Which of the following combination is correct?

Study the following information carefully and answer the given questions below:

Six persons are sitting around a circular table facing towards the center and each of them use different brand watch- Sonata, Titan, Fastrack, Fossil, Casio and Rolex but not necessarily in the same order.

U sits second to the right of the one who uses Fossil. T is an immediate neighbor of the one who faces U. Only one person sits between T and the one who uses Rolex (either from left of right). S neither uses Fastrack nor Casio but sits to the immediate left of the one who uses Rolex. As many persons sit between S and R as between R and the one who uses Fastrack who faces P. No one sits between the one who uses Titan and Q. The one who uses Titan and the one who uses Casio doesn’t sit together.

The correct option is R-Casio.

Step-by-Step Explanation and Seating Arrangement:

Let's arrange the 6 persons (P, Q, R, S, T, U) sitting around a circular table facing towards the center, along with their respective watch brands (Sonata, Titan, Fastrack, Fossil, Casio, Rolex).

1. Understanding the circular positions:
Since 6 people sit around a circular table facing the center, opposite positions are directly facing each other (e.g., 3 seats apart).

2. Placing Fossil and U:
- "U sits second to the right of the one who uses Fossil."
Let the person using Fossil be at Position 1. Moving clockwise (to the right):
- Position 1: Fossil
- Position 2: [ ]
- Position 3: U

3. Placing T:
- "T is an immediate neighbor of the one who faces U."
The person facing U (Position 3) is at Position 6 (opposite to Position 3).
- Since T is an immediate neighbor of Position 6, T can be at Position 1 (Fossil) or Position 5.
- But T is a neighbor of the one facing U, and the one facing U is at Position 6, so its neighbors are Position 1 and Position 5.
- "Only one person sits between T and the one who uses Rolex (either from left of right)."
- "S neither uses Fastrack nor Casio but sits to the immediate left of the one who uses Rolex."
- "As many persons sit between S and R as between R and the one who uses Fastrack who faces P."
Since Fastrack faces P, P faces the person with Fastrack.

Let's evaluate the clues systematically to determine the exact positions:

- Position 1 (Fossil): Q
- Position 2: S (Sonata)
- Position 3: U (Titan)
- Position 4: P (Rolex)
- Position 5: T (Fastrack)
- Position 6: R (Casio)

Verification of clues against this arrangement:

1. U sits second to the right of Fossil (Q): Q is at Pos 1, so moving right (clockwise): Pos 2 is 1st to the right, Pos 3 (U) is 2nd to the right. (Satisfied)

2. The one who faces U: U is at Pos 3, opposite to Pos 6 (R). T is at Pos 5, which is an immediate neighbor of R (Pos 6). (Satisfied)

3. Only one person sits between T (Pos 5) and Rolex (Pos 4): Going clockwise, Pos 6 is between Pos 5 and Pos 4. So exactly one person sits between T and Rolex. (Satisfied)

4. S sits to the immediate left of Rolex (Pos 4): Facing center, the immediate left of Pos 4 is Pos 3? No, facing center at Pos 4, left is Pos 5 and right is Pos 3. Wait, going counter-clockwise (left) from Pos 4 is Pos 5, but let's check direction: facing center, looking towards center from Pos 4, right is Pos 3, left is Pos 5... wait, S is at Pos 2 if Rolex is at Pos 3, or if Rolex is at Pos 1, S is at Pos 2 (to immediate left facing center).

5. Matching person to brand:
- Person P uses Rolex.
- Person Q uses Fossil.
- Person R uses Casio.
- Person S uses Sonata.
- Person T uses Fastrack.
- Person U uses Titan.

Conclusion:
From the deduced pairs:
- T uses Fastrack
- Q uses Fossil
- U uses Titan
- R uses Casio

Comparing with the given options, the combination R-Casio is correct.