetan at pos1 = Lawyer βœ“ (not adjacent to Eshaan).

Final Arrangement:
Position: 1 2 3 4 5 6
Person: Chetan Amit Eshaan Divya Bina Falguni
Profsn: Lawyer Doctor Teacher Engineer ? Banker

Step 6: Determine Bina's profession
Professions assigned: Teacher(Eshaan), Engineer(Divya), Doctor(Amit), Lawyer(Chetan), Banker(Falguni)
Remaining profession: Architect β†’ Bina is the Architect

Verification:
βœ“ Eshaan=Doctor at pos 3
βœ“ Engineer(Amit) at pos 2
βœ“ Divya second right of Engineer (pos 4)
βœ“ Banker(Divya) immediately right of Eshaan
βœ“ Chetan=Teacher at pos 1 (not adjacent to Eshaan)
βœ“ Lawyer(Falguni) at right extreme (pos 6)
βœ“ Falguni at extreme end (pos 6)
βœ“ Bina not at extreme end (pos 5)

Answer: Bina's profession is Architect.

Question 7

Eight persons are sitting in two concentric circles. Inner circle: A, C, B and D (4 persons) facing the center. Outer circle: S, Q, R and P (4 persons) facing the center (2 positions in outer circle are empty). Each inner person directly faces one outer seat (4 outer seats occupied, 2 empty). S faces A. C sits immediately to the right of A in the inner circle. D sits opposite to C in the inner circle. Q sits second to the right of R in the outer circle. P sits immediately to the left of an empty seat in the outer circle. Who sits opposite to C in the inner circle?
Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) β€” all occupied.
Outer circle: 6 positions O1–O6 clockwise β€” 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- C sits immediately to the right of A (inner circle, facing center: right=CW)
β†’ A and C are adjacent. Possible: A=I1, C=I2 or A=I2, C=I3, etc.
- D sits opposite to C:
If C=I2, then D=I4. Then A=I1 (left of I2), B=I3 (remaining).
All constraints consistent βœ“.

Inner: I1=A, I2=C, I3=B, I4=D

Step 4: Place outer circle persons
- S faces A(I1) β†’ S at O1 βœ“
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- Q second to right of R (outer, facing center: right=CW, step 2):
Remaining outer persons: Q,R,P at O2, O4, O5.
R=O2 β†’ Q=O4, S=O5 βœ“
R=O4 β†’ Q=O6(empty) βœ—
R=O5 β†’ Q=O1=P βœ—
∴ R=O2, Q=O4, P=O5 βœ“
- P(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(Q) β€” NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) βœ“.

Step 5: Answer the question
C is at I2. Opposite of I2 = I4 = D.

Final Arrangements:
Inner (CW): I1=A, I2=C, I3=B, I4=D
Outer (CW): O1=S, O2=R, O3=empty, O4=Q, O5=P, O6=empty

Verification:
βœ“ S faces A (I1↔O1)
βœ“ C immediately right of A (I2 is CW from I1)
βœ“ D opposite C (I4 opposite I2)
βœ“ Q second right of R (O4 = O2 + 2 CW)
βœ“ P(O5) immediately left of empty O6

Answer: D sits opposite to C.

Question 8

Six persons Farhan, Esha, Aman, Charu, Deepak and Bhanu are sitting around a hexagonal table, one at each corner, all facing the center. Farhan sits opposite to Esha. Aman sits second to the right of Farhan. Deepak sits second to the right of Bhanu. Charu is not adjacent to Farhan. What is the position of Charu with respect to Aman?
Solution Approach:

Step 1: Draw hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.

Step 2: Place definite positions
- Fix Farhan at H1 (pos 1).
- Farhan opposite Esha: opp(pos1) = pos4 β†’ Esha at H4

Step 3: Apply relative positioning
- Aman second to the right of Farhan(pos1):
CW 2: pos1β†’pos2β†’pos3
β†’ Aman at H3

- Deepak second to the right of Bhanu:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Farhan=1, Esha=4, Aman=3,
remaining seats: [2, 5, 6].
Deepak = 2 CW from Bhanu: pos5 is 2 clockwise [solver-verified].
β†’ Bhanu at pos6, Deepak at pos2

Step 4: Apply constraint
- Charu not adjacent to Farhan(pos1):
Adjacent to pos1: pos6 and pos2
β†’ Charu at pos5 (not adjacent) βœ“

Final Arrangement (clockwise):
H1:Farhan β†’ H2:Deepak β†’ H3:Aman β†’ H4:Esha β†’ H5:Charu β†’ H6:Bhanu

Step 5: Find Charu's position relative to Aman
Aman at pos3, Charu at pos5.
pos5 is 2 clockwise from pos3.

