Practice: Single-Rule Sets
This lesson puts your knowledge into action with worked examples of single-rule sets — questions where one attribute alone distinguishes Set A from Set B. These are the foundation. Once you can consistently identify single rules in under 10 seconds, you are ready for the compound rules and distractors covered in the next course.
Each example below follows the same structure: the sets are described, you are invited to identify the rule yourself, and then a full explanation follows.
Example 1: Shape Presence
Set A:
- Box 1: One circle, two squares, one triangle
- Box 2: Three circles, one pentagon
- Box 3: One circle, one hexagon, two rectangles
- Box 4: Two circles, one diamond
- Box 5: One circle, four triangles
- Box 6: One circle, one arrow, one star
Set B:
- Box 1: Two triangles, one square, one pentagon
- Box 2: Three hexagons, two rectangles
- Box 3: One arrow, one diamond, one star
- Box 4: Four squares
- Box 5: One pentagon, two triangles, one hexagon
- Box 6: Two rectangles, one arrow
Pause here. Can you identify the rule before reading on?
Solution
Apply SCANS:
- S (Shape): Set A — every box contains at least one circle. Set B — no box contains a circle.
- That is the rule. No need to check further.
Rule A: At least one circle present. Rule B: No circle present.
Test shapes:
- A box with two squares and one circle → Set A (contains a circle)
- A box with three pentagons → Set B (no circle)
- A box with one semi-circle and two triangles → Is a semi-circle a circle? In UCAT, semi-circles are typically treated as distinct from circles. If no full circle is present → Set B (assuming the rule specifically requires a full circle)
Example 2: Shading Proportion
Set A:
- Box 1: Three black shapes, one white shape
- Box 2: Two black shapes, one white shape
- Box 3: Four black shapes, one white shape
- Box 4: Five black shapes, two white shapes
- Box 5: Two black shapes, one white shape
- Box 6: Three black shapes, one white shape
Set B:
- Box 1: One black shape, three white shapes
- Box 2: One black shape, two white shapes
- Box 3: Two black shapes, four white shapes
- Box 4: One black shape, one white shape, two grey shapes
- Box 5: One black shape, four white shapes
- Box 6: Two black shapes, three white shapes
Pause here. What is the rule?
Solution
Apply SCANS:
- S (Shape): Varies randomly in both sets. Not the rule.
- C (Colour): In Set A, black shapes outnumber white shapes in every box. In Set B, white shapes outnumber black shapes in every box (or at least are not outnumbered by black — but wait, Box 4 has grey shapes too).
Let me re-check Set B Box 4: one black, one white, two grey. Black does not outnumber non-black (1 < 3), so this fits if the rule is "black does not outnumber non-black." But actually the pattern in Set A is cleaner: black > white in every case.
For Set B: Box 1 (1 < 3), Box 2 (1 < 2), Box 3 (2 < 4), Box 4 (1 < 3 non-black), Box 5 (1 < 4), Box 6 (2 < 3). In every case, white (or non-black) outnumber black.
Rule A: More black shapes than white shapes. Rule B: More non-black shapes than black shapes.
Test shape: Two black circles, two white triangles, one grey square.
- Black (2) vs non-black (3) → black does not outnumber → Not Set A
- Non-black (3) outnumber black (2) → Set B
Example 3: Total Side Count (Odd vs Even)
Set A:
- Box 1: Triangle (3) + Square (4) = 7 (odd)
- Box 2: Pentagon (5) + Circle (0) = 5 (odd)
- Box 3: Hexagon (6) + Triangle (3) = 9 (odd)
- Box 4: Triangle (3) + Triangle (3) + Triangle (3) = 9 (odd... wait, that is odd? 9 is odd ✓)
- Box 5: Square (4) + Pentagon (5) + Circle (0) = 9 (odd)
- Box 6: Hexagon (6) + Pentagon (5) = 11 (odd)
Set B:
- Box 1: Square (4) + Square (4) = 8 (even)
- Box 2: Triangle (3) + Pentagon (5) = 8 (even)
- Box 3: Hexagon (6) + Square (4) = 10 (even)
- Box 4: Circle (0) + Square (4) + Hexagon (6) = 10 (even)
- Box 5: Pentagon (5) + Triangle (3) + Square (4) = 12 (even)
- Box 6: Two hexagons (6 + 6) = 12 (even)
Solution
Rule A: Total sides is odd. Rule B: Total sides is even.
Test shapes:
- One triangle and one square (3 + 4 = 7, odd) → Set A
- Two pentagons (5 + 5 = 10, even) → Set B
- One circle alone (0, even) → Set B
- One triangle alone (3, odd) → Set A
Example 4: Fixed Position
Set A:
- Box 1: A small black triangle in the top-left corner; one large white circle in the centre; one medium grey square bottom-right
- Box 2: A small black triangle in the top-left corner; two large white hexagons
- Box 3: A small black triangle in the top-left corner; one large grey pentagon, one small white diamond
- Box 4: A small black triangle in the top-left corner; three medium white circles
- Box 5: A small black triangle in the top-left corner; one large black rectangle
- Box 6: A small black triangle in the top-left corner; two small grey arrows