Quicknotes on Series Test

Series

Here , In this Page How to Solve Number Series Questions Quickly is given.

Number system is the standard of representing numbers . The same sequence of numbers or symbols may represent different value of numbers in different numeral systems.

In this Page different Types of Questions is also given.

Solving Number Series Questions Effectively Tips and Tricks

On this page you will find the easiest and most effective way to solve any number series. You never will need any other resource to study.

There are following types of number Series patterns –

Numeric Number Series (This page)
Alphabet Series (Visit Alphabet Series Page)
Alpha Numeric Series(Not asked in Placements, only in CAT exam)

There are the following most popular number series, We will discuss all these in details here we are just introducing them to you, so don’t worry if you don’t see the pattern just yet, after this post you will be able solve any Number Series Question in the world .

Types of Number Series Problems –

Add up Series (+) : Just adding a constant number everytime. For example: (13, 18, 23, 28 ….).
Add up Series (- ): , Just subtracting a constant number every time. For example : (28, 23, 18, 13 ……).
Step up Series (+/-) : Adding/Subtracting a variable number, in this case we are adding 2n for n = 0, 1, 2, 3 …… For example : 0, 2, 6, 12, 20…. or 20, 12, 6, 2, 0, 0 …..
Square up (+/-) – Given series is in the square of n where n= 1,2,3,4,5,6… i.e. 1,4,9,16,25,36…
Square add up Series(+/-) : Adding n² every time and incrementing value of n starting from 1 i.e. 1,5, 14, 30, 55, …… and Subtracting n² every time and decrementing value of n i.e. 34, 33, 29, 20,
Cube Up Series : Given series is in the cube of n where n = 1,2,3,4,5,6… i.e. 1,8,27,64,125,216….
Cube add up Series : Adding n³ every time with incrementing of n by 1 i.e. 1,9,36…
Prime up(+/-) : Sequence consist of Prime numbers i.e. 2,3,5,7,11…
Prime Square up(+/-) : Sequence consist of squares of prime numbers i.e. 4,9,25,49,121..
Arithmetic Series: Sequence consist of Arithmetic Progression i.e. 3,6,9,…
Geometric Series : Sequence consist of Geometric Progression i.e. 2,6,18,54,…

Add up Series

Add up Series + Probability of asking – Very Low Difficulty – Low Reason – to Introduce Concept These problems are never asked they are very easy, we are talking about them to introduce the number series from basic. Rule – Just Add a number ‘N’ to the last number. E.g. – 5, (5 + 3 = 8), (8 + 3 = 11), ( 11 + 3= 14) …. Result – 5, 8, 11, 14, 17 ……..

Add up Series – Probability of asking – Very Low Difficulty – Low Reason – to Introduce Concept Rule : Just Add a number ‘N’ to the last number. E.g. : 4, (4 – 5 = (-1)), (-1 -5 = -6), ( -6 – 5 = -11) …. Result : 4, -1, -6, -11, -16 ……..

Step Up Series +

It is like Add up series, but in Add up a constant number was added, but in step up the number added is not constant, the following type of additions can be there –

Ap: + 2, +4, +6
GP: +3, +6. +12, +24
Sum of last 2 nos

Examples –

Type1(easy to identify) –

Rule – Just Add a number ‘aX’ to the last number. i.e 4 +aX = 4 + 1(3) increment value of a: 1, 2, 3, 4 ..

E.g. – 4, (4 + 1(3) = 7), (7 + 2(3) = 13), ( 13 + 3(3) = 22) ….

Result – 4, 7, 13, 22, 34 ……..

Type 2(medium to identify) –

Rule – For a number a, multiply with last added number. 6 + a(4) for a = 2.

E.g. – 4, (4 + 1(3) = 7), (7 + 2(3) = 13), ( 13 + 3(3) = 22) ….

Result – 4, 7, 13, 22, 34 ……..

Type1(easy to identify) –

Rule – Just Add a number ‘aX’ to the last number. i.e 4 +aX = 4 + 1(3) increment value of a: 1, 2, 3, 4 ..

E.g. – 6,
( 6 + 2(4) = 6 + 8 = 14)
( 14 + 2(8) = 14 + 16 = 30)
(30 + 2(16) = 30 + 32 = 62)
(62 + 2(32) = 62 + 64 = 126)

Result – 14, 30, 62, 22, 126 ……..

Type 3(Hard to identify) –

Rule – For a number a increment from 1, 2, 3, 4 ….. and multiply with last added number.

E.g. – 4
4 + 1(2) = 4 + 2 = 6
6 + 2(2) = 6 + 4 = 10
10 + 3(4) = 10 + 12 = 22
22 + 4(12) = 22 + 48 = 70

Result – 6, 10, 22, 70 …..
Same as Step up Series + but instead of adding subtract

Square up and Square Add up Series

Probability of asking – Medium

Difficulty – Medium

Reason – Infosys, IBM etc

Square up +(Easy to Identify)

Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + a^2

E.g. – 5
5 + 22 = 5 + 4 = 9
9 + 32 = 9 + 9 = 18
18 + 42 = 18 + 16 = 34
34 + 52 = 34 + 25 = 59

Result – 5, 9, 18, 34, 59 …..

