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Classification (Figures)

Reasoning · Non-Verbal Reasoning

7 Part1 worked examples4 practice questions

Imagine five children standing in a row. Four wear red caps and one wears a blue cap. You would say at once that the blue-cap child is “different”. Figure classification questions ask for exactly this — only instead of children there are five figures, and instead of a cap there is a hidden property.

In the exam you get five figures named A to E. Four of them share a property (say, five sides each) and one does not. Your job is to find that property and pick the odd figure. The property is never announced — that is the real challenge.

In this chapter we learn, one by one, the properties that are tested again and again. For each property you first see how to check it, then a fully solved example, then questions to practise. Every figure set was built by counting, so each question has exactly one correct answer.

The checklist of properties

CheckWhat you look atWhere to read
Sides / pointsHow many straight edges or star pointsPart 2
Lines and closed partsTotal straight lines, enclosed partsPart 2
Shaded partsShaded cells, or the shaded fractionPart 2
SymmetryFold lines along which the halves matchPart 3
Open / closed, straight / curvedThe nature of the outlinePart 3
Dots, mirror image, relationsPosition, direction and the link between two countsPart 4
NoteFollow this order in every question: look at all five → pick a property that seems common to four → test it on all five → choose the odd one. If the first property fails, try the next one; the checklist is there for this.

How to use this chapter

  1. Read — each part first explains a property and shows how to check it.
  2. Study the solved example — the “Example” box has the question figures first, then the step-by-step solution, and last the same figures with the counts written under them.
  3. Try it yourself — in “Try it yourself first” look at the figures and choose from (A)–(E). The solution is hidden; take the hint if stuck and open the solution only at the end.
  4. Know the level — Basic, Standard, Advanced; make the basic ones solid first.
1

Foundation — what does “different” mean?

Find the property, catch the difference, ignore the decoration

What an odd figure is, the order of the search, and how to ignore decorations such as size and tilt.

What an odd figure is and how to find it

A property shared by four, missing in one

The definition of an odd figure and a four-step search method.

A property is something you can count or test: the number of sides, the number of lines, the shaded parts and so on. The odd figure is the one whose value of this property differs from the other four. In the figures below the property is “number of sides”; the count is written under every figure.

A5B3C5D5E5
Four figures show the same number; the one that differs has the orange frame
Four steps of the search
1. Look at all five figures at a glance2. Pick a property (sides? lines? shaded parts?)3. Count or test it in all five4. The one that stands alone is the answer
CheckA property is right only when it comes out the same in exactly four figures. If the split is two–two or three–two, this is not the property — try another one.
ABCDE
Figures A to E
Example 1 · Basic
Which one of the five figures above is different from the other four?
Solution, step by step
  1. 1Count the sides (straight edges) of every figure. Put a finger on one corner and go round once.
  2. 2A: 3 · B: 3 · C: 3 · D: 3 · E: 4
  3. 3E has 4, while the other four have 3. So E is the odd one.
Answer E
The sizes and turns differ, but counting the sides leaves no confusion.
A3B3C3D3E4
Solved figure: the count under every figure; the odd one has the orange frame
ABCDE
Figures A to E
BasicTry it yourself first
Which one of the five figures above is different from the other four?
ABCDE
Figures A to E
BasicTry it yourself first
Which one of the five figures above is different from the other four?

Ignoring the decoration

Size, tilt, place and colour are not differences

Which changes are not real differences, and what tricks the eye.

In the exam the figures are deliberately shown differently — one big, one small, one tilted. These changes are decoration. If you pay attention to them, every figure will look different and you will miss the real property.

Changes that do NOT matterChanges that DO matter
Making it bigger or smallerA side or line added or removed
Turning (tilting)The number of shaded parts changing
Moving to another placeFlipping (a mirror image) — this is a difference, see later
Same build with a different kind of shape (a rectangle for a square when the property is only sides)A dot moving from inside to outside
A6B6C7D6E6
Every figure differs in size and tilt, yet the odd one is caught at once by the number of sides

Another trick is appearance: sometimes a figure looks like the others but has one side more or less. So choose the answer by counting, not just by looking.

ABCDE
Figures A to E
StandardTry it yourself first
Which one of the five figures above is different from the other four?
ABCDE
Figures A to E
BasicTry it yourself first
Which one of the five figures above is different from the other four?
2

Properties you count

Sides, points, lines, closed parts and shaded parts

The most frequently asked properties — they only need careful counting.

Sides and star points

Count corner by corner

A safe way to count the sides of a polygon and the points of a star.

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Lines and small shapes

Every straight piece is a line, every separate piece a shape

Three ways lines appear and how to count scattered small shapes.

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Closed parts (enclosed regions)

Into how many small rooms do the lines divide the figure?

How to count closed parts and the formula-like shortcuts.

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Shaded parts and the fraction shaded

How many are shaded — and what fraction of the whole?

Counting shaded parts, and recognising equal fractions in different divisions.

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3

Build and symmetry

What is the outline like? Do the halves match when folded?

Open or closed, straight or curved lines, and counting lines of symmetry.

Open or closed, straight or curved

Run a finger along the line

Two properties based on the outline, and a simple way to test them.

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Lines of symmetry

Fold it — if the two halves match exactly, that line is a line of symmetry

What a line of symmetry means, how to test it by folding and a table for common figures.

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4

Position, direction and relations

What sits where, which way it faces and how counts are linked

The position of dots, mirror images and the rule linking two counts.

Inside and outside

Equal in total, different in place

Finding the odd figure by counting which dots are inside and which are outside.

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Turning versus flipping (mirror image)

What matches by turning is the same; what matches only by flipping is different

How to recognise a mirror image and which figures change when flipped.

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The link between two counts

The same link in every figure — broken in one

When two counts such as sides and dots are tied by a rule.

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5

Strategy guide

Which property to test first and where the tricks are

The order for spotting the property, first-glance clues and common mistakes.

The order for spotting the property

From the first glance to the right property

A table telling which property to test from what you see.

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Common traps and time-savers

The mistakes that keep happening

The commonest reasons for losing marks in figure classification and how to avoid them.

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6

Mixed practice

All properties mixed — first spot the property, then solve

Questions on different properties together, in three levels.

Basic practice

One direct property, a clear difference

Direct questions on sides, lines, parts, shaded parts, symmetry and build.

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Standard practice

Differences of one, lopsided figures, fractions

Neighbouring counts, lopsided polygons, fractions and dots in and out.

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Advanced practice

Fine differences and links between two counts

Seven and eight sides, harder symmetry, turned mirror images and questions on relations.

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7

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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