Conditional and Compound Rules

The most challenging AR questions are those that use conditional rules (where one feature depends on another) or compound rules (where two or more independent rules operate simultaneously). These questions are where strong candidates pull ahead — they are too complex to solve by instinct alone and require a systematic, methodical approach.

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What Are Compound Rules?

A compound rule is simply two or more independent rules that both apply to every box in a set. Each rule, on its own, would be straightforward. Together, they create apparent complexity.

Example of a Compound Rule

Set A:

• Rule 1: Every box contains exactly 3 shapes
• Rule 2: The shapes in every box alternate in colour (black-white-black or white-black-white)

Both rules must be satisfied simultaneously. A box with 3 shapes that are all black violates Rule 2. A box with 4 alternating-colour shapes violates Rule 1.

Why Compound Rules Are Tricky

Most candidates find one rule and stop looking. They then encounter a test shape that satisfies Rule 1 but violates Rule 2, and they incorrectly assign it to the set.