Figure Series | 4th Std Scholarship · Intelligence Test

The turning arrow

From everyday life

The hand of a clock turns every day in the same direction and at a fixed speed. The arrow in a figure series also turns by a fixed angle.

Simple definition

In a figure series every figure is made from the one before by a fixed rule. The arrow turns by the same angle and in the same direction every time.

Turning of the arrow

Turn	Degrees
quarter turn	90°
half turn	180°
three-quarter turn	270°
one-eighth turn	45°

Rule 1

See by how many degrees and in which direction the arrow turned between the first two figures.

e.g. up → right : 90° clockwise.

Rule 2

Check that the same rule fits the third and the fourth figure.

e.g. right → down : again 90°.

Rule 3

Turn by the same angle once more to get the next figure.

e.g. down → left.

Rule 4

Compare the arrow of the answer with the arrows of the options; the option with the opposite turn is out.

e.g. an option that went anticlockwise is wrong.

Example 1 · easy

Which figure comes in place of ? in the series in the top row?

Rule : the arrow turns 90° clockwise at every step.
Option 1 is out : the arrow stayed the same.
Option 3 is out : the arrow went twice as far.
Option 4 is out : the arrow went the other way.
Answer : 2.

Example 2 · medium

Which figure comes in place of ? in the series in the top row?

Rule : the arrow turns 90° anticlockwise at every step.
Option 1 is out : the arrow went twice as far.
Option 2 is out : the arrow went the other way.
Option 3 is out : the arrow is wrong.
Answer : 4.

Example 3 · exam-style

Which figure comes in place of ? in the series in the top row?

Rule : the arrow turns 45° clockwise at every step.
Option 2 is out : the arrow went twice as far.
Option 3 is out : the arrow went the other way.
Option 4 is out : the arrow stayed the same.
Answer : 1.

Remember

First decide by how many degrees and in which direction the arrow turns; then find the next figure.

Common mistake

Looking only at the tip and forgetting to check the direction (clockwise or not).

Shortcut

Memory clue : "How many degrees, which way."

Shortcut

A 90° turn goes up → right → down → left; after four turns the arrow is back where it began.

Spot the difference

Rule	Order of the arrow
90° clockwise	up, right, down, left
90° anticlockwise	up, left, down, right
45° clockwise	up, slanted right, right ...

Practice questions

Easy

1 Which figure comes in place of ? in the top row?
2 Which figure comes in place of ? in the top row?
3 Which figure comes in place of ? in the top row?

Medium

4 Which figure comes in place of ? in the top row?
5 Which figure comes in place of ? in the top row?
6 Which figure comes in place of ? in the top row?

Challenging

7 Which figure comes in place of ? in the top row?
8 Which figure comes in place of ? in the top row?

Show answers (try them yourself first)

13 (the arrow turns 90° clockwise at every step).
22 (the arrow turns 90° anticlockwise at every step).
32 (the arrow turns 90° clockwise at every step).
43 (the arrow turns 45° clockwise at every step).
54 (the arrow turns 45° anticlockwise at every step).
63 (the arrow turns 135° clockwise at every step).
74 (the arrow turns 90° clockwise at every step).
82 (the arrow turns 135° anticlockwise at every step).

The symbol that changes place

From everyday life

In a bus queue everyone moves one step ahead. A symbol moves from place to place round the edge of the figure.

Simple definition

A symbol has four places : top, right, bottom, left. It moves in the same direction and by the same number of places every time.

Order of the places

Direction	Order
clockwise	top, right, bottom, left
anticlockwise	top, left, bottom, right

Rule 1

See where the symbol is in the first figure and where in the second.

e.g. top → right.

Rule 2

Decide by how many places and in which direction it moved.

e.g. top → right : one place clockwise.

Rule 3

If it moves two places it skips one place.

e.g. top → bottom → top.

Rule 4

Apply the same rule to get the next place and match it with the options.

e.g. bottom → left.

Example 1 · easy

Which figure comes in place of ? in the series in the top row?

Rule : the box moves one place(s) clockwise at every step.
Option 1 is out : the box stayed the same.
Option 3 is out : the box went the other way.
Option 4 is out : the box went twice as far.
Answer : 2.

Example 2 · medium

Which figure comes in place of ? in the series in the top row?

