GATE CS 2019 Q.10 (GA Q.10): Spatial Aptitude

Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests.

Request by X: Due to pollen allergy, I want to avoid a wing next to the garden.
Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell.
Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

The shaded rooms are already occupied. WR is washroom.

Option (A). Hostel floor plan: a ring of rooms around a courtyard whose compass is drawn diagonally (N top-left, E top-right, S bottom-right, W bottom-left), so the top row is the north-east wing, the right side the south-east wing, the bottom row the south-west wing and the left side the north-west wing. Washrooms (WR) are at the top-left and bottom-left corners, gardens lie beside the top-right and bottom-right rooms, the entrance is in the middle of the right side, and shaded rooms are occupied. X is in the bottom row, second room (next to the washroom); Y is in the bottom row, fifth room; Z is on the left side, middle room.

Option (B). Hostel floor plan: a ring of rooms around a courtyard whose compass is drawn diagonally (N top-left, E top-right, S bottom-right, W bottom-left), so the top row is the north-east wing, the right side the south-east wing, the bottom row the south-west wing and the left side the north-west wing. Washrooms (WR) are at the top-left and bottom-left corners, gardens lie beside the top-right and bottom-right rooms, the entrance is in the middle of the right side, and shaded rooms are occupied. X is in the top row, right-end room (beside the garden); Y is on the right side, lower room; Z is on the left side, middle room.

Option (C). Hostel floor plan: a ring of rooms around a courtyard whose compass is drawn diagonally (N top-left, E top-right, S bottom-right, W bottom-left), so the top row is the north-east wing, the right side the south-east wing, the bottom row the south-west wing and the left side the north-west wing. Washrooms (WR) are at the top-left and bottom-left corners, gardens lie beside the top-right and bottom-right rooms, the entrance is in the middle of the right side, and shaded rooms are occupied. X is in the bottom row, second room; Y is on the right side, lower room; Z is in the top row, right-end room (beside the garden).

Option (D). Hostel floor plan: a ring of rooms around a courtyard whose compass is drawn diagonally (N top-left, E top-right, S bottom-right, W bottom-left), so the top row is the north-east wing, the right side the south-east wing, the bottom row the south-west wing and the left side the north-west wing. Washrooms (WR) are at the top-left and bottom-left corners, gardens lie beside the top-right and bottom-right rooms, the entrance is in the middle of the right side, and shaded rooms are occupied. X is in the bottom row, second room; Y is on the right side, lower room; Z is in the bottom row, fifth room.

Official answer and solution

Official answer: D
From: Official GATE 2019 answer key

Solution

Read the wing directions from the diagonal compass, then check each plan against the three requests.

Orientation. The compass in the floor plan is drawn diagonally: N at the top-left, E at the top-right, S at the bottom-right and W at the bottom-left. So the top row is the North-East wing, the right side is the South-East wing, the bottom row is the South-West wing and the left side is the North-West wing. The washrooms (WR) are at the top-left and bottom-left corners, and the gardens are beside the top-right and bottom-right rooms.

Constraints:

X must avoid a wing next to the garden, so X cannot take the rooms at the right end (beside the gardens).
Y wants to be as far as possible from the washrooms, which are at the left end, so Y should be at the right end.
Z wants the South-West wing, i.e. the bottom row.

Evaluate the options:

(A): Z is on the left side (North-West wing). Fails Z.
(B): X is at the right end of the top row, beside the garden, and Z is on the left side (North-West wing). Fails X and Z.
(C): Z is at the right end of the top row (North-East wing). Fails Z.
(D): Z is in the bottom row (South-West wing), X is in the bottom row away from the gardens, and Y is on the right side, farthest from the washrooms. All requests are met.

Hence the allocation plan is (D).

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2019 Computer Science and Information Technology (CS)
Question: 10 of 65, printed as GA Q.10
Section: General Aptitude

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