Square up Add up +(Hard to Identify)

Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + a2 + b for b some pattern.

E.g. – 5
5 + 22 + 3 = 5 + 4 + 3 = 12
12 + 32 + 3 = 12 + 9 + 3 = 24
24 + 42 + 3 = 24 + 16 + 3 = 43
43 + 52 + 3 = 43 + 25 + 3 = 71
Result – 5, 12, 24, 43, 71 …..

Result – 5, 12, 24, 43, 71 …..
Square up Step up +(Very hard to identify not asked mostly unless paper is very tough)

Rule – For a number X and for a number a where a = 1, 2, 3….. do next number $ = x + a^{2}$ + b for b some pattern.

E.g. – 5
$5 + 2^{2} + 3 = 5 + 4 + 3 = 12$
$12 + 3^{2} + 8(3+5) = 12 + 9 + 8 = 29$
$29 + 4^{2} + 13(8+5) = 29 + 16 + 13 = 58$
$58 + 5^{2} + 18(13+5) = 58 + 25 + 18 = 101$

Result – 5, 12, 29, 58, 101 ..

Same for Step Up Series -, but instead of adding, Subtract.

Prime up and Prime Square up Series(Very hard to Identify)

Probability of asking – Medium

Difficulty – Hard

Reason – Infosys, IBM etc

Prime Add up +(Easy to Identify)

Rule – For a number X add prime numbers( 2, 3, 5, 7, 11, 13, 17, 19 …) iteratively

E.g. – 11
11 + 7 = 18
18 + 11 = 29
29 + 13 = 42
42 + 17 = 59

Result – 11, 18, 29, 42, 59 ….

Prime Add up -(Easy to Identify)

Rule – For a number X add prime numbers(2, 3, 5, 7, 11, 13, 17, 19 …) iteratively

E.g. :11
11 – 5 = 6
6 – 7 = -1
-1 – 11 = -12
-12 – 13 = -25

Result – 11, 6, -1, -12, -25 ….

Prime Square up +(Medium to Identify)

Rule – For a number X add Squares of prime numbers(22, 32, 52, 72, 112…) iteratively

E.g. – 3
3 + 52= 28
28 + 72 = 76
76 + 112 = 197
Result – 3, 28, 76, 197 ….

Rule – For a number X subtract Squares of prime numbers(22, 32, 52, 72, 112…) iteratively

Type 1.How to Solve Number Series Questions Quickly – Perfect Square questions

1.Find the missing numbers from the series?
225, 256, 289, —, 361—, 441

A. 324, 400

B. 325, 450

C. 320, 392

D. None of the above

Answer: A

Explanations:

(15)2= 15 x 15= 225
(16)2= 16 x 16= 256
(17)2= 17 x 17= 289
(18)2= 18 x 18= 324
(19)2= 19 x 19= 361
(20)2= 20 x 20= 400
(21)2= 21 x 21= 441

2.Find the missing number from the series?
4, 16, 36, –, 100, —, 196

A. 49, 121

B. 64, 144

C. 81, 169

D. None of the above

Answer: B

Explanations:

Here the series contains a perfect square of ever alternate even number like
2 x 2 = 4
4 x 4 = 16
6 x 6 = 36
8 x 8 = 64
10 x 10 = 100
12 x 12 = 144

3.Find the wrong number in the series?
50, 75, 111, 160, 225

A. 181

B. 224

C. 225

D. None of the above.

Answer: C

Explanations:

Here the first number is 50 which is not a perfect square, the next number is 75, which again is not a perfect square. Hence this is evident that the series is not a perfect square series, but the difference between the two perpetual numbers of the series is 25 (75-50), 36 (111-75), 49 (160-111) and all these numbers are perfect squares, Hence the next number shall be 160+64= 224 But here its 225, Hence Option C is the correct One.

Type 2. How to Solve Number Series Questions Quickly : Perfect cube series

Such series consists of numbers that perfect cubes. Some of its examples are mentioned below:

1.Fill in the blank with a number that will follow the below-mentioned series?
343, 729, —-, 2197, 3375

A. 1331

B. 1000

C. 4096

D. None of the above

Answer: A

Explanations:

This series consists of perfect cubes of perpetual odd numbers beginning from 7. Like 7, 9, 11, 13, 15 and so on.
343 (7 x 7 x 7)
729 (9 x 9 x 9)
1331 (11 x 11 x 11)
2197 (13 x 13 x 13)
3375 (15 x 15 x 15)

2.There is one wrong number which is not following the pattern of the series. Find out that number from the options given below?
2197, 5832, 12168, 21952, 35937

A. 12168

B. 2197

C. 21952

D. 35973

Answer: A

Explanations:

Here the series contains a perfect square of ever alternate even number like
$13^3= 2197$
$18^3= 5832$
$23^3= 12167$
$28^3= 21952$
$33^3= 35952$
In this series 5 is added to each cube digit to get the next cube number. Like (13+5)= 18; (18+5)= 23….