Rule : the box moves one place(s) anticlockwise at every step.
Option 2 is out : the box stayed the same.
Option 3 is out : the box went twice as far.
Option 4 is out : the box went the other way.
Answer : 1.

Example 3 · exam-style

Which figure comes in place of ? in the series in the top row?

Rule : the box moves one place(s) clockwise at every step; the outer shape alternates between circle and square.
Option 1 is out : the box stayed the same.
Option 3 is out : the box went twice as far.
Option 4 is out : the outer shape stayed the same.
Answer : 2.

Remember

First decide by how many places and in which direction the symbol moves.

Common mistake

Taking the direction the wrong way round; mixing clockwise with anticlockwise.

Shortcut

Memory clue : "Top, right, bottom, left : the clock order."

Shortcut

Get the rule from two figures, check it on the third; then find the answer.

Spot the difference

Rule	Step
one place	top, right, bottom, left
two places	top, bottom, top, bottom
other way	top, left, bottom, right

Practice questions

Easy

1 Which figure comes in place of ? in the top row?
2 Which figure comes in place of ? in the top row?
3 Which figure comes in place of ? in the top row?

Medium

4 Which figure comes in place of ? in the top row?
5 Which figure comes in place of ? in the top row?
6 Which figure comes in place of ? in the top row?

Challenging

7 Which figure comes in place of ? in the top row?
8 Which figure comes in place of ? in the top row?

Show answers (try them yourself first)

13 (the box moves one place(s) clockwise at every step).
21 (the box moves one place(s) anticlockwise at every step).
32 (the box moves one place(s) clockwise at every step).
43 (the box moves one place(s) clockwise at every step; the shaded part grows by one quarter at every step).
53 (the box moves one place(s) clockwise at every step; the outer shape alternates between circle and square).
62 (the box moves one place(s) anticlockwise at every step; the outer shape alternates between circle and square).
74 (the box moves one place(s) clockwise at every step; the arrow turns 90° clockwise at every step).
81 (the box moves one place(s) anticlockwise at every step; the arrow turns 90° anticlockwise at every step).

Dots that increase and decrease

From everyday life

On Diwali, if you light one more lamp every day, the number of lamps grows by one each day. The dots in a figure also grow or shrink like that.

Simple definition

The number of dots in a figure grows or shrinks by a fixed number every time. The dots always fill in the same order.

Rules for dots

Rule	Example
+1	1, 2, 3, 4
−1	5, 4, 3, 2
+2	1, 3, 5, 7

Rule 1

Count the dots in every figure.

e.g. 2, 3, 4, 5.

Rule 2

Find the difference between two figures : increase or decrease, and by how much.

e.g. 3 − 2 = 1 more.

Rule 3

Apply the same difference to the fourth number to get the next number.

e.g. 5 + 1 = 6.

Rule 4

Count the dots in the options; the option with that number is the answer.

e.g. the option with 6 dots.

Example 1 · easy

Which figure comes in place of ? in the series in the top row?

Rule : the dots increase by 1 at every step.
Option 2 is out : the dots stayed the same.
Option 3 is out : the dots went the other way.
Option 4 is out : the dots went twice as far.
Answer : 1.

Example 2 · medium

Which figure comes in place of ? in the series in the top row?

Rule : the dots decrease by 1 at every step.
Option 1 is out : the dots stayed the same.
Option 2 is out : the dots went the other way.
Option 3 is out : the dots is wrong.
Answer : 4.

Example 3 · exam-style

Which figure comes in place of ? in the series in the top row?

Rule : the dots increase by 1 at every step; the shaded part grows by one quarter at every step.
Option 1 is out : the dots went the other way.
Option 2 is out : the shaded part went the other way.
Option 4 is out : the dots is wrong.
Answer : 3.

Remember

Count the dots, find the difference and apply the same difference further.

Common mistake

Judging by eye; if you do not count carefully the difference goes wrong.

Shortcut

Memory clue : "Count, subtract, carry on."

Shortcut

Write the numbers of dots : seeing 2, 3, 4, 5 shows the +1 rule at once.

Spot the difference

Series	Rule
1, 2, 3, 4	+1
6, 5, 4, 3	−1
1, 3, 5, 7	+2

Practice questions

Easy

1 Which figure comes in place of ? in the top row?
2 Which figure comes in place of ? in the top row?
3 Which figure comes in place of ? in the top row?

