HAST Spatial Reasoning 1 — Questions and Answers
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?
- 12 (Correct answer)
- 8
- 6
- 1
Correct answer: 12
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?
- 9 (Correct answer)
- 3
- 6
- 12
Correct answer: 9
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?
- Cube (rectangular prism) (Correct answer)
- Triangular prism
- Tetrahedron
- Octahedron
Correct answer: Cube (rectangular prism)
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?
- 10 cm × 8 cm (Correct answer)
- 5 cm × 4 cm
- 25 cm × 20 cm
- 50 cm × 40 cm
Correct answer: 10 cm × 8 cm
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?
- Down-right (Correct answer)
- Up-left
- Down-left
- Up-right
Correct answer: Down-right
A 90° clockwise rotation turns up-right to down-right (the upward component becomes rightward and the rightward becomes downward).
Question 6: How many cubes are needed to build a 3×3×3 solid cube if the center is hollow (one cube missing from the exact center)?
- 26 (Correct answer)
- 27
- 24
- 25
Correct answer: 26
A full 3×3×3 cube requires 27 small cubes; removing the 1 center cube leaves 26.
HAST Spatial Reasoning 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?