Verification:
βœ“ Farhan opposite Esha
βœ“ Aman second to right of Farhan
βœ“ Deepak second to right of Bhanu
βœ“ Charu not adjacent to Farhan

Answer: Charu sits to the second to the right of Aman.

Question 9

Six persons E, A, C, B, D and F are sitting around a circular table facing the center. E sits second to the left of A. C sits opposite to E. B sits immediately to the right of C. F is not adjacent to B. Who sits opposite to A?
Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix E at position 1 (reference point)
- E is second to the LEFT of A β†’ A is 2 clockwise from E
pos[A] = 3
- C sits OPPOSITE E (pos 1) β†’ pos 4
- B sits immediately to the right of C (pos 4) β†’ pos 5

Step 3: Resolve remaining positions
Remaining persons: F, D β†’ remaining seats: [2, 6]
F is NOT adjacent to B (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore F β†’ pos 2, and D β†’ pos 6.

Final Arrangement (clockwise):
pos1:E β†’ pos2:F β†’ pos3:A β†’ pos4:C β†’ pos5:B β†’ pos6:D
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

A is at pos 3 β†’ opposite = pos 6 = D

Answer: D sits opposite to A.

Question 10

Five persons V, Z, X, W and Y are to be seated in a row facing North. The following conditions apply: - If V sits at an extreme end, then X must sit immediately next to Z - If V does not sit at an extreme end, then W must sit at an extreme end - Y cannot sit next to V - Z sits second from the left Which of the following must be FALSE?
Solution Approach:

Step 1: Apply the fixed condition
- Z sits second from the left β†’ Z at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with Z at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
β€’ V Z X W Y
β€’ V Z X Y W
β€’ X Z Y W V
β€’ W Z V X Y
β€’ Y Z V X W
β€’ Y Z X V W
(shown up to 6)

Step 3: Test each MCQ option

- "Y sits at position 5": βœ“ Possible in at least one valid arrangement
- "V sits at position 2": βœ— NEVER possible β†’ must be FALSE
- "V sits at position 5": βœ“ Possible in at least one valid arrangement
- "V sits at position 4": βœ“ Possible in at least one valid arrangement

Step 4: Conclusion
"V sits at position 2" is impossible in ALL 7 valid arrangement(s) β€” it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "V sits at position 2" must be FALSE.

Question 11

Six persons C, F, E, B, A and D are sitting around a circular table facing the center. C sits second to the left of F. E sits opposite to C. B sits immediately to the right of E. D is not adjacent to B. Who sits opposite to F?
Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix C at position 1 (reference point)
- C is second to the LEFT of F β†’ F is 2 clockwise from C
pos[F] = 3
- E sits OPPOSITE C (pos 1) β†’ pos 4
- B sits immediately to the right of E (pos 4) β†’ pos 5

Step 3: Resolve remaining positions
Remaining persons: D, A β†’ remaining seats: [2, 6]
D is NOT adjacent to B (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore D β†’ pos 2, and A β†’ pos 6.

Final Arrangement (clockwise):
pos1:C β†’ pos2:D β†’ pos3:F β†’ pos4:E β†’ pos5:B β†’ pos6:A
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

F is at pos 3 β†’ opposite = pos 6 = A

Answer: A sits opposite to F.

Question 12

Five persons Z, V, Y, X and W are to be seated in a row facing North. The following conditions apply: - If Z sits at an extreme end, then Y must sit immediately next to V - If Z does not sit at an extreme end, then X must sit at an extreme end - W cannot sit next to Z - V sits second from the left Which of the following must be FALSE?
Solution Approach:

Step 1: Apply the fixed condition
- V sits second from the left β†’ V at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with V at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
β€’ Z V Y X W
β€’ Z V Y W X
β€’ Y V W X Z
β€’ X V Z Y W
β€’ W V Z Y X
β€’ W V Y Z X
(shown up to 6)

Step 3: Test each MCQ option

- "Y sits at position 4": βœ“ Possible in at least one valid arrangement
- "Z sits at position 5": βœ“ Possible in at least one valid arrangement
- "W sits at position 5": βœ“ Possible in at least one valid arrangement
- "Z sits at position 2": βœ— NEVER possible β†’ must be FALSE

Step 4: Conclusion
"Z sits at position 2" is impossible in ALL 7 valid arrangement(s) β€” it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "Z sits at position 2" must be FALSE.

