UDEE Figural Reasoning and Patterns 3 — Questions and Answers

Question 1: A sequence shows shapes alternating between filled and outlined: filled circle, outlined circle, filled square, outlined square, filled triangle, ? What comes next?

Outlined triangle (Correct answer)
Filled triangle
Outlined circle
Filled pentagon

Correct answer: Outlined triangle

The pattern alternates filled then outlined for each shape. After filled triangle comes outlined triangle.

This tests dual-variable pattern recognition: shape type (circle, square, triangle repeating) and fill state (filled, outlined alternating). The sequence: filled circle → outlined circle → filled square → outlined square → filled triangle → outlined triangle. After a filled shape always comes an outlined version of the same shape. The next element is outlined triangle. Tracking two variables simultaneously is a core UDEE figural reasoning skill.

Question 2: In a number pattern displayed visually: Row 1 has 1 dot; Row 2 has 3 dots; Row 3 has 6 dots; Row 4 has 10 dots. How many dots are in Row 5?

15 (Correct answer)
13
12
14

Correct answer: 15

The differences between rows are +2, +3, +4, +5. Row 5 = 10 + 5 = 15 dots.

This is the triangular number sequence: 1, 3, 6, 10, 15. Differences: 1→3 (+2), 3→6 (+3), 6→10 (+4), 10→15 (+5). Each difference increases by 1. Row 5 adds 5 dots to Row 4's 10, yielding 15. Visual dot arrangements in rows test spatial-numerical reasoning — candidates must count accurately and extract the second-order pattern (the pattern of differences).

Question 3: An officer studies a series of maps. Each map shows a patrol route represented by lines. In map 1, the route has 4 turns. In map 2, it has 6 turns. In map 3, it has 8 turns. In map 4, how many turns does the route have?

10 (Correct answer)
9
11
12

Correct answer: 10

The pattern adds 2 turns per map: 4, 6, 8, 10. Map 4 has 10 turns.

Arithmetic sequence: 4, 6, 8 — each step increases by 2. The next term: 8 + 2 = 10. In the context of figural/diagrammatic reasoning, this type of question presents the information visually (as patrol route maps) and requires extracting the numerical rule from a visual sequence. The ability to identify consistent arithmetic progressions is a standard UDEE figural reasoning competency.

Question 4: A figure shows a square divided into 4 equal quadrants. In step 1, the top-left quadrant is shaded. In step 2, top-right is shaded. In step 3, bottom-right is shaded. In step 4, which quadrant is shaded?

Bottom-left (Correct answer)
Top-left
Bottom-right
Top-right

Correct answer: Bottom-left

The shading moves clockwise: top-left → top-right → bottom-right → bottom-left.

Clockwise movement through four quadrants: top-left (NW) → top-right (NE) → bottom-right (SE) → bottom-left (SW). This is a complete clockwise cycle. Step 4 shades the bottom-left quadrant. Spatial tracking of position movement through a defined clockwise sequence tests a candidate's ability to mentally simulate rotational or sequential movement — a skill required for surveillance, navigation, and tactical awareness.

Question 5: In a visual analogy: Circle is to Sphere as Square is to:

Cube (Correct answer)
Rectangle
Cylinder
Pyramid

Correct answer: Cube

A circle extended to 3D becomes a sphere; a square extended to 3D becomes a cube.

Visual analogies test abstract relational reasoning: what is the relationship between circle and sphere? A sphere is the 3-dimensional version of a circle — a circle 'extended' or 'rotated' into three dimensions. Applying this rule: what is the 3D version of a square? A cube — six square faces, equal dimensions in all three directions. A cylinder is the 3D version of a rectangle (not a square). Pyramid has a square base but is not the 3D equivalent in the same way.

Question 6: A grid pattern shows: Row 1 → ▲ ▲ ▲; Row 2 → ▲ ▲ ▲ ▲; Row 3 → ▲ ▲ ▲ ▲ ▲; Row 4 → ? How many triangles are in Row 4?

6 (Correct answer)
5
7
8

Correct answer: 6

Each row adds one triangle: 3, 4, 5, 6. Row 4 has 6 triangles.

Arithmetic sequence in a visual grid: Row 1 = 3, Row 2 = 4, Row 3 = 5. Each row increases by 1. Row 4 = 5 + 1 = 6 triangles. This is a foundational figural reasoning pattern — extracting a linear arithmetic rule from a visual array. Simple but requires accurate counting and the ability to abstract a rule from a visual pattern rather than a written number sequence.

UDEE Figural Reasoning and Patterns 3

A sequence shows shapes alternating between filled and outlined: filled circle, outlined circle, filled square, outlined square, filled triangle, ? What comes next?