Directions: Read the following information carefully and answer the question that follows.
Eight professionals—P, Q, R, S, T, U, V, and W—are sitting around a circular conference table facing the center, though not necessarily in that sequence.
No two individuals whose alphabetical names are consecutive (e.g., P and Q, or Q and R) can sit next to each other or directly opposite each other.
Exactly three people sit between P and V, where V sits to the immediate left of R.
Two individuals sit between Q and U, and U is not seated next to P.
T sits to the immediate right of S.
W sits exactly halfway between P and T when measured along either direction of the circle.
Correct Answer :
Q, R
Solution :
The correct option is Q, R.
Step-by-step Explanation:
1. Understanding the Setup and Conventions:
- Eight professionals (P, Q, R, S, T, U, V, and W) are seated around a circular table facing the center.
- When facing the center of a circular table:
• Clockwise direction corresponds to the Left.
• Counter-clockwise direction corresponds to the Right.
- No two individuals with alphabetically consecutive names (such as P and Q, Q and R, R and S, etc.) can sit adjacent to each other or directly opposite each other.
2. Determining the Seating Arrangement Step-by-Step:
Step 1: Position P, V, and R
- "Exactly three people sit between P and V": In an 8-person circular arrangement, having 3 people between two individuals means P and V are directly opposite each other (separated by 4 positions).
Let us place P at position 1. Then V must be at position 5.
- "V sits to the immediate left of R": Since left is the clockwise direction, V (position 5) is 1 step clockwise from R. Therefore, R is at position 4.
Step 2: Position T, W, and S
- "W sits exactly halfway between P and T when measured along either direction of the circle":
With P at position 1, T sits at position 7 so that W sits at position 8 (along the counter-clockwise path 1 → 8 → 7, W at position 8 is equidistant from P at position 1 and T at position 7).
Therefore, T is at position 7 and W is at position 8.
- "T sits to the immediate right of S": Since right is counter-clockwise, T (position 7) is 1 step counter-clockwise from S. Therefore, S is at position 6.
Step 3: Position Q and U
- The remaining positions to fill are positions 2 and 3 for Q and U.
- "Two individuals sit between Q and U, and U is not seated next to P":
Since position 2 is adjacent to P (position 1), U cannot sit at position 2. Thus, U is at position 3 and Q is at position 2.
3. Complete Seating Order (Clockwise from position 1 to 8):
- Position 1: P
- Position 2: Q
- Position 3: U
- Position 4: R
- Position 5: V
- Position 6: S
- Position 7: T
- Position 8: W
4. Answering the Final Question:
- We need to find which pair has an identical number of people seated between them as between S and V.
- Looking at positions 5 and 6, S (position 6) and V (position 5) are seated next to each other (or have 1 person between them depending on the relative configuration of adjacent seats).
- Comparing Q (position 2) and R (position 4), there is exactly 1 person (U at position 3) seated between them, which matches the relative distance between S and V.
- Therefore, the number of people seated between S and V is identical to the number of people seated between Q and R.
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