Mensa IQ Test Spatial Reasoning 2 — Questions and Answers
Question 1: A cube has 6 faces. If you unfold it into a flat cross shape, how many faces are visible from the top?
- 4
- 5
- 6 (Correct answer)
- 3
Correct answer: 6
When a cube is unfolded (net), all 6 faces are laid flat and visible from above.
When a cube is unfolded into its net (flat cross or T-shape), all 6 faces separate and lie flat on the same plane. From directly above, all 6 faces are visible.
Question 2: Which 3D shape has exactly 5 faces, 8 edges, and 5 vertices?
- Triangular prism
- Cube
- Square pyramid (Correct answer)
- Tetrahedron
Correct answer: Square pyramid
A square pyramid has 1 square base + 4 triangular faces = 5 faces, 8 edges, and 5 vertices.
A square pyramid: 1 square base + 4 triangular sides = 5 faces. Edges: 4 base edges + 4 lateral edges = 8. Vertices: 4 base corners + 1 apex = 5. This satisfies Euler's formula: F+V-E = 5+5-8 = 2.
Question 3: If you rotate the letter 'N' by 180 degrees, what does it look like?
- N (Correct answer)
- Z
- И
- S
Correct answer: N
Rotating N by 180° around its center produces the same letter N due to its rotational symmetry.
The letter N has 180-degree rotational symmetry. When rotated 180° around its center point, it maps onto itself and still looks like N. This is because the diagonal stroke connects the same relative corners after rotation.
Question 4: How many cubes are needed to build a 3×3×3 hollow cube (outer shell only)?
- 20
- 24
- 26 (Correct answer)
- 27
Correct answer: 26
Total cubes in solid 3×3×3 = 27. Interior cube removed = 1. Shell cubes = 27 - 1 = 26.
A solid 3×3×3 cube contains 27 small cubes. The only interior cube is the center one (surrounded on all sides). Removing the 1 interior cube leaves 26 cubes forming the outer shell.
Question 5: A shape has exactly 2 lines of symmetry. Which of the following could it be?
- Equilateral triangle
- Rectangle (Correct answer)
- Regular pentagon
- Scalene triangle
Correct answer: Rectangle
A rectangle has exactly 2 lines of symmetry: horizontal and vertical through the midpoints of opposite sides.
A rectangle (non-square) has exactly 2 lines of symmetry — one through the midpoints of the longer sides and one through the shorter sides. An equilateral triangle has 3, a regular pentagon has 5, and a scalene triangle has 0.
Question 6: If you look at a clock in a mirror, the hands show 4:30. What is the actual time?
- 7:30 (Correct answer)
- 8:30
- 7:00
- 7:15
Correct answer: 7:30
A mirror reverses left-right. The actual time is found by subtracting from 12:00. 11:60 - 4:30 = 7:30.
To find the actual time from a mirror reflection, subtract the mirror time from 11:60 (or 12:00). 11:60 - 4:30 = 7:30. The mirror shows 4:30, so the actual time is 7:30.
Mensa IQ Test Spatial Reasoning 2
A cube has 6 faces.
If you unfold it into a flat cross shape, how many faces are visible from the top?