Medium

4 Which figure comes in place of ? in the top row?
5 Which figure comes in place of ? in the top row?
6 Which figure comes in place of ? in the top row?

Challenging

7 Which figure comes in place of ? in the top row?
8 Which figure comes in place of ? in the top row?

Show answers (try them yourself first)

11 (the dots increase by 1 at every step).
22 (the dots decrease by 1 at every step).
34 (the dots increase by 1 at every step).
43 (the dots decrease by 1 at every step).
54 (the dots increase by 1 at every step; the shaded part grows by one quarter at every step).
64 (the dots decrease by 1 at every step; the outer shape alternates between circle and square).
73 (the dots increase by 1 at every step; the shaded part grows by one quarter at every step; the outer shape alternates between circle and square).
81 (the dots decrease by 1 at every step; the shaded part shrinks by one quarter at every step).

Shading and changing shapes

From everyday life

If you colour one more part of a picture every day, the whole picture slowly gets coloured. In a figure series one more part gets shaded or the outer shape changes turn by turn.

Simple definition

A figure has four parts (quarters). The shaded parts grow or shrink by a fixed number. The outer shape alternates between circle and square.

Rules for shading

Rule	Shaded parts
+1	0, 1, 2, 3
−1	4, 3, 2, 1
shape change	circle, square, circle, square

Rule 1

Count the shaded parts in every figure.

e.g. 1, 2, 3.

Rule 2

See whether the shading goes clockwise or the other way.

e.g. starts at the top right, then bottom right.

Rule 3

If the outer shape changes see that it alternates.

e.g. circle, square, circle, ? → square.

Rule 4

If two rules are together apply each rule separately.

e.g. shading +1 and shape alternating.

Example 1 · easy

Which figure comes in place of ? in the series in the top row?

Rule : the shaded part grows by one quarter at every step.
Option 1 is out : the shaded part is wrong.
Option 2 is out : the shaded part stayed the same.
Option 3 is out : the shaded part went the other way.
Answer : 4.

Example 2 · medium

Which figure comes in place of ? in the series in the top row?

Rule : the shaded part shrinks by one quarter at every step.
Option 1 is out : the shaded part went the other way.
Option 2 is out : the shaded part is wrong.
Option 3 is out : the shaded part stayed the same.
Answer : 4.

Example 3 · exam-style

Which figure comes in place of ? in the series in the top row?

Rule : the shaded part grows by one quarter at every step; the outer shape alternates between circle and square.
Option 2 is out : the shaded part went the other way.
Option 3 is out : the outer shape stayed the same.
Option 4 is out : the shaded part stayed the same.
Answer : 1.

Remember

Count the shading and check the outer shape separately; the two rules are independent.

Common mistake

Choosing an option after looking at only one of two rules.

Shortcut

Memory clue : "Count the colour, see the shape."

Shortcut

First apply the shape rule to strike out half of the options; then check the shading.

Spot the difference

Feature	Kind of rule
shaded parts	increase or decrease
outer shape	alternating
arrow	turning

Practice questions

Easy

1 Which figure comes in place of ? in the top row?
2 Which figure comes in place of ? in the top row?
3 Which figure comes in place of ? in the top row?

Medium

4 Which figure comes in place of ? in the top row?
5 Which figure comes in place of ? in the top row?
6 Which figure comes in place of ? in the top row?

Challenging

7 Which figure comes in place of ? in the top row?
8 Which figure comes in place of ? in the top row?

Show answers (try them yourself first)

11 (the shaded part grows by one quarter at every step).
21 (the shaded part shrinks by one quarter at every step).
33 (the shaded part grows by one quarter at every step).
43 (the shaded part grows by one quarter at every step; the outer shape alternates between circle and square).
53 (the shaded part shrinks by one quarter at every step; the outer shape alternates between circle and square).
62 (the shaded part grows by one quarter at every step; the arrow turns 90° clockwise at every step).
74 (the shaded part grows by one quarter at every step; the arrow turns 90° anticlockwise at every step; the outer shape alternates between circle and square).
83 (the shaded part shrinks by one quarter at every step; the arrow turns 45° clockwise at every step).