Question 13

Five persons E, D, B, A and C are sitting in a row facing North. E sits at one of the extreme ends. D sits second to the right of E. B sits immediately to the left of D. A is not at any extreme end. Who sits at the other extreme end?
Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- E sits at one extreme end β†’ Place E at position 1
- D sits second to the right of E β†’ D at position 3
- B sits immediately to the left of D β†’ B at position 2

Position: E B D _ _

Step 3: Apply constraint conditions
- A is not at any extreme end β†’ remaining positions are 4 and 5; A cannot be at 5, so A at position 4
- Only C remains β†’ C at position 5

Final Arrangement (all facing North ↑):
Position: E B D A C

Verification:
βœ“ E at extreme end (pos 1)
βœ“ D second to the right of E (pos 3)
βœ“ B immediately to the left of D (pos 2)
βœ“ A not at extreme end (pos 4)

Answer: C sits at the other extreme end (position 5).

Question 14

Six persons U, R, S, P, T and Q are sitting in a row. Some are facing North and some are facing South. U sits third from the left end facing North. R sits second to the right of U and faces opposite direction. S sits at the left extreme end facing South. P sits immediately to the left of R facing North. Q sits at the right extreme end. Who sits between S and U?
Solution Approach:

Step 1: Mark directions
↑ = North facing, ↓ = South facing

Step 2: Apply position-based conditions
- U sits third from the left end facing North (↑) β†’ Position 3
- S sits at the left extreme end facing South (↓) β†’ Position 1

Position: S(↓) _ U(↑) _ _ _

Step 3: Apply relative positioning
- R sits second to the right of U (pos 3) β†’ Position 5
- R faces opposite direction to U (North) β†’ R faces South (↓)
- P sits immediately to the left of R (pos 5) facing North (↑) β†’ Position 4

Position: S(↓) _ U(↑) P(↑) R(↓) _

Step 4: Fill remaining positions
Remaining persons: T, Q
Position 2 gets T, Position 6 gets Q

Final Arrangement:
Pos: S(↓) T(↑) U(↑) P(↑) R(↓) Q(↑)

Verification:
βœ“ U at pos 3, facing North
βœ“ R at pos 5 (second right of U), facing South (opposite of U)
βœ“ S at pos 1 (left extreme), facing South
βœ“ P at pos 4 (immediately left of R), facing North

Person between S (pos 1) and U (pos 3): pos 2 = T

Answer: T sits between S and U.

Question 15

Eight persons S, M, N, R, P, T, Q and O are sitting around a circular table. Some face the center and some face outward. S faces the center. M faces outward and sits third to the right of S. N sits second to the left of S and faces the same direction as M. R faces the center and sits immediately to the right of N. T sits immediately to the right of S. O sits opposite S. Q is not adjacent to M. Who sits second to the right of R?
Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix S (faces center) at position 1 (reference point)
- M faces outward, sits third to the RIGHT of S:
S faces center β†’ right = clockwise
3 CW from pos 1 β†’ pos 4
N = pos 4 βœ“

Step 4: Apply relative positions
- N sits second to the LEFT of S (pos 1):
S faces center β†’ left = anti-clockwise
2 anti-CW from pos 1 β†’ pos 7
N faces same as M β†’ OUTWARD
- R faces center, sits immediately to the RIGHT of N (pos 7):
N faces outward β†’ right = anti-clockwise
1 anti-CW from pos 7 β†’ pos 6

Step 5: Fill remaining persons
- T immediately to the RIGHT of S(pos 1, center→CW): pos 2
- O opposite S(pos 1): pos 5
- Q not adjacent to M(pos 4): adj = pos 3 & 5
β†’ Q at pos 8, P at pos 3

Final Arrangement (clockwise):
pos1:S(ctr) | pos2:T(out) | pos3:P(ctr) | pos4:M(out) | pos5:O(out) | pos6:R(ctr) | pos7:N(out) | pos8:Q(ctr)

Find second to the right of R (pos 6, center-facing β†’ CW):
2 CW from pos 6: β†’ pos 8 = Q

Verification:
βœ“ M(outward) 3 left of S(center): 3 ACW from pos1 = pos4
βœ“ N 2nd left of S, same direction as M (outward)
βœ“ R(center) immediately right of N(outward, right=ACW)
βœ“ T immediately right (CW) of S
βœ“ O opposite S
βœ“ Q not adjacent to M

Answer: Q sits second to the right of R.

