Question Details

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?

Options

A

Immediate left

B

4th to the right

C

3rd to the right

D

2nd to the right

E

2nd to the left

Show Answer

Correct Answer :

Option E

2nd to the left

Solution :

Correct Answer: 2nd to the left

Let us step through the logical reasoning to deduce the complete seating arrangement and facing directions of all eight individuals.

Step 1: Determine the positions of the individuals from left to right (positions 1 to 8).
- There are 8 positions in a row, numbered 1 to 8 from left to right.
- "P is seated at the extreme left end of the row."
⇒ Position 1 = P.
- "Y is positioned at the extreme right end of the row."
⇒ Position 8 = Y.
- "X sits to the immediate left of Y."
⇒ Position 7 = X.
- "Exactly three individuals sit between P and U."
⇒ Between Position 1 (P) and U, there are 3 seats (positions 2, 3, 4). Thus, Position 5 = U.

Current positions layout:
Position 1: P
Position 2: _
Position 3: _
Position 4: _
Position 5: U
Position 6: _
Position 7: X
Position 8: Y

Step 2: Place Q, V, R, and T into the remaining empty positions (2, 3, 4, 6).
- "R sits adjacent to both Q and T."
⇒ R must be between Q and T, forming a contiguous block of three seats: Q-R-T or T-R-Q.
- The available empty positions are 2, 3, 4, and 6.
- The only 3 contiguous available positions are 2, 3, and 4. Therefore, {Q, R, T} occupy positions 2, 3, and 4, leaving Position 6 for V.
⇒ Position 6 = V.
- "V sits fourth to the right of Q, who faces north."
- V is at position 6. Since Q faces North, "right" means towards the higher position numbers (to the right).
- If V (position 6) is 4th to the right of Q, then Q must be at position 6 - 4 = 2.
⇒ Position 2 = Q.
- Since Q is at position 2 and R is adjacent to both Q and T:
⇒ Position 3 = R.
⇒ Position 4 = T.

Complete arrangement of persons from position 1 to 8:
1: P | 2: Q | 3: R | 4: T | 5: U | 6: V | 7: X | 8: Y

Step 3: Determine the facing directions (North or South).
- "Y ... faces north." ⇒ Y = North
- "Q faces north." ⇒ Q = North
- "V faces south." ⇒ V = South
- "P and Q face the same direction." ⇒ P = North
- "X and V face in opposite directions." Since V = South, X = North.
- "R and T face the same direction."
- "T and U face opposite directions."
- Check the condition: "No more than two adjacent individuals face the same direction."
- Positions 7 (X) and 8 (Y) both face North.
- Positions 1 (P) and 2 (Q) both face North. If Position 3 (R) also faced North, three consecutive individuals (P, Q, R) would face North, which violates the condition. Therefore, R must face South.
⇒ R = South.
- Since "R and T face the same direction", T must also face South.
⇒ T = South.
- Since "T and U face opposite directions", U must face North.
⇒ U = North.

Summary of facing directions:
1: P (North)
2: Q (North)
3: R (South)
4: T (South)
5: U (North)
6: V (South)
7: X (North)
8: Y (North)

Step 4: Find the position of R with respect to U.
- U is at Position 5 and faces North.
- For a person facing North, "left" refers to lower position numbers (towards Position 1).
- R is at Position 3.
- Position 3 is 2 places to the left of Position 5 (U).
⇒ Therefore, R is 2nd to the left of U.

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