Mensa Spatial Reasoning 5 — Questions and Answers
Question 1: A strip of paper is given a single half-twist and its ends are joined. How many distinct sides does the resulting Möbius strip have?
- 1 (Correct answer)
- 2
- 3
- 0
Correct answer: 1
A Möbius strip has only one continuous side, which you can verify by tracing your finger along the surface without lifting it.
Question 2: Five identical unit cubes are joined so each shares exactly one face with the next. Which property is guaranteed to be the same for all such arrangements?
- Total surface area
- Ability to fit in a 1×1×5 box
- Rotational symmetry
- Total volume (Correct answer)
Correct answer: Total volume
Volume depends only on the number and size of cubes, not on their spatial arrangement.
Question 3: An equilateral triangle is subdivided so each triangle is split into 4 smaller equilateral triangles per iteration. After 3 iterations starting from 1 triangle, how many smallest triangles exist?
- 64 (Correct answer)
- 27
- 48
- 81
Correct answer: 64
Each iteration multiplies the count by 4, so after 3 iterations: 4³ = 64 triangles.
Question 4: A spider at the bottom corner of a 10 ft × 8 ft × 7 ft room wants to crawl to the diagonally opposite top corner. What is the shortest surface-crawl distance?
- Approximately 17.7 ft (Correct answer)
- Approximately 15.6 ft
- 25 ft
- Approximately 19.4 ft
Correct answer: Approximately 17.7 ft
Unfolding the walls, the shortest path = √((10+7)² + 8²) = √(289+64) = √353 ≈ 18.8 ft, selecting the minimum unfolding route.
Question 5: A triangular prism has 5 faces, 9 edges, and 6 vertices. Which other common polyhedron shares the same number of faces?
- Square pyramid (Correct answer)
- Tetrahedron
- Cube
- Octahedron
Correct answer: Square pyramid
A square pyramid also has 5 faces (1 square base + 4 triangular sides), matching the triangular prism's face count.
Question 6: A 2D figure is symmetric about both the x-axis and the y-axis. Which additional symmetry must the figure necessarily have?
- Rotational symmetry of order 4
- Symmetry about the line y = x
- 180° rotational symmetry about the origin (Correct answer)
- Symmetry about the line y = −x
Correct answer: 180° rotational symmetry about the origin
Reflecting across both the x-axis and y-axis in sequence is equivalent to a 180° rotation about the origin.
Question 7: A solid cylinder is cut by a plane that passes through the full top circle but only through the midpoint of the bottom edge on one side. What shape is the cross-section?
- Ellipse (Correct answer)
- Circle
- Trapezoid
- Rectangle
Correct answer: Ellipse
Any oblique planar cut through a cylinder that is neither parallel nor perpendicular to the base produces an elliptical cross-section.
Mensa Spatial Reasoning 5
A strip of paper is given a single half-twist and its ends are joined.
How many distinct sides does the resulting Möbius strip have?