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Difficulty: MediumSeating Arrangement

Eight friends—S, T, U, V, W, X, Y, and Z—are sitting in a straight line facing North.

- V sits fourth to the left of W.
- W sits at one of the extreme ends of the line.
- Only two people sit between V and X.
- Y sits third to the right of S.
- S is not an immediate neighbor of V.
- Z sits to the immediate left of T.

Which of the following statements are correct?

  1. U sits exactly between S and V.Answer
  2. Y sits second to the left of T.Answer
  3. C
    T sits to the immediate left of Z.
  4. D
    X sits at the extreme right end of the line.

Answer

The statements 'U sits exactly between S and V' and 'Y sits second to the left of T' are correct.
Based on the systematic deduction of the constraints, the exact left-to-right order of the eight friends is X, S, U, V, Y, Z, T, W. In this confirmed arrangement, U (position 3) is situated directly between S (position 2) and V (position 4). Additionally, T is at position 7, meaning the second position to its left is position 5, which is exactly where Y sits.

Step-by-Step Solution

1
Determine the positions of W and V.
W is at position 8 (extreme right) and V is at position 4.
W is at an extreme end, and V is 4th to the left of W. If W were at the left end (position 1), V couldn't physically be to its left. Thus, W must be at the extreme right (8). Counting 4 spots left places V at 4.
2
Locate X based on V's position.
X must be at position 1.
Two people sit between V (4) and X. This means X can either be at 1 or 7. We test both possibilities in the next steps.
3
Evaluate the scenario where X is at position 7.
This scenario leads to a logical contradiction and is eliminated.
If X=7, S (who cannot be adjacent to V at 3 or 5) must be at 1 or 2. If S=1, Y becomes 4, which is already occupied by V. If S=2, Y becomes 5. This leaves spots 1, 3, and 6 empty. However, Z and T require adjacent spots, which are unavailable here. Thus, X cannot be 7.
4
Finalize positions with X at position 1.
The final arrangement from left to right is: X, S, U, V, Y, Z, T, W.
With X=1, testing valid spots for S yields S=2 (since S cannot be 3 or 5) and Y=5. The remaining empty spots are 3, 6, and 7. Since Z sits to the immediate left of T, they must take the adjacent spots 6 and 7 (Z=6, T=7). U must take the last remaining spot, which is 3.

Key Concept

Linear Seating Arrangement with North-Facing Orientation
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Topics

Seating Arrangement

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