Symbol series, the wrong term and mixed questions

From everyday life

In a rangoli the same pattern comes again and again. A series of symbols is made likewise, by a group repeating or by a group that keeps growing.

Simple definition

A symbol series has two kinds of rules : a group repeats, or a group keeps growing. The wrong term is the term that does not fit the rule.

● ■ ▲ ● ■ ▲ ● ■ ▲ ●

Kinds of series

Kind	Example
repeating group	● ■ ▲ ● ■ ▲ ●
growing group	● ■ ● ● ■ ● ● ● ■
wrong term	● ■ ▲ ● ★ ▲ ● ■ ▲

Rule 1

See when the first symbol comes again; that is the length of the group.

e.g. ● ■ ▲ ● : a group of 3 symbols.

Rule 2

If the group repeats the next term is the next symbol of the group.

e.g. ● ■ ▲ ● ■ ? → ▲.

Rule 3

If a group of one symbol keeps growing count the gap between the two other symbols.

e.g. ● ■ ● ● ■ ● ● ● ■ : the groups of ● are 1, 2, 3.

Rule 4

To find the wrong term compare every term with the group; the one that does not fit is wrong.

e.g. ● ■ ▲ ● ★ ▲ : the 5th term ★ is wrong, ■ should be there.

Example 1 · easy

● ■ ▲ ● ■ ▲ ● ? Which symbol comes in place of ?

■ (the group ●■▲ repeats).

Example 2 · medium

◆ ■ ◆ ◆ ■ ◆ ◆ ◆ ■ ◆ ◆ ◆ ? Which symbol comes in place of ?

◆ (the group of ◆ grows by one each time and ■ follows each group).

Example 3 · exam-style

● ■ ★ ● ■ ★ ● ◆ ★ Which term of this series is wrong?

Term 8 (■ should be there in place of ◆).

Remember

Spot the group, decide whether it repeats or grows; the wrong term does not fit the group.

Common mistake

Counting the length of the group wrongly; count until the first symbol comes again.

Shortcut

Memory clue : "The group ends when the first symbol comes again."

Shortcut

To find a wrong term divide the series into boxes of the size of the group; the faulty box shows up easily.

Spot the difference

Series	Rule
● ■ ● ■ ● ■	group of 2 : ● ■
● ■ ● ● ■ ● ● ●	the group grows
● ■ ▲ ● ★ ▲	★ is wrong

Practice questions

Easy

1● ■ ● ■ ● ? Which symbol comes in place of ?
2● ★ ▲ ● ★ ▲ ● ? Which symbol comes in place of ?
3■ ● ★ ■ ● ★ ■ ? Which symbol comes in place of ?

Medium

4◆ ■ ○ ◆ ● ○ ◆ ■ ○ Which term of this series is wrong?
5● ▲ ● ● ▲ ● ● ● ? Which symbol comes in place of ?
6■ ◆ ● ○ ■ ◆ ● ○ ■ ? Which symbol comes in place of ?

Challenging

7 Which figure comes in place of ? in the top row?
8■ ◆ ▲ ■ ◆ ■ ■ ◆ ▲ ■ Which term of this series is wrong?

Show answers (try them yourself first)

1■ (the group ●■ repeats).
2★ (the group ●★▲ repeats).
3● (the group ■●★ repeats).
4Term 5 (■ should be there in place of ●).
5▲ (the group of ● grows by one each time and ▲ follows each group).
6◆ (the group ■◆●○ repeats).
71 (the arrow turns 90° clockwise at every step; the shaded part grows by one quarter at every step; the outer shape alternates between circle and square).
8Term 6 (▲ should be there in place of ■).

Quick revision of the whole lesson

Topic	Memory clue
Arrow	How many degrees, which way
Place of the symbol	top, right, bottom, left
Dots	Count, subtract, carry on
Shading and shape	Count the colour, see the shape
Symbol series	The group ends when the first symbol comes again

🎯 Most important points for the exam

In a figure series every figure is made by a fixed rule.
Arrow : decide by how many degrees and in which direction it turns.
Symbol : decide by how many places and in which direction it moves.
Count the dots and the shaded parts and find the difference.
If there is more than one rule apply each rule separately.
The wrong term is the term that does not fit the rule.

🧠 Study mantra

"Find the rule, apply the same rule further."