Mensa Mensa IQ Spatial Reasoning and Patterns 4 — Questions and Answers
Question 1: A sequence of shapes follows this rule: circle, square, triangle, circle, square, triangle… What is the 17th shape in the sequence?
- Circle
- Square (Correct answer)
- Triangle
- Diamond
Correct answer: Square
The sequence repeats every 3 shapes; 17 mod 3 = 2 (since 3×5=15, remainder 2), which maps to position 2 in the cycle — square.
Question 2: A 3D cube is painted red on all faces, then cut into 27 equal smaller cubes. How many small cubes have exactly 2 red faces?
- 8
- 12 (Correct answer)
- 6
- 4
Correct answer: 12
Edge pieces (not corner) of a 3×3×3 cube have exactly 2 painted faces; there are 12 edges on a cube, each contributing 1 such piece.
Question 3: Looking at a grid pattern where odd rows shift right by half a unit, what type of tiling is described?
- Square tiling
- Brick or offset tiling (Correct answer)
- Hexagonal tiling
- Triangular tiling
Correct answer: Brick or offset tiling
Offsetting alternating rows by half a unit creates a brick-bond (running bond) tiling pattern.
Question 4: A flat cross-shaped net is folded into a 3D shape. The cross has one center square and four squares extending from each side. What shape does it form?
- Rectangular prism
- Tetrahedron
- Cube (Correct answer)
- Pyramid
Correct answer: Cube
A cross-shaped net with one center square and four arms folds into a cube (one face remains open unless a sixth square is added, but the standard 6-square cross net forms a cube).
Question 5: In a number pattern: 2, 6, 18, 54, ___ . What comes next?
- 108
- 162 (Correct answer)
- 216
- 72
Correct answer: 162
Each term is multiplied by 3 (geometric sequence with ratio 3), so 54 × 3 = 162.
Question 6: A shape is rotated 90° clockwise, then reflected over a vertical axis. Which single transformation is equivalent to this combined operation?
- 90° counterclockwise rotation
- 180° rotation
- Reflection over a horizontal axis (Correct answer)
- 90° clockwise rotation followed by reflection over horizontal axis
Correct answer: Reflection over a horizontal axis
A 90° clockwise rotation followed by a vertical reflection is equivalent to a single reflection over a horizontal axis.
Question 7: Which figure completes the analogy: solid square is to hollow square as solid circle is to ___?
- Solid triangle
- Hollow circle (Correct answer)
- Solid diamond
- Hollow triangle
Correct answer: Hollow circle
The analogy transforms a filled shape into its outline equivalent, so a solid circle becomes a hollow (outline) circle.
Mensa Mensa IQ Spatial Reasoning and Patterns 4
A sequence of shapes follows this rule: circle, square, triangle, circle, square, triangle… What is the 17th shape in the sequence?