Common Pattern Categories

The single most important thing you can do to improve your Abstract Reasoning score is to learn the pattern categories. Every AR question is built around one or more of these categories. If you have a systematic checklist of what to look for, you can work through it rapidly and identify patterns that would otherwise take minutes of unfocused staring.

This lesson introduces the SCANS framework — a mnemonic that covers the five main categories of patterns you will encounter.

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The SCANS Framework

Shape — Colour — Arrangement — Number — Size

Each letter represents a category of features that test designers use to construct rules. When you look at a set of shapes and cannot immediately see the pattern, work through SCANS systematically.

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S — Shape

Shape-based rules focus on the type of shapes present in each box.

What to Check

Feature	Examples
Shape type	All boxes contain at least one triangle; all boxes contain a curved shape
Number of sides	All shapes have 4+ sides; total sides in each box is always 10
Straight vs curved	Set A has only straight-sided shapes; Set B has at least one curved shape
Regular vs irregular	All shapes are regular polygons (equal sides and angles)
Specific shapes	Every box contains exactly one arrow; every box has a star
Open vs closed	Some shapes are open (like an angle bracket < ) vs closed (like a triangle)

Common Shape Rules

• Every box contains at least one shape with exactly 5 sides
• The total number of sides across all shapes in each box equals a specific number
• All shapes in Set A are curved; all shapes in Set B are straight-sided
• Every box contains exactly one of: triangle, square, pentagon, or hexagon
• Shapes in Set A have an odd number of sides; shapes in Set B have an even number of sides

Worked Example

Set A boxes contain: a triangle and two circles; a pentagon and a square; three triangles; a hexagon; a triangle and a rectangle; a pentagon and a circle.

What is the rule? Look at the total number of straight-sided shapes in each box:

• Triangle (1) + two circles (0) = 1 straight-sided shape → Hmm, let us try a different approach
• Count total sides: 3 + 0 + 0 = 3; 5 + 4 = 9; 3 + 3 + 3 = 9; 6; 3 + 4 = 7; 5 + 0 = 5
• These are all odd numbers! The rule is: the total number of sides in each box is odd

This illustrates an important principle: the rule is often not about individual shapes but about a numerical property of the shapes combined.

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C — Colour (Shading and Fill)

Colour-based rules focus on the fill or shading of shapes.

What to Check

Feature	Examples
Fill types	Black (solid), white (empty/outline), grey, striped/hatched, dotted
Number of each fill	Each box has exactly 2 black shapes and 1 white shape
Proportion	More black shapes than white in every box
Consistent fills	All shapes in a box are the same colour
Conditional fills	Large shapes are always black; small shapes are always white
Alternating fills	Shapes alternate black-white-black around the box

Common Colour Rules

• Each box contains exactly one black, one white, and one grey shape
• The largest shape is always black
• Circles are always striped; squares are always solid
• The number of black shapes equals the number of white shapes in every box
• All shapes are the same shade within each box (but the shade varies between boxes)

Worked Example

Set A boxes contain shapes with these fills: (black, white, grey); (grey, black, white); (white, grey, black); (black, grey, white)

What is the rule? Every box contains exactly three shapes: one black, one white, and one grey. The rule is about having one of each fill type.

Conditional Colour Rules

These are trickier rules where the colour depends on another property:

• If a shape has 4 or more sides → it is black; if fewer than 4 sides → it is white
• The shape in the top half of the box is always the opposite colour to the shape in the bottom half
• Shapes with an even number of sides are grey; shapes with an odd number are striped

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A — Arrangement (Position, Orientation, Symmetry)

Arrangement-based rules focus on where shapes are placed and how they are oriented.

What to Check

Feature	Examples
Position	A specific shape is always in the top-right corner; shapes are always along the diagonal
Orientation	Arrows always point clockwise; triangles always point upward
Symmetry	The arrangement has a line of symmetry (vertical, horizontal, or diagonal)
Relative position	The circle is always above the square; small shapes are always inside large shapes
Overlap	Shapes do or do not overlap
Touching	Shapes do or do not touch each other
Containment	One shape is always inside another

Common Arrangement Rules