Read the following campus layout information carefully and answer the question that follows:

Eight miniature models of university facilities are placed on a display table at various distances from each other. The model of the Admin Building is 50 inches to the west of the Science Lab model. The Library model is 70 inches to the east of the Main Gate model. The Hostel model is 20 inches to the north of the Dining Hall model, which is 30 inches to the west of the Parking Lot model. The Admin Building model is 40 inches to the south of the Main Gate model. The Science Lab model is 40 inches to the north of the Sports Center model. The Hostel model is 30 inches to the west of the Sports Center model.

In which direction is the Admin Building model with respect to the Dining Hall model?

The correct option is North-west.

Let us map out the positions of each university facility model on a 2D Cartesian coordinate grid, taking the Admin Building model as our reference origin point (0, 0).

Step 1: Determine coordinates of key points relative to the Admin Building (0, 0):

1. Admin Building (Admin):
Let coordinates of Admin = (0, 0).

2. Science Lab (Lab):
The Admin Building model is 50 inches to the west of the Science Lab model.
This means the Science Lab is 50 inches to the east of the Admin Building.
Coordinates of Science Lab = (50, 0).

3. Main Gate (Gate):
The Admin Building model is 40 inches to the south of the Main Gate model.
This means the Main Gate is 40 inches to the north of the Admin Building.
Coordinates of Main Gate = (0, 40).

4. Sports Center (Sports):
The Science Lab model is 40 inches to the north of the Sports Center model.
This means the Sports Center is 40 inches to the south of the Science Lab.
Coordinates of Sports Center = (50, 0 - 40) = (50, -40).

5. Hostel:
The Hostel model is 30 inches to the west of the Sports Center model.
Coordinates of Hostel = (50 - 30, -40) = (20, -40).

6. Dining Hall (Dining):
The Hostel model is 20 inches to the north of the Dining Hall model.
This means the Dining Hall is 20 inches to the south of the Hostel model.
Coordinates of Dining Hall = (20, -40 - 20) = (20, -60).

Step 2: Determine the position of Admin Building relative to Dining Hall:

Coordinates of Admin Building = (0, 0)
Coordinates of Dining Hall = (20, -60)

To find the direction of the Admin Building with respect to the Dining Hall, we evaluate the change in coordinates from Dining Hall to Admin Building:
Change in X (East/West) = 0 - 20 = -20 (West)
Change in Y (North/South) = 0 - (-60) = +60 (North)

Since the change in position moves towards the North and West, the Admin Building model is in the North-west direction with respect to the Dining Hall model.