Analyze the details provided below and answer the question that follows.
Eight individuals P, Q, R, T, U, V, X, and Y are seated in a single straight row, with some facing north and others facing south. No more than two adjacent individuals face the same direction.
Y is positioned at the extreme right end of the row and faces north. X sits to the immediate left of Y. P is seated at the extreme left end of the row, and exactly three individuals sit between P and U. V sits fourth to the right of Q, who faces north. R sits adjacent to both Q and T. X and V face in opposite directions. P and Q face the same direction, while T and U face opposite directions. R and T face the same direction, and V faces south.
Based on the arrangement, what is the position of R with respect to U?
Correct Answer :
2nd to the left
Solution :
Correct Answer: 2nd to the left
Step-by-Step Explanation:
1. Understanding the Setup:
There are 8 positions in a straight row (numbered 1 to 8 from left to right):
[Pos 1, Pos 2, Pos 3, Pos 4, Pos 5, Pos 6, Pos 7, Pos 8]
2. Placing Fixed End Positions:
- "Y is positioned at the extreme right end of the row and faces north."
Pos 8 = Y (Facing North)
- "X sits to the immediate left of Y."
Pos 7 = X
- "P is seated at the extreme left end of the row, and exactly three individuals sit between P and U."
Pos 1 = P
Since 3 individuals sit between P and U, U must be at Pos 5 (Pos 2, 3, 4 are between 1 and 5).
Current Row State:
Pos 1: P | Pos 2: _ | Pos 3: _ | Pos 4: _ | Pos 5: U | Pos 6: _ | Pos 7: X | Pos 8: Y (North)
3. Placing Q, V, R, and T:
- "V sits fourth to the right of Q, who faces north."
Since Q faces North, 4th to the right means V is 4 positions to the right of Q (Pos of V = Pos of Q + 4).
Let's check possible positions for Q facing North:
- If Q is at Pos 2, V would be at Pos 6 (2 + 4 = 6).
- If Q is at Pos 3, V would be at Pos 7, but Pos 7 is occupied by X.
Thus, Q must be at Pos 2, which puts V at Pos 6.
- Now remaining empty positions are Pos 3 and Pos 4 for R and T.
- "R sits adjacent to both Q and T."
Since Q is at Pos 2, R must be at Pos 3 to be adjacent to Q, and T must be at Pos 4 so that R is adjacent to both Q and T.
Complete Seating Positions (Left to Right):
Pos 1: P
Pos 2: Q
Pos 3: R
Pos 4: T
Pos 5: U
Pos 6: V
Pos 7: X
Pos 8: Y
4. Determining Directions Faced by Each Individual:
- Q faces North (given).
- V faces South (given).
- "P and Q face the same direction" ⇒ P faces North.
- "X and V face in opposite directions" ⇒ Since V faces South, X faces North.
- "R and T face the same direction."
- "T and U face opposite directions."
- Constraint: "No more than two adjacent individuals face the same direction."
- Pos 7 (X) faces North, Pos 8 (Y) faces North.
Therefore, Pos 6 (V) must face South (which matches our given info that V faces South).
- Pos 1 (P) faces North, Pos 2 (Q) faces North.
Since no three adjacent individuals can face North, Pos 3 (R) MUST face South.
- Since R and T face the same direction, T faces South.
- Since T faces South and T & U face opposite directions, U faces North.
Summary of Directions:
P (North), Q (North), R (South), T (South), U (North), V (South), X (North), Y (North)
5. Answering the Question:
We need to find the position of R with respect to U.
- U is at Pos 5 and faces North.
- Relative to a person facing North at Pos 5:
- Pos 4 is 1st to the left.
- Pos 3 is 2nd to the left.
- R is located at Pos 3.
Therefore, R is 2nd to the left of U.
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