Multi-Rule Patterns

By now you have learned about sequences, analogies, codes, and matrices. In all of these, you have seen that shapes can change according to rules. In easier questions there is usually just one rule. But in the trickiest CEM questions, two, three, or even four rules operate at the same time. This lesson teaches you how to handle multi-rule patterns with confidence.

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Why Multi-Rule Patterns Are Harder

When only one property changes, you can spot the rule quickly. But when multiple properties change simultaneously, it is easy to:

• Miss a rule (you spot one change but overlook another)
• Confuse the rules (you mix up which property follows which pattern)
• Lose track (you correctly identify the rules but make an error when applying them all)

The solution is to be systematic — track each property separately and combine the results at the end.

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The Property-Tracking Method

This is the most reliable strategy for multi-rule patterns:

Step 1: List the Properties

Write down (or think carefully about) every property that could change:

Property	What to track
Shape type	Circle, triangle, square, pentagon, etc.
Size	Large, medium, small
Shading	Black, white, grey, striped
Rotation	0, 45, 90, 135, 180 degrees, etc.
Border style	Solid, dashed, thick, thin
Internal elements	Dots, lines, crosses — how many and where
Position	Where is the shape or element within a box

Step 2: Track Each Property Across the Sequence

Create a mental (or written) table:

Step	Shape	Size	Shading	Dot position
1	Triangle	Large	Black	Top
2	Triangle	Small	White	Right
3	Triangle	Large	Black	Bottom
4	?	?	?	?

Step 3: Identify the Rule for Each Property

Property	Pattern	Next value
Shape	Same (triangle) throughout	Triangle
Size	Alternates: large, small, large	Small
Shading	Alternates: black, white, black	White
Dot position	Cycles clockwise: top, right, bottom	Left

Step 4: Combine

The answer is a small white triangle with a dot on the left.

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Worked Example 1 — Three Rules

A sequence of shapes in five boxes:

Box 1	Box 2	Box 3	Box 4	Box 5
Large black circle, 1 dot inside	Small grey triangle, 2 dots inside	Large white square, 3 dots inside	Small black pentagon, 4 dots inside	?

Tracking:

Property	Box 1	Box 2	Box 3	Box 4	Rule	Box 5
Shape (sides)	Circle (0)	Triangle (3)	Square (4)	Pentagon (5)	Sides: 0, 3, 4, 5 — increases by pattern	Hexagon (6)
Size	Large	Small	Large	Small	Alternates	Large
Shading	Black	Grey	White	Black	Cycles: black, grey, white	Grey
Dot count	1	2	3	4	Increases by 1	5

Answer: Large grey hexagon with 5 dots inside.

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Worked Example 2 — Matrix with Two Rules

	Column 1	Column 2	Column 3
Row 1	Large black circle	Large grey circle	Large white circle
Row 2	Medium black triangle	Medium grey triangle	Medium white triangle
Row 3	Small black square	Small grey square	?

Row rule 1 (shading): Each row goes black, grey, white.