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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

✅ Correct Option: 3

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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