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Analogy (Figures)

Reasoning · Non-Verbal Reasoning

8 Part2 worked examples6 practice questions

In a word analogy you are asked “pen : write :: knife : ?”. In a figure analogy the words are replaced by figures: the second figure B has been made from the first figure A by some change. You must run the same change on the third figure C and choose the fourth figure (?).

It is a game of one question: “what happened to A?” — did it turn, flip, gain something, lose something, change colour, change size, or swap inner and outer? Say it in words, then do the same to C.

Every question here is built by computer. While building it was also checked that among all possible changes of the same kind (single ones and pairs of two) every one that turns A into B gives the same answer on C — so whichever sensible rule you think of, the answer is the same.

How to use this chapter

  1. Read — understand one kind of change at a time and learn to say it in words.
  2. Study the solved example — every example states the change in words and ends with a picture of the completed analogy.
  3. Try it yourself — say the change in your own words first, then choose.
  4. Know the level — Basic (one change), Standard (every kind), Advanced (two changes together).
NoteThe wrong options always hold three kinds of slips: C unchanged, a copy of B, and a half-done change. Get used to recognising them.
1

Foundation — how to catch the relation

Six kinds of change and a three-step method

The kinds of change in a figure analogy and a three-step method for every question.

Kinds of change

Turn · flip · add-remove · fill · size · swap

Six basic changes with a sample of each.

In each pair below the right figure was made from the left figure by one change. In order: a turn, a flip, a fill, a dot added, getting bigger, inner and outer swapping.

Six sample pairs (A → B in each)
ChangeHow to recogniseUsual step
TurnThe same figure facing another way; watch the pointed part45° · 90° · 135° · 180°
FlipLike a mirror; cannot be turned to match the originalleft-right / top-bottom
Add-removeA small part appeared or vanished insidea dot / a small shape
FillColoured ↔ emptythe outer or the inner part
SizeThe same figure, bigger or smallerbigger / smaller
Swap / sidesThe inner and outer shapes changed places, or a side was added or removedtriangle → square → pentagon
One side more: triangle to square
RememberA pair can hold two changes — such as turned and filled. In the “Advanced” questions this is what happens; then both must be run on C.
::?ABCD
Example 1 · Basic
B is related to A in a certain way. Which figure is related to C in the same way?
Solution, step by step
  1. 1From A to B: the figure turns 90° clockwise.
  2. 2Run the same change on C: the figure turns 90° clockwise.
  3. 3Answer C. The rest: A = the right kind of change but the wrong amount; B = the right kind of change but the wrong amount; D = the right kind of change but the wrong amount.
Answer Figure C
There was only one change, so saying it in words was easy.
::
The completed analogy
::?ABCD
BasicTry it yourself first
B is related to A in a certain way. Which figure is related to C in the same way?
::?ABCD
BasicTry it yourself first
B is related to A in a certain way. Which figure is related to C in the same way?
::?ABCD
BasicTry it yourself first
B is related to A in a certain way. Which figure is related to C in the same way?

The three-step method

Say it → run it on C → match the options

The order that works on every figure analogy and its check.

Three steps
1. Look at A and B carefully and say the change in words2. Run the same change on C and make your own figure in your head3. Find that figure among the options; before matching, cut the “copy” and the “unchanged” options

In step 1 watch all the parts, not just one: the outer shape, the inner mark, the colour, the size, the direction. Count what has changed; if two things changed both are part of the rule.

A check before step 2: can the change happen in C? (For example “remove the dot” works only if C has a dot.) Exam questions are made so that the change can be run on C.

Form of a wrong optionHow to catch it
C unchangedNothing changed — though A→B did change
A copy of BThis is the answer of the first pair, not of C
A half changeOnly one of the two changes ran
Wrong amount / direction45° instead of 90°, or the wrong way
NoteIf two changes seem to give the same result (such as a 180° turn and a flip left-right plus top-bottom) do not worry: they will also give the same result on C. Questions are built this way.
::?ABCD
Example 2 · Standard
B is related to A in a certain way. Which figure is related to C in the same way?
Solution, step by step
  1. 1From A to B: the main shape loses its colour (becomes empty).
  2. 2Run the same change on C: the main shape loses its colour (becomes empty).
  3. 3Answer B. The rest: A = a copy of B (the change from A→B was not applied to C); C = C unchanged; D = a different kind of change.
Answer Figure B
We stated the change, ran it on C and then matched the options.
::
The completed analogy
::?ABCD
BasicTry it yourself first
B is related to A in a certain way. Which figure is related to C in the same way?
::?ABCD
BasicTry it yourself first
B is related to A in a certain way. Which figure is related to C in the same way?
::?ABCD
StandardTry it yourself first
B is related to A in a certain way. Which figure is related to C in the same way?
2

Turning and flipping

Two changes of direction — learn to tell them apart

The angle and direction of a turn, the two forms of a flip and how they differ from a turn.

Turning

Track the pointed part

A trick for measuring the angle of a turn and a way to find its direction.

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Flipping

Left-right, top-bottom and the 180° turn

The two forms of a flip and how they differ from a turn.

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3

Adding-removing, shading and size

Changes inside the figure, in colour and in size

Adding and removing a dot, the change of shading and getting bigger or smaller.

Adding and removing

A mark came or went inside

When a small dot or mark is added to or removed from a figure.

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Change of shading

Coloured ↔ empty, outside or inside

The filling and emptying of the outer shape or of the inner mark.

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Change of size

Bigger ↔ smaller, the whole figure together

When the whole figure, with its inner marks, becomes bigger or smaller.

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4

Inside-outside and sides

A shape inside a shape: swapping, and gaining or losing a side

The swap of the outer and inner shapes and the change of sides of the outer shape.

Swapping inner and outer

The outer shape goes in and the inner one comes out

When the big shape becomes small and goes inside, and the inner shape becomes big and comes outside.

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Gaining and losing a side

Triangle → square → pentagon → hexagon

The change of the number of sides of the outer shape.

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5

Two changes together

Two rules in one pair and a firm check

When two changes turned A into B, and the check for a unique answer.

Two changes at once

Spot both and run both

Splitting a mixed change (such as turn + fill) into its parts.

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A firm check of the answer

Does no other rule fit?

What to do when more than one rule seems to fit, and the two-column check.

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6

Strategy guide

The order of checks and the slips to avoid

What to look at first in any figure analogy, common traps and time-savers.

The order of checks

What changed in A?

A straight order to follow for each kind of change.

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Common traps and time-savers

The mistakes that keep happening

The commonest reasons for losing marks in figure analogy.

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7

Mixed practice

All types mixed

Different kinds of change in three levels.

Basic practice

One change

Pairs with one change.

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Standard practice

Single changes of every kind

Every kind of change, one at a time.

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Advanced practice

Two changes together

Two changes in every pair.

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8

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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