Analyzing Seating Arrangement Data Sufficiency

Understanding the Questions and Statements

The objective is to determine if the provided statements are sufficient to answer two specific questions about individuals seated around a circular table:

• Question 1: Who is sitting opposite to Q?
• Question 2: Who is sitting to the right of Q?

The given statements are:

• Statement 1: P and U are sitting on the left and right sides of T, respectively. This establishes a relative order: U is to T's left, and P is to T's right.
• Statement 2: P, Q, R, S, T, and U are sitting around a round table with six chairs. This defines the number of participants (6) and the arrangement type (circular).
• Statement 3: Q is NOT sitting on the immediate left side of R. This acts as a constraint, eliminating certain seating possibilities.

Testing Sufficiency of All Statements

To assess sufficiency, we combine all three statements and check if a unique arrangement or unique answers emerge. We assume standard conventions for round table problems where 'left' and 'right' are from the perspective of a person seated at the table, facing inwards.

From Statement 2, there are 6 seats. Let's number them 1 through 6 clockwise.

From Statement 1, the relative order U-T-P occurs sequentially counter-clockwise. If we place T at Seat 1, then U must be at Seat 6 (T's left) and P must be at Seat 2 (T's right). The arrangement is partially fixed:

Seat 1: T
Seat 2: P
Seat 3: ?
Seat 4: ?
Seat 5: ?
Seat 6: U

The remaining individuals Q, R, and S must occupy Seats 3, 4, and 5. We need to check permutations of Q, R, S against Statement 3 (Q is NOT on the immediate left of R).

Scenario A: Valid Arrangement

Consider the arrangement T-P-Q-S-R-U in clockwise order (Seats 1-6).

• Check Statement 3: R is at Seat 5. The seat to the immediate left of R (Seat 5) is Seat 4, which is occupied by S. Q is at Seat 3. Since S is to the left of R, not Q, this arrangement satisfies Statement 3 and is VALID.
• Analysis for Questions: In this arrangement (T P Q S R U):
  • Q is at Seat 3.
  • The seat opposite Q (Seat 3) is Seat 5, occupied by R.
  • The seat to the right of Q (Seat 3) is Seat 4, occupied by S.
• Potential Answers: Opposite Q = R; Right of Q = S.

Scenario B: Valid Arrangement

Consider the arrangement T-P-R-Q-S-U in clockwise order (Seats 1-6).

• Check Statement 3: R is at Seat 3. The seat to the immediate left of R (Seat 3) is Seat 2, occupied by P. Q is at Seat 4. Since P is to the left of R, not Q, this arrangement satisfies Statement 3 and is VALID.
• Analysis for Questions: In this arrangement (T P R Q S U):
  • Q is at Seat 4.
  • The seat opposite Q (Seat 4) is Seat 1, occupied by T.
  • The seat to the right of Q (Seat 4) is Seat 5, occupied by S.
• Potential Answers: Opposite Q = T; Right of Q = S.

Conclusion on Data Sufficiency

We have identified two distinct, valid seating arrangements (Scenario A and Scenario B) that satisfy all three statements.

• In Scenario A, the person opposite Q is R.
• In Scenario B, the person opposite Q is T.

Because the identity of the person opposite Q differs between these valid scenarios, we cannot definitively answer Question 1. Similarly, while 'Right of Q' is S in both scenarios shown, the existence of multiple possibilities for 'Opposite Q' means the overall data is insufficient.

Therefore, the questions cannot be answered even with all statements.