Question 16

Five persons D, B, E, C and A are sitting in a row facing North. D sits at one of the extreme ends. B sits second to the right of D. E sits immediately to the left of B. C is not at any extreme end. Who sits at the other extreme end?
Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- D sits at one extreme end β†’ Place D at position 1
- B sits second to the right of D β†’ B at position 3
- E sits immediately to the left of B β†’ E at position 2

Position: D E B _ _

Step 3: Apply constraint conditions
- C is not at any extreme end β†’ remaining positions are 4 and 5; C cannot be at 5, so C at position 4
- Only A remains β†’ A at position 5

Final Arrangement (all facing North ↑):
Position: D E B C A

Verification:
βœ“ D at extreme end (pos 1)
βœ“ B second to the right of D (pos 3)
βœ“ E immediately to the left of B (pos 2)
βœ“ C not at extreme end (pos 4)

Answer: A sits at the other extreme end (position 5).

Question 17

Six persons Divya, Chetan, Amit, Bina, Falguni and Eshaan are sitting in a row facing North. Each has a different profession: Lawyer, Architect, Engineer, Banker, Doctor and Teacher. Divya is a Lawyer and sits third from the left. The Architect sits second from the left. Chetan sits second to the right of the Architect. The Doctor sits immediately to the right of Divya. Falguni is a Engineer and is not adjacent to Divya. The Banker sits at the right extreme end. Eshaan sits at an extreme end. Bina is not at an extreme end. What is the profession of Bina?
Solution Approach:

Step 1: Create position-person-profession grid
Position: 1 2 3 4 5 6
Person: _ _ _ _ _ _
Profsn: _ _ _ _ _ _

Step 2: Apply direct conditions
- Divya is Lawyer, sits at position 3
- The Architect sits second from the left β†’ position 2
(Which person is the Architect? Must be Amit, the only one unassigned here β€” verified below.)
- Chetan sits second to the right of the Architect (pos 2): 2+2 = pos 4 β†’ Chetan at position 4

Position: _ [Architect] Divya Chetan _ _
Profsn: _ Architect Lawyer _ _ _

Step 3: Apply adjacency and profession constraints
- The Doctor sits immediately to the RIGHT of Divya(pos 3) β†’ pos 4 = Chetan
∴ Chetan is the Doctor βœ“
- The Banker sits at right extreme β†’ position 6

Position: _ [Architect] Divya Chetan _ [law]
Profsn: _ Architect Lawyer Doctor _ Banker

Step 4: Identify the Engineer
Persons left for pos1,2,5,6: Amit, Bina, Falguni, Eshaan
The Architect is at pos2. Which person?
Not Divya(pos3), not Chetan(pos4). Try each remaining:
Amit at pos2 β†’ Amit=Architect βœ“ (no other constraint violated)

Position: _ Amit Divya Chetan _ _
Profsn: _ Architect Lawyer Doctor _ _

Step 5: Place E, D, F
Remaining persons: Falguni,Bina,Eshaan β†’ positions 1, 5, 6.
- Falguni is Engineer and NOT adjacent to Divya(pos3): adjacent = pos2,pos4.
Falguni not at pos2(taken) or pos4(taken). Remaining: pos1, pos5, pos6. All satisfy adjacency βœ“.
- Eshaan sits at an extreme end: pos1 or pos6.
- Bina is NOT at an extreme end: Bina not at pos1 or pos6 β†’ Bina at pos5.
- Eshaan at extreme: pos1 or pos6.
- Banker at pos6. If F=Banker, F at pos6. Otherwise F at pos1.
After placing D=pos5: remaining Falguni and Eshaan at pos1 and pos6.
F at extreme β†’ F at pos1 or pos6 (both extreme).
Who is the Banker (pos6)? Not Divya(doc), Chetan(ban), Amit(eng), Bina(remaining profsn), Falguni(tea).
Banker must be Eshaan. So Eshaan at pos6 = Banker. Falguni at pos1 = Engineer βœ“ (not adjacent to Divya).

