Direction: Read the following information carefully and answer the question…
2025
Direction: Read the following information carefully and answer the question based on the given information.
A certain number of persons sit in a horizontal row, all facing North. Only three persons sit between S and W. Only two persons sit between X and R. M sits at the extreme end. H sits second to the left of X. E sits exactly in the middle of S and W. R sits two places away from M. E sits immediately to the right of H. W sits to the right of X. F sits to the right of X. The number of persons sitting to the left of S is the same as the number sitting to the right of F. Y and W sit immediately next to each other.
Who among the following sits immediately to the left of S?
- A.
X
- B.
H
- C.
Y
- D.
R
- E.
None
Attempted by 2 students.
Show answer & explanation
Correct answer: E
Concept:
In a linear seating-arrangement puzzle, every directional clue -- "to the right of", "second to the left of", "immediately next to", "X places away" -- converts into an equation on each person's absolute seat number, counted left to right. Anchor the equations at a fixed point (an extreme end, a stated gap) and chain them outward; the total number of seats in the row must itself be derived from the clues, never assumed to equal the count of named people.
Application:
Let seat positions increase left to right. From "H sits second to the left of X" (H = X - 2) and "E sits immediately to the right of H" (E = H + 1), E = X - 1, so H, E and X occupy three consecutive seats.
"E sits exactly in the middle of S and W" with "only three persons sit between S and W" (a gap of exactly four seats) means E is exactly two seats from both S and W. Since W must sit to the right of X and E = X - 1, only W = E + 2 = X + 1 satisfies that, which fixes S = E - 2 = X - 3.
Seats X-3 to X+1 are therefore, in left-to-right order: S, H, E, X, W.
"Only two persons sit between X and R" gives R = X - 3 or R = X + 3; R = X - 3 would coincide with S's own seat, so R = X + 3. "Y sits immediately next to W" similarly gives Y = X (colliding with X itself) or Y = X + 2, so Y = X + 2.
For the row of N seats: "the number of persons to the left of S equals the number to the right of F" gives F = N - S + 1 = N - X + 4. "R sits two places away from M", with M at an extreme end, only resolves (without colliding with W) if M is the far end at seat N and M = R + 2 = X + 5, so N = X + 5 -- fixing F = (X + 5) - X + 4 = 9 for every value of X.
"F sits to the right of X" then requires 9 > X, and S = X - 3 >= 1 requires X >= 4, so X can only be 4, 5, 6, 7 or 8. Checking each, with F fixed at seat 9: X = 4 puts M (seat N = 9) on F's own seat; X = 6 puts R (seat X + 3 = 9) on F's seat; X = 7 puts Y (seat X + 2 = 9) on F's seat; X = 8 puts W (seat X + 1 = 9) on F's seat. Only X = 5 leaves all nine seats distinct, giving the unique row length N = 10.
With X = 5: S = 2, H = 3, E = 4, W = 6, Y = 7, R = 8, F = 9, and M takes the only remaining seat, 10 -- the row's extreme end -- with every one of the ten seats now accounted for.
Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
Occupant | (unnamed) | S | H | E | X | W | Y | R | F | M |
Cross-check:
Between S (seat 2) and W (seat 6): H, E, X occupy seats 3-5 -- exactly three persons, matching "only three persons sit between S and W".
Between X (seat 5) and R (seat 8): W, Y occupy seats 6-7 -- exactly two persons, matching "only two persons sit between X and R".
M (seat 10) sits at the extreme end, and R (seat 8) is exactly two places away from M, matching both clues.
Persons to the left of S (seat 2): just seat 1, one person. Persons to the right of F (seat 9): just seat 10, one person -- equal, matching the count clue.
Y (seat 7) sits immediately next to W (seat 6), matching the last clue.
Every named person's seat is now fixed, and the single seat immediately to the left of S -- seat 1 -- belongs to this unnamed tenth occupant, not to X, H, Y or R. None of the four named options sits immediately to the left of S.