5.3 Classification
Key Takeaways
- Classification asks you to GROUP figures by a shared property, not exclude one — typically sort four or five figures into those that satisfy the rule and those that do not.
- Common classification properties: shape family (quadrilateral vs triangle), symmetry (number of lines of symmetry), element count, and orientation family.
- Classification differs from odd-one-out: odd-one-out finds the single breaker of a 3-vs-1 rule; classification reports the full grouping for every figure.
- State the rule as a countable property before sorting — vague impressions like 'roundish' or 'pointy' produce unreliable groups on PAF items.
5.3 Classification
Quick Answer: Classification gives you a handful of figures and asks which ones share a stated or implied property — for example, 'which figures are quadrilaterals?' State the rule as a countable property, then sort every figure into the matching group or the non-matching group. Unlike odd-one-out, you are grouping, not excluding a single breaker.
Classification is the third non-verbal item type on the PAF GD Pilot Initial Test. It looks similar to odd-one-out but the task is different: instead of picking the one figure that breaks a rule, you sort the set into groups based on a shared property. The question may name the property ('which of these are quadrilaterals?') or may ask you to identify the property that best sorts the set.
Classification vs Odd-One-Out
The two item types are easy to confuse. The table below makes the distinction explicit.
| Aspect | Odd-One-Out | Classification |
|---|---|---|
| Task | Find the ONE figure that breaks the rule | GROUP all figures by a shared property |
| Typical split | 3 vs 1 | Often 2 vs 2, 3 vs 2, or 'all that share X' |
| Output | A single figure | A subset (sometimes two subsets) |
| Rule direction | Find the rule after seeing the split | Rule may be given; sort figures into it |
Common Classification Properties
The properties that drive PAF classification items are the same ones used for odd-one-out, but applied to the whole set rather than to a 3-vs-1 split.
| # | Property | Example rule | How to test |
|---|---|---|---|
| 1 | Shape family | Quadrilaterals vs non-quadrilaterals | Count sides of the main shape |
| 2 | Symmetry count | 2 lines of symmetry vs 1 line vs 0 lines | Count fold axes |
| 3 | Element count | Figures with 3 internal elements vs 2 | Count small shapes inside each figure |
| 4 | Orientation family | Upward-pointing vs downward-pointing | Compare the main axis direction |
| 5 | Closed vs open | Closed outlines vs open curves | Check whether the outline is a complete loop |
Worked Example 1 — Shape Family
Figures described in words: A is a square, B is a triangle, C is a rectangle, D is a pentagon, E is a parallelogram.
Question: which figures are quadrilaterals?
State the rule as a countable property: 'a quadrilateral has exactly four sides.' Now sort each figure:
- A (square) — 4 sides — quadrilateral
- B (triangle) — 3 sides — not a quadrilateral
- C (rectangle) — 4 sides — quadrilateral
- D (pentagon) — 5 sides — not a quadrilateral
- E (parallelogram) — 4 sides — quadrilateral
The matching group is {A, C, E}. The non-matching group is {B, D}.
Worked Example 2 — Symmetry Count
Figures described in words: A is a square, B is a rectangle, C is an equilateral triangle, D is a scalene triangle, E is a circle.
Question: group the figures by number of lines of symmetry.
Count fold axes for each:
- A (square) — 4 lines of symmetry
- B (rectangle) — 2 lines of symmetry
- C (equilateral triangle) — 3 lines of symmetry
- D (scalene triangle) — 0 lines of symmetry
- E (circle) — infinite lines of symmetry
Groups: {A: 4}, {B: 2}, {C: 3}, {D: 0}, {E: infinite}. A common PAF follow-up asks which figure has the MOST lines of symmetry — the circle (E), because its symmetry count is unbounded.
Worked Example 3 — Closed vs Open
Figures described in words: A is a circle, B is a U-shape (open at the top), C is a triangle, D is a spiral that does not close, E is a square.
Question: which figures are closed outlines?
- A (circle) — closed loop — closed
- B (U-shape) — open at the top — not closed
- C (triangle) — closed loop — closed
- D (spiral) — does not return to its start — not closed
- E (square) — closed loop — closed
The closed group is {A, C, E}. The open group is {B, D}.
Worked Example 4 — Orientation Family
Figures described in words: All four figures are identical arrows. A points up, B points up, C points down, D points up-right.
Question: which figures point upward (within 45° of vertical)?
- A — up — upward family
- B — up — upward family
- C — down — not upward
- D — up-right — within 45° of vertical — upward family
The upward group is {A, B, D}. The non-upward group is {C}.
The Vague-Impression Trap
Like odd-one-out, classification distractors exploit vague impressions. 'Roundish' is not a property; 'closed curve with no corners' is. 'Pointy' is not a property; 'three vertices' is. Always state the rule as a countable or fold-testable property before sorting. If you cannot state it as a property, you are guessing on looks and PAF distractors are built to punish exactly that.
A Mermaid View of the Method
The flow below shows the classification process: state the rule as a property, test every figure, then report the groups.
Given figures A square, B triangle, C rectangle, D pentagon, E parallelogram: which are quadrilaterals?
Given A square, B rectangle, C equilateral triangle, D scalene triangle, E circle: which figure has the MOST lines of symmetry?
Given A circle, B U-shape open at top, C triangle, D spiral that does not close, E square: which figures are closed outlines?
Four identical arrows: A points up, B points up, C points down, D points up-right. Which figures belong to the upward-pointing family (within 45° of vertical)?