Practice: Multi-Rule and Distractor Sets

This lesson brings together everything from this course: compound rules, conditional rules, distractors, counting patterns, spatial relationships, and the "Neither" trap. Each example is designed to challenge you with realistic, UCAT-level complexity. Work through them systematically, applying SCANS and the heuristics from the previous lesson.

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Example 1: Compound Rule with Distractors

Set A:

• Box 1: Two large black triangles, one small white circle (3 shapes; sides: 3+3+0 = 6)
• Box 2: One large black square, one small white pentagon, one large black hexagon (3 shapes; sides: 4+5+6 = 15)
• Box 3: Three large black circles, one small white triangle, two large black pentagons (6 shapes; sides: 0+0+0+3+5+5 = 13)
• Box 4: One large black rectangle, one small white diamond (2 shapes; sides: 4+4 = 8)
• Box 5: Two large black hexagons, one small white square, one large black triangle (4 shapes; sides: 6+6+4+3 = 19)
• Box 6: One large black pentagon, one small white rectangle, one large black circle (3 shapes; sides: 5+4+0 = 9)

Pause and try to identify the rule(s) before reading on.

Analysis

S (Shape): Various shapes — no consistent type. → Distractor

C (Colour): Every box has both black and white shapes. Looking more closely: large shapes are always black, small shapes are always white. → Potential rule!

A (Arrangement): No consistent positions. → Distractor

N (Number): Shape counts: 3, 3, 6, 2, 4, 3. Not constant, not consistently odd/even. Side totals: 6, 15, 13, 8, 19, 9. No obvious pattern. → Distractor

S (Size): Every box has at least one large and at least one small shape. Large shapes are always black, small shapes are always white. → Confirms the colour-size link.

Rule: Large shapes are always black. Small shapes are always white. Size determines shading.

Test shapes:

• One large white pentagon, one small black circle → Large is white (should be black) ✗ → Not Set A
• One large black hexagon, one small white triangle → Large is black ✓, small is white ✓ → Set A
• One medium grey square → Neither large-black nor small-white → Need to check if Set A accommodates medium shapes. None of the Set A boxes have medium shapes, so this is an unfamiliar size. → Likely Neither (or check Set B)

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Example 2: Conditional Rule

Set A:

• Box 1: Black circle, black triangle, black square (all black, circle present)
• Box 2: White pentagon, white hexagon, white rectangle (all white, no circle)
• Box 3: Black circle, black diamond, black arrow (all black, circle present)
• Box 4: White triangle, white square (all white, no circle)
• Box 5: Black circle, black pentagon (all black, circle present)
• Box 6: White hexagon, white arrow, white diamond, white rectangle (all white, no circle)

Set B:

• Box 1: Black triangle, white circle, grey pentagon (mixed colours, circle present but not all black)
• Box 2: Grey square, black hexagon, white arrow (mixed colours, no circle)
• Box 3: White circle, black diamond (circle present but white, not all black)
• Box 4: Black pentagon, grey triangle, white square (mixed, no circle)
• Box 5: Grey circle, black rectangle (circle present but grey)
• Box 6: Black arrow, white hexagon, grey triangle (mixed, no circle)

Pause and identify the rule.

Analysis

Set A: When a circle is present, all shapes are black. When no circle is present, all shapes are white. This is a conditional rule: "IF circle present, THEN all shapes are black. IF no circle, THEN all shapes are white."

Alternatively stated: "Boxes either contain a circle with all-black shapes, or no circle with all-white shapes." The common thread is uniform shading — all shapes in each box are the same colour.

Set B: Colours are mixed within boxes. No uniform shading pattern.

Revised, simpler rule:

• Set A: All shapes in each box are the same colour (all black or all white)
• Set B: Shapes are mixed colours (at least two different shadings)

The circle-colour correlation is a red herring within Set A — the actual rule is simply uniform vs mixed shading.

Lesson within the lesson: Always look for the simplest explanation. The conditional "if circle then black" is more complex than "all shapes are the same colour." UCAT questions use the simplest rule that fits.

Test shapes:

• Three grey hexagons → All same colour (grey) → Set A
• One black square, one white triangle → Mixed → Set B
• One black circle → Single shape, uniform by definition → Set A

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Example 3: Counting Rule with "Neither" Trap

Set A:

• Box 1: Triangle (3) + Pentagon (5) + Square (4) = 12 sides
• Box 2: Three squares (4+4+4) = 12 sides
• Box 3: Hexagon (6) + Hexagon (6) = 12 sides
• Box 4: Four triangles (3+3+3+3) = 12 sides
• Box 5: Pentagon (5) + Hexagon (6) + Circle (0) + Triangle (3? — wait, 5+6+0 = 11, not 12)

Let me fix: Pentagon (5) + Pentagon (5) + Circle (0) + two sides? No. Let me use: Hexagon (6) + Triangle (3) + Triangle (3) = 12 ✓

• Box 6: Square (4) + Pentagon (5) + Triangle (3) = 12

Set B:

• Box 1: Triangle (3) + Triangle (3) + Triangle (3) + Triangle (3) + Triangle (3) = 15 sides
• Box 2: Pentagon (5) + Pentagon (5) + Pentagon (5) = 15 sides
• Box 3: Hexagon (6) + Pentagon (5) + Square (4) = 15 sides
• Box 4: Three pentagons (15) ✓ — same as Box 2, let me vary: Hexagon (6) + Hexagon (6) + Triangle (3) = 15 sides
• Box 5: Pentagon (5) + Hexagon (6) + Square (4) = 15 sides
• Box 6: Five triangles (3×5) = 15 sides

Rule A: Total sides = 12. Rule B: Total sides = 15.

Test shapes:

• Two hexagons (12) → Set A
• Five triangles (15) → Set B
• One pentagon + one hexagon (11) → Not 12, not 15 → Neither
• One hexagon + one pentagon + one square (6+5+4=15) → Set B
• One triangle + one circle (3+0=3) → Not 12, not 15 → Neither

"Neither" is very common with specific-number rules because most random combinations will not hit the exact target.