3.Find the missing numbers from the series?
9261, 32768,——– , 157464, 274625,———

A. 79507, 438976

B. 81454, 398676

C. 68921, 458876

D. None of the above.

Answer: A

Explanations:

21^3 = 9261
$32^3 = 32768$
$43^3 = 79507$
$54^3 = 157464$
$65^3 = 274625$
$76^3 = 438976$
Here 11 is added to each cube digit to get the next cube number like 21+11= 32
31+11= 43 and so on.

Type 3. How to Solve Number Series Questions Quickly : Ration Series

This series contains numbers arranged in a particular order, and there is a set pattern of variance between each digit of the series. Now we have to analyze that pattern and accordingly calculate the next missing number of the series.

1. Find the missing numbers from the series?
12, 24, —, 96, —, 384

A. 48, 192

B. 36, 108

C. 72, 288

D. None of the above

Answer: A

Explanations:

In this series, it is evident that 2 is multiplied to each consecutive number to get the next number. Which is mentioned below:
12 x 2 = 24
24 x 2 = 48
48 x 2 = 96
96 x 2 = 192
192 x 2 = 384
Therefore option A is the correct one.

2.Which one is/are the wrong number which is not following the series trend?
12, 24, 48, 816, 16214, 32424

A. 16214

B. 12, 24

C. 48, 816

D. 32424

Answer: A

Explanations:

If we separate unit digit of the number:
(1+1= 2; 2+2= 4)= 24
(2+2= 4; 4+4= 8)= 48
(4+4= 8; 8+8= 16)= 816
(81+81= 162; 6+6= 12)= 16212
(162+162= 324; 12+12= 24)= 32424
Hence option A is the correct one.

3.Find the missing numbers from the series below?
3, 21, 147, ____ , 7203, _____

A. 2209

B. 1029

C. 6172

D. None of the above.

Answer: B

Explanations:

This series consists of a sequence where each number is multiplied by 7:
3
3 x 7 = 21
21 x 7 = 147
147 x 7= 1029
1029 x 7 = 7203
7203 x 7 = 50421

Type 4. How to Solve Number Series Questions Quickly : Geometric series

Geometric series is a formula based series wherein the missing number is calculated by either adding, multiplying, subtracting or dividing the consecutive term with a constant number.
Its formula is mentioned below:
G S $= {a, ar, ar^2, ar^3,….}$
Where the a= first term of the series
R= factor or difference between the term, also known as the common ratio.

1. Find the missing numbers from the below-mentioned series?
1, 3, 9, 27 , –, 243, —

A. 81, 729

B. 27, 729

C. 81, 486

D. None of the above

Answer: A

Explanations:

Here a = 1 (first term of the series)
R = 3 ( common number that is multiplied with the consecutive number of the series) Hence we get:
1 x $3^0$ = 1
1 x $3^1$ = 3
1 x $3^2$ = 9
1 x $3^3$ = 27
1 x $3^4$ = 81
1 x $3^5$ = 243
1 x $3^6$ = 729

2.Find the wrong number which does not follow the series pattern?
5, 7, 15, 35, 77 , 161

A. 15

B. 5

C. 7

D. 35

Answer: A

Explanations:

5 x 0 + 7 = 7
7 x 1 + 7= 14
14 x 2 + 7 = 35
35 x 2 + 7 = 77
77 x 2 + 7 = 161

3.Find the missing number from the below series?
9, 81, —, 6561, 59049

A. 648

B. 729

C. 3281

D. None of the above.

Answer: B

Explanations:

9
9 x 9 = 81
81 x 9 = 729
729 x 9 = 6561
6561 x 9 = 59049

Type 5. How to Solve Number Series Questions Quickly : Mixed series

1. Find out the missing numbers from the below series?
81, 80, 84, –, 91, 66, —, 53

A. 88, 76

B. 75, 102

C. 76, 95

D. None of the above

Answer: B

Explanations:

$81+ 0^2= 81$
$81- 1^2= 80$
$80+ 2^2= 84$
$84- 3^2= 75$
$75+ 4^2= 91$
$91- 5^2= 66$
$66+ 6^2= 102$
$102- 7^2= 53$

2.There is one wrong number in the below series which is not following the series pattern. Find out that number?
39, 120, 365, 1092

A. 39

B. 365

C. 120

D. 1092

Answer: B

Explanations:

12
12 x 3 + 3 = 39
39 x 3 + 3 = 120
120 x 3 + 3 = 363

3.Below series contains a wrong number, find the one which does not follow the series trend?
12, 61, 307, 7656, 38281

A. 12

B. 307

C. 61

D. 7656

Answer: B

Explanations:

12 + 12 x 5+1= 61
61 x 5 +1= 306
306 x 5+1= 1531
1531 x 5+1= 7656
7656 x 5+1= 38281