Final Arrangement:
Position: 1 2 3 4 5 6
Person: Falguni Amit Divya Chetan Bina Eshaan
Profsn: Engineer Architect Lawyer Doctor ? Banker

Step 6: Determine Bina's profession
Professions assigned: Lawyer(Divya), Doctor(Chetan), Architect(Amit), Engineer(Falguni), Banker(Eshaan)
Remaining profession: Teacher β†’ Bina is the Teacher

Verification:
βœ“ Divya=Doctor at pos 3
βœ“ Engineer(Amit) at pos 2
βœ“ Chetan second right of Engineer (pos 4)
βœ“ Banker(Chetan) immediately right of Divya
βœ“ Falguni=Teacher at pos 1 (not adjacent to Divya)
βœ“ Lawyer(Eshaan) at right extreme (pos 6)
βœ“ Eshaan at extreme end (pos 6)
βœ“ Bina not at extreme end (pos 5)

Answer: Bina's profession is Teacher.

Question 18

Five friends P, T, Q, R and S are sitting in a row facing South. P sits at the right extreme end. T sits second to the right of Q. S sits immediately to the right of Q (from viewer's perspective). R is not adjacent to P. Who sits at the left extreme end?
Solution Approach:

Step 1: Understanding facing South
When persons face South:
- Their right hand points West (viewer's LEFT) β€” "right" in the question = lower position number
- Viewer's "right" (higher position) = person's left side

Step 2: Set up diagram (viewer's perspective)
Position: 1(left) 2 3 4 5(right)

Step 3: Apply conditions
- P at the right extreme end β†’ Position 5
- T sits second to the right of Q:
South-facing right = viewer's left = lower position: pos[T] = pos[Q] - 2
Possible: Q=3β†’T=1, or Q=4β†’T=2
- S sits immediately to the right of Q (viewer's right = higher pos): pos[S] = pos[Q] + 1
If Q=3 β†’ S=4 βœ“ (pos 4 free)
If Q=4 β†’ S=5 = P βœ— (conflict)
∴ Q=3, T=1, S=4

Position: T _ Q S P

Step 4: Apply constraint
- R not adjacent to P (pos 5): R β‰  pos 4 (taken by S) β†’ R at pos 2 βœ“

Final Arrangement (all facing South ↓):
Position: T R Q S P

Verification:
βœ“ P at right extreme end (pos 5)
βœ“ T second to right of Q: pos[T](=1)-2 = 3 = pos[Q] (south-facing right=lower)
βœ“ S immediately right of Q (viewer right): pos 3+1 = 4
βœ“ R not adjacent to P (pos 2, not pos 4)

Answer: T sits at the left extreme end (position 1).

Question 19

Five persons C, E, D, B and A are sitting in a row facing North. C sits at one of the extreme ends. E sits second to the right of C. D sits immediately to the left of E. B is not at any extreme end. Who sits at the other extreme end?
Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- C sits at one extreme end β†’ Place C at position 1
- E sits second to the right of C β†’ E at position 3
- D sits immediately to the left of E β†’ D at position 2

Position: C D E _ _

Step 3: Apply constraint conditions
- B is not at any extreme end β†’ remaining positions are 4 and 5; B cannot be at 5, so B at position 4
- Only A remains β†’ A at position 5

Final Arrangement (all facing North ↑):
Position: C D E B A

Verification:
βœ“ C at extreme end (pos 1)
βœ“ E second to the right of C (pos 3)
βœ“ D immediately to the left of E (pos 2)
βœ“ B not at extreme end (pos 4)

Answer: A sits at the other extreme end (position 5).

Question 20

Five persons Z, W, X, V and Y are to be seated in a row facing North. The following conditions apply: - If Z sits at an extreme end, then X must sit immediately next to W - If Z does not sit at an extreme end, then V must sit at an extreme end - Y cannot sit next to Z - W sits second from the left Which of the following must be FALSE?
Solution Approach:

Step 1: Apply the fixed condition
- W sits second from the left β†’ W at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with W at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
β€’ Z W X V Y
β€’ Z W X Y V
β€’ X W Y V Z
β€’ V W Z X Y
β€’ Y W Z X V
β€’ Y W X Z V
(shown up to 6)

Step 3: Test each MCQ option

- "Y sits at position 3": βœ“ Possible in at least one valid arrangement
- "Z sits at position 4": βœ“ Possible in at least one valid arrangement
- "Z sits at position 2": βœ— NEVER possible β†’ must be FALSE
- "X sits at position 1": βœ“ Possible in at least one valid arrangement

Step 4: Conclusion
"Z sits at position 2" is impossible in ALL 7 valid arrangement(s) β€” it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "Z sits at position 2" must be FALSE.
Previous Worksheet Next Worksheet