Mensa Mensa IQ Spatial Reasoning and Patterns 5 — Questions and Answers
Question 1: A matrix has 3 rows and 3 columns. Row 1: △ ○ □ | Row 2: ○ □ △ | Row 3: □ △ ? What shape belongs in the bottom-right cell?
- Triangle
- Square
- Circle (Correct answer)
- Diamond
Correct answer: Circle
Each row and column contains each of the three shapes exactly once (Latin square pattern), so the missing shape must be ○ (circle).
Question 2: How many squares of ALL sizes are in a 4×4 grid of unit squares?
- 16
- 20
- 30 (Correct answer)
- 24
Correct answer: 30
A 4×4 grid contains 16 (1×1) + 9 (2×2) + 4 (3×3) + 1 (4×4) = 30 squares total.
Question 3: A spiral pattern grows outward: the 1st ring has 8 cells, the 2nd ring has 16 cells, the 3rd ring has 24 cells. How many cells does the 5th ring have?
- 32
- 36
- 40 (Correct answer)
- 48
Correct answer: 40
Each ring adds 8 more cells than the previous (arithmetic sequence with common difference 8), so the 5th ring has 8 × 5 = 40 cells.
Question 4: An object viewed from the front appears as a circle, from the side as a rectangle, and from the top as a rectangle. What 3D shape is it?
- Sphere
- Cone
- Cylinder (Correct answer)
- Cube
Correct answer: Cylinder
A cylinder has a circular front view and rectangular side and top views.
Question 5: In a pattern of alternating black and white triangles arranged in a row, the 1st is black, 2nd white, 3rd black… What color is the 44th triangle?
- Black
- White (Correct answer)
- Gray
- Cannot be determined
Correct answer: White
Even-numbered positions are white in this alternating pattern, and 44 is even, so the 44th triangle is white.
Question 6: A shape undergoes 4 successive 90° clockwise rotations. What is the net result?
- 90° clockwise
- 180° rotation
- 270° clockwise
- Back to the original orientation (Correct answer)
Correct answer: Back to the original orientation
Four 90° clockwise rotations total 360°, returning the shape to its original orientation.
Question 7: In a 5×5 grid, how many unique paths exist from the top-left corner to the bottom-right corner if you can only move right or down?
- 48
- 56
- 70 (Correct answer)
- 64
Correct answer: 70
Moving from corner to corner in a 5×5 grid requires 4 rights and 4 downs; the number of paths is C(8,4) = 70.
Mensa Mensa IQ Spatial Reasoning and Patterns 5
A matrix has 3 rows and 3 columns.
Row 1: △ ○ □ | Row 2: ○ □ △ | Row 3: □ △ ? What shape belongs in the bottom-right cell?