Each of the following questions is based on the following information: Six…

2024

Each of the following questions is based on the following information: Six flats on a floor in two rows facing North and South are allotted to P, Q, R, S, T and U. Q gets a North facing flat and is not next to S. S and U get diagonally opposite flats. R, next to U, gets a South facing flat, and T gets a North facing flat. Which other pair of flats, besides S-U, is diagonally opposite to each other?

Answer: A. QPConcept: In a two-row, three-seat facing arrangement, the two rows sit opposite each other with one row facing North and the other facing South. Seats sharing…

  1. A.

    QP

  2. B.

    QR

  3. C.

    PT

  4. D.

    TS

Attempted by 2 students.

Show answer & explanation

Correct answer: A

Concept: In a two-row, three-seat facing arrangement, the two rows sit opposite each other with one row facing North and the other facing South. Seats sharing the same position (left-left, middle-middle, right-right) are directly opposite each other, while the two seats at opposite end positions across the rows are diagonally opposite -- so a middle seat never has a diagonal partner, only a direct one. "Next to" is always adjacency within the same row, never across rows.

Application:

  1. R is given a South-facing flat and sits next to U, so U also belongs to the South-facing row (adjacency only happens within one row).

  2. S and U are diagonally opposite, so S must sit in the North-facing row, at the end position diagonal to U's end position.

  3. Q and T are both given North-facing flats, so the North-facing row is exactly {Q, S, T}, and the South-facing row is exactly the remaining three, {P, R, U}.

  4. In a row of three seats, the only two seats that are not adjacent to each other are the two end seats; since Q is not next to S, Q and S must occupy the two ends of the North row, leaving T in the middle seat.

  5. S sits at one end of the North row; its diagonal partner U therefore sits at the opposite end of the South row, matching the given S-U diagonal condition.

  6. In the South row, R must sit next to U; the only South-row seat adjacent to U's end seat is the middle seat, so R takes the middle seat, leaving P at the remaining end seat.

  7. With T (North, middle) and R (South, middle) directly opposite each other, the only unassigned seats are the two remaining end seats, one in each row, and they belong to Q and P -- so Q and P are the "other" pair (besides S-U) that is diagonally opposite.

Cross-check: Swapping which end Q and S occupy only relabels left and right without changing which pair ends up diagonal: Q and P remain the pair left over once the S-U diagonal and R's middle seat are fixed, confirming the result independent of that left-right choice; this also matches the diagram method of laying out both rows and reading the corner pairs directly.

Answer: The pair diagonally opposite each other, other than S-U, is Q and P.

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