Q.NO. 7
P, Q, R, S, T, U, V, and W are seated around a circular table.
l. S is seated opposite to W,
II. U is seated at the wcond place to the right of R.
Ill. T is seated at the third place to the left of R.
I V. V is a neighbour of S.
Which Of the following must be true?
A) P is a neighbour of R.
B) Q is a neighbour of R.
C) P is not seated opposite to Q.
D) R is the left neighbour Of S.
C) P is not seated opposite to Q must be true in all possible arrangements.
The seating puzzle involves eight people—P, Q, R, S, T, U, V, and W—around a circular table with specific conditions that allow multiple valid configurations but only one option holds universally.
Arrangement Rules
Conditions fix key positions relative to each other:
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S opposite W (4 seats apart).
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U two seats right of R (clockwise).
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T three seats left of R (counterclockwise).
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V adjacent to S (left or right).
R, U, T occupy distinct spots, leaving positions for S, W, V, P, Q without conflicts.
Possible Configurations
Sixteen valid setups exist after placing R, U, T, S, W, V; P and Q fill remaining spots arbitrarily.
Examples (positions 0-7 clockwise):
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R=0, U=2, T=5, S=3, W=7, V=4; remaining 1,6 for P,Q.
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R=0, U=2, T=5, S=7, W=3, V=6; remaining 1,4 for P,Q.
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R=1, U=3, T=6, S=0, W=4, V=7; remaining 2,5 for P,Q.
P and Q always occupy the two leftover seats in each case.
Option Analysis
| Option | Statement | True in All? | Explanation |
|---|---|---|---|
| A | P neighbor of R | No | E.g., R=0, remaining 1,6: P at 6 not adjacent (neighbors 7,1). P at 1 adjacent, but not always. |
| B | Q neighbor of R | No | Symmetric to A; depends on assignment. |
| C | P not opposite Q | Yes | Remaining seats never 4 apart (e.g., 1-6=3 mod8≠4, 1-4=3≠4, 2-5=3≠4). |
| D | R left neighbor of S | No | E.g., R=0,S=3: between them 1,2 (not adjacent). Other cases vary. |
Only C holds across all arrangements.
Introduction to Circular Seating Arrangement Puzzle
Circular table seating puzzles challenge logical deduction skills, common in exams like GATE. This puzzle features P, Q, R, S, T, U, V, W seated around a circular table: S opposite W, U second to right of R, T third to left of R, V neighbor of S. Determine which statement must be true among options.
Step-by-Step Solution Guide
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Fix opposites and relatives: Place R arbitrarily (rotationally symmetric). U at R+2 (right), T at R-3 (left, mod 8). S-W pairs at distance 4, avoiding R/U/T.
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Add V: Next/prev to S, unoccupied.
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Remaining seats: Always two non-opposite spots for P,Q.
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Test options: Only “P not opposite Q” persists universally.
Why P Not Opposite Q in Every Case
In 8-seat circle, opposites differ by 4 mod 8. Post-fixing R/U/T/S/W/V, free seats (e.g., distance 3 or 5) prevent P-Q opposition.
Tips for Similar Puzzles
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Use modular arithmetic for positions.
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Enumerate cases via code/diagram for “must be true.”
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Check options against all configs.
