Basic Ability Test Basic Ability Spatial Reasoning and Visualization 5 — Questions and Answers
Question 1: A solid shape has 12 edges, 8 vertices, and 6 faces. What shape is it?
- Triangular prism
- Square pyramid
- Cube (Correct answer)
- Octahedron
Correct answer: Cube
A cube has exactly 6 faces, 12 edges, and 8 vertices, confirmed by Euler's formula.
Question 2: A path goes: 3 blocks north, 4 blocks east, 3 blocks south. How far (straight line) are you from the start?
- 3 blocks
- 4 blocks (Correct answer)
- 5 blocks
- 7 blocks
Correct answer: 4 blocks
The north and south legs cancel out, leaving a net displacement of 4 blocks east.
Question 3: You look at the reflection of a digital clock showing 10:10 in a mirror. What time does the reflection show?
- 10:10
- 01:50 (Correct answer)
- 10:01
- 02:50
Correct answer: 01:50
A mirror reverses left and right; 10:10 reflected becomes 01:50.
Question 4: A shape has 3 lines of symmetry. Which shape is it most likely to be?
- Square
- Rectangle
- Equilateral triangle (Correct answer)
- Circle
Correct answer: Equilateral triangle
An equilateral triangle has exactly 3 lines of symmetry, one through each vertex and midpoint.
Question 5: A blueprint shows a room that is 4 cm × 6 cm at a scale of 1 cm = 3 m. What is the actual area of the room?
- 24 m²
- 72 m²
- 144 m² (Correct answer)
- 216 m²
Correct answer: 144 m²
Actual dimensions are 12 m × 12 m = 144 m² (each cm becomes 3 m, so area scales by 3² = 9; 24 × 9 = 216).
Question 6: A cube is painted red on all sides and then cut into 27 equal smaller cubes. How many small cubes have exactly 2 red faces?
- 6
- 8
- 12 (Correct answer)
- 24
Correct answer: 12
The 12 edge cubes (not corners) of a 3×3×3 cube each have exactly 2 painted faces.
Question 7: A wheel with a diameter of 2 feet rolls forward until it has made exactly 3 full rotations. How far has it traveled?
- 6 ft
- 6π ft (Correct answer)
- 3π ft
- 9 ft
Correct answer: 6π ft
Each rotation covers π × diameter = 2π ft; 3 rotations = 6π ft ≈ 18.85 ft.
Basic Ability Test Basic Ability Spatial Reasoning and Visualization 5
A solid shape has 12 edges, 8 vertices, and 6 faces.
What shape is it?