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Difficulty: MediumSeating Arrangement

Seven colleagues—T, U, V, W, X, Y, and Z—are seated in a straight line. Some of them are facing North while others are facing South.

- T sits exactly in the middle of the line and faces North.
- W sits second to the left of T.
- U sits third to the right of W.
- Only one person sits between U and X.
- Y sits to the immediate right of X.
- V sits third to the right of Y.
- The immediate neighbors of T face opposite directions (i.e., if one faces North, the other faces South, and vice versa).
- Persons sitting at the extreme ends of the line face opposite directions.
- Z and U face the same direction, which is opposite to the direction faced by V.

Based on the given seating arrangement, which of the following statements are correct?

  1. Z sits to the immediate left of W.Answer
  2. B
    Y sits to the immediate left of U.
  3. Three people sit between V and X.Answer
  4. D
    V sits to the immediate right of T.

Answer

The correct statements are that Z sits to the immediate left of W, and three people sit between V and X.
Based on the step-by-step seating arrangement, the final left-to-right order is Z(North), W(North), V(South), T(North), U(North), Y(South), and X(South). Therefore, Z is to the immediate left of W, and there are three people (T, U, Y) sitting between V and X.

Step-by-Step Solution

1
Place T in the middle of the 7 positions and determine W's position.
T is at position 4 facing North. W is at position 2.
The middle of 7 spots is the 4th spot. W is second to the left of T, who is facing North.
2
Determine the position and facing direction of W, then place U.
W faces North, and U is placed at position 5.
U sits third to the right of W. If W faced South, the 3rd right would be off the line to the left (position -1). Thus, W faces North, placing U at position 5.
3
Locate X and Y based on U's position.
X is at position 7 facing South, and Y is at position 6.
Only one person sits between U (position 5) and X, so X must be at position 3 or 7. However, if X is at 3, Y cannot be to the immediate right (positions 2 and 4 are occupied). Thus, X is at 7. For Y to be at position 6, X must face South.
4
Place V and deduce Y's facing direction.
Y faces South, and V is placed at position 3.
V sits third to the right of Y. If Y faced North, the 3rd right would be position 9 (invalid). Therefore, Y faces South, placing V at position 3.
5
Place Z and determine all remaining facing directions.
Z is at position 1 facing North. U faces North, and V faces South.
Z takes the only empty spot. Extreme ends face opposite directions; X faces South, so Z faces North. Z and U face the same direction (North), opposite to V (South). This perfectly matches the condition that T's neighbors (V and U) face opposite directions.

Key Concept

Analytical seating arrangements with mixed facing directions (North and South).
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Topics

Seating Arrangement

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