Mensa Spatial Reasoning 5

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?

Accepted Answer

1

Answer

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?

Accepted Answer

Total volume

Answer

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?

Accepted Answer

64

Answer

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?

Accepted Answer

Approximately 17.7 ft

Answer

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?

Accepted Answer

Square pyramid

Answer

A square pyramid also has 5 faces (1 square base + 4 triangular sides), matching the triangular prism's face count.

Mensa Practice Test

Mensa Practice Test

Mensa Spatial Reasoning 5