Mensa Mensa IQ Spatial Reasoning and Patterns 5

Question 1

A matrix has 3 rows and 3 columns. Row 1: △ ○ □ | Row 2: ○ □ △ | Row 3: □ △ ? What shape belongs in the bottom-right cell?

Accepted Answer

Circle

Answer

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?

Accepted Answer

30

Answer

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?

Accepted Answer

40

Answer

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?

Accepted Answer

Cylinder

Answer

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?

Accepted Answer

White

Answer

Even-numbered positions are white in this alternating pattern, and 44 is even, so the 44th triangle is white.

Mensa Practice Test

Mensa Practice Test

Mensa Mensa IQ Spatial Reasoning and Patterns 5