P, Q, R, S, T, U and V are sitting around a circular table facing the center but not necessarily in the same order. S is not a neighbor of Q and V. P is a neighbor of Q and R. U, who is second to the right of S, is the neighbor of T and V. Which of the following must be true?
(A) V is not seated next to Q.
(B) T is sitting third to the left of Q.
(C) R is sitting third to the right of V.
(D) R and S are not neighbors.
Choose the correct answer from the options given below:
P, Q, R, S, T, U and V are sitting around a circular table facing the center but not necessarily in the same order. S is not a neighbor of Q and V. P is a neighbor of Q and R. U, who is second to the right of S, is the neighbor of T and V. Which of the following must be true?
(A) V is not seated next to Q.
(B) T is sitting third to the left of Q.
(C) R is sitting third to the right of V.
(D) R and S are not neighbors.
Choose the correct answer from the options given below:
Solution
Given constraints:
- S is not a neighbor of Q and V
- P is a neighbor of Q and R
- U is second to the right of S, and U is neighbor of T and V
Starting with U being second to the right of S. Let's place S at position 1.
Then U is at position 3 (second to the right in circular seating).
U is neighbor of T and V, so T and V occupy positions 2 and 4.
Since S (position 1) is not a neighbor of V, and V must be at position 2 or 4:
- S's neighbors are positions 2 and 7
- V cannot be at position 2
- Therefore, V is at position 4 and T is at position 2
Current arrangement:
- Position 1: S
- Position 2: T
- Position 3: U
- Position 4: V
Remaining people: P, Q, R for positions 5, 6, 7
Since S is not a neighbor of Q, and S's neighbors are positions 2 and 7:
- Q cannot be at position 7
- Q must be at position 5 or 6
P is neighbor of both Q and R, meaning P sits between them.
If Q is at position 5:
- P must be neighbor of Q → P at position 6 (position 4 is V)
- P must be neighbor of R → R at position 7 (position 5 is Q)
Final arrangement:
- Position 1: S, Position 2: T, Position 3: U, Position 4: V
- Position 5: Q, Position 6: P, Position 7: R
Checking each statement:
(A) V is not seated next to Q
- V (position 4) and Q (position 5) are neighbors
- FALSE
(B) T is sitting third to the left of Q
- Q (position 5) → left: 4, 3, 2 → T is at position 2
- TRUE
(C) R is sitting third to the right of V
- V (position 4) → right: 5, 6, 7 → R is at position 7
- TRUE
(D) R and S are not neighbors
- R (position 7) and S (position 1) are neighbors in circular arrangement
- FALSE
Only (B) and (C) are true.
Therefore, the correct answer is Option 3: (B) and (C) only.
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