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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.
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.
Set A:
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.
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.
The fix: After identifying a rule, always ask: "Is there something ELSE going on?" Check the remaining SCANS categories.
A conditional rule is one where a feature of a shape depends on another feature. These take the form: "IF [condition], THEN [consequence]."
| Condition | Consequence |
|---|---|
| If the shape is large | Then it is black |
| If the shape is small | Then it is white |
| If the shape has an even number of sides | Then it is at the top of the box |
| If the shape has an odd number of sides | Then it is at the bottom of the box |
| If there are 3 or more shapes in the box | Then at least one is striped |
| If a shape is a circle | Then it is inside another shape |
They look inconsistent at first glance. In one box, a triangle is black; in another, a triangle is white. A candidate might think "colour is irrelevant because it changes" — but the colour is actually determined by size, not by shape type.
Use SCANS to identify the most obvious pattern. Verify it across all six boxes.
If the first rule explains everything, great. But if some boxes seem to have "extra" elements or features that are not explained by the first rule, there is a second rule.
Now that you know Rule 1, focus on features that Rule 1 does not address. For example:
Check that BOTH rules are satisfied in every box in the set. If they are, you have found the compound rule.
| Box | Contents |
|---|---|
| Box 1 | Large black circle, small white triangle |
| Box 2 | Large black square, small white pentagon |
| Box 3 | Large black hexagon, small white circle |
| Box 4 | Large black triangle, small white square |
| Box 5 | Large black pentagon, small white hexagon |
| Box 6 | Large black arrow, small white diamond |
Looking at number: every box has exactly 2 shapes. ✓
But "2 shapes per box" is quite simple. What else?
Rule 1: Every box has exactly 2 shapes Rule 2 (conditional): Large shapes are black; small shapes are white
Pick two boxes where one feature is the same but another feature differs:
Box 1: Large black circle, small white square Box 2: Large black triangle, small white hexagon
What is the same? Large shapes are black, small shapes are white. What differs? The shape types.
Conclusion: Colour depends on size, not on shape type. This is a conditional rule.
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