HAST Spatial Reasoning

Question 1

A cube is painted red on all faces and then cut into 27 equal smaller cubes. How many small cubes have exactly 2 red faces?

Accepted Answer

12

Answer

Edge cubes (not corner, not face center) have exactly 2 painted faces; a 3×3×3 cube has 12 edge positions.

Question 2

Looking at a clock from the front, the minute hand points to 12 and the hour hand points to 3. If you look at the clock in a mirror, where does the hour hand point?

Accepted Answer

9

Answer

A mirror reverses left and right; what was on the right (3 o'clock) now appears on the left (9 o'clock).

Question 3

A 3D shape has 6 faces, 12 edges, and 8 vertices. What is it?

Accepted Answer

Cube (rectangular prism)

Answer

A cube has exactly 6 faces, 12 edges, and 8 vertices, satisfying Euler's formula (V − E + F = 2).

Question 4

A floor plan shows a room 5 m × 4 m. At a scale of 1:50, what are the dimensions on the plan?

Accepted Answer

10 cm × 8 cm

Answer

Scale 1:50 means every 1 cm on the plan = 50 cm in reality; 5 m = 500 cm ÷ 50 = 10 cm; 4 m = 400 cm ÷ 50 = 8 cm.

Question 5

A shape is rotated 90° clockwise. If it originally faced up-right, which direction does it face after rotation?

Accepted Answer

Down-right

Answer

A 90° clockwise rotation turns up-right to down-right (the upward component becomes rightward and the rightward becomes downward).

HAST - Higher Ability Selection Test Practice Test

HAST - Higher Ability Selection Test Practice Test

HAST Spatial Reasoning