# How To Solve Number Series Question Quickly

## How to solve Number Systems Problems Quickly

**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.**

### 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 examlple : (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 i= 0,1,2,3,4,5,6… i.e. 1,4,9,16,25..**Square add up Series(+/-) :**Adding n^{2}every time and incrementing value of n starting from 1 i.e. 1,5, 14, 30, 55, …… and Subtracting n^{2}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 i= 0,1,2,3,4,5,6… i.e. 1,8,27,64….**Cube add up Series :**Adding n^{3}every time with incrementing of n by 1 i.e. 1,9,36…**Prime up(+/-) :**Sequence consist of Prime numbers i.e. 1,3,5,7,11…**Prime Square up(+/-) :**Sequence consist of sqare of prime numbers i.e. 1,9,25,49,121..**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,…

Now lets try to learn each of these in detail, do let us know in comments section if you’re not able to understand any problem concept, we will help you out with alter logic.

### 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

- Probability of asking – Medium
- Difficulty – Low
- Reason – Infosys, IBM etc
- After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 30% students are not able figure out correct series of such problems

**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

Example –

**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. – 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 …..

**Step Up Series –**

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
- After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 50% students are not able figure out correct series of such problems

**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 + 2
^{2 }= 5 + 4 = 9 - 9 + 3
^{2}= 9 + 9 = 18 - 18 + 4
^{2}= 18 + 16 = 34 - 34 + 5
^{2}= 22 + 25 = 77

- 5 + 2
- Result – 9, 18, 34, 77 …..

**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 + a
^{2 }+ b for b some pattern. - E.g. – 5
- 5 + 2
^{2 }+ 3= 5 + 4 + 3 = 12 - 12 + 3
^{2}+ 8^{(3+5)}= 9 + 9 + 8 = 29 - 29 + 4
^{2}+13^{(8+5)}= 29 + 16 + 13 = 58 - 58 + 5
^{2}+ 18^{(13+5)}= 58 + 25 + 18 = 101

- 5 + 2
- Result – 5, 12, 29, 58, 101 …..

**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 + a2 + b for b some pattern.
- E.g. –
- 5
- 5 + 22 + 3= 5 + 4 + 3 = 12
- 12 + 32 + 8(3+5) = 9 + 9 + 8 = 29
- 29 + 42 +13(8+5) = 29 + 16 + 13 = 58
- 58 + 52 + 18(13+5) = 58 + 25 + 18 = 101

- Result – 5, 12, 29, 58, 101 ..

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

### Square up and Square Add up Series

- Probability of asking – Low
- Difficulty – Hard
- Reason – Infosys(very rarely) etc
- After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 90% students are not able figure out correct series of such problems

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

- Probability of asking – Medium
- Difficulty – Hard
- Reason – Infosys, IBM. etc
- After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 70% students are not able figure out correct series of such problems

**Prime Add up +(Easy to Identify)**

- Rule – For a number X add prime numbers(1, 2, 3, 5, 7, 11, 13, 17, 19 …) iteratively
- E.g. – 11
- 11 + 7
^{ }= 18 - 18 + 11 = 29
- 29 + 13 = 42
- 42 + 17 = 59

- 11 + 7
- Result – 11, 18, 29, 42, 59 ….

**Prime Add up -(Easy to Identify)**

- Rule – For a number X add prime numbers(1, 2, 3, 5, 7, 11, 13, 17, 19 …) iteratively
- E.g. :11
- 11 – 5
^{ }= 6 - 6 – 7 = -1
- -1 – 11 = -12
- -12 – 13 = -25

- 11 – 5
- Result – 11, 6, -1, -12, -25 ….

**Prime Square up +(Medium to Identify)**

- Rule – For a number X add Squares of prime numbers(1
^{2}, 2^{2}, 3^{2}, 5^{2}, 7^{2}, 11^{2}…) iteratively - E.g. – 3
- 3 + 5
^{2}= 28 - 28 + 7
^{2}= 76 - 76 + 11
^{2}= 197

- 3 + 5
- Result – 3, 28, 76, 197 ….

**Prime Square up -(Hard to Identify)**

- Rule – For a number X subtract Squares of prime numbers(1
^{2}, 2^{2}, 3^{2}, 5^{2}, 7^{2}, 11^{2}…) iteratively

- Rule – For a number X subtract Squares of prime numbers(1

**HOW TO SOLVE** NUMBER** SERIES-**

**Number series:**- A series of different numbers following some logical pattern of various mathematical concepts. One has to analyze the concept used and accordingly find out the missing number of the series.

Generally, there are 5 different types of series, which are explained below with examples:

**Type 1.Perfect Square questions**

**Question 1. ****Find the missing numbers from the series?**

**225, 256, 289, —, 361—, 441**

**Options:**

**A. 324, 400**

**B. 325, 450**

**C. 320, 392**

**D. None of the above**

** **

**Solution: **(15)^{2}= 15*15= 225

(16)^{2}= 16*16= 256

(17)^{2}= 17*17= 289

(18)^{2}= 18*18= 324

(19)^{2}= 19*19= 361

(20)^{2}= 20*20= 400

(21)^{2}= 21*21= 441

**Correct option: A**

**Question 2. ****Find the missing number from the series?**

**4, 16, 36, –, 100, —, 196**

**Options:**

**A. 49, 121**

**B. 64, 144**

**C. 81, 169**

**D. None of the above**

**Solution: **Here the series contains a perfect square of ever alternate even number like

2*2= 4

4*4= 16

6*6= 36

8*8= 64

10*10= 100

12*12= 144

**Correct option: B**

**Question 3. Find the wrong number in the series?**

**50, 75, 111, 160, 225**

**Options:**

**A. 181**

**B. 224**

**C. 225**

**D. None of the above.**

** **

**Solution: **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.

**Correct option: C**

**Type 2. Perfect cube series**

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

**Question 1. ****Fill in the blank with a number that will follow the below-mentioned series?**

**343, 729, —-, 2197, 3375**

**Options:**

**A. 1331**

**B. 1000**

**C. 4096**

**D. None of the above**

**Solution: **This series consists of perfect cubes of perpetual odd numbers beginning from 7. Like 7, 9, 11, 13, 15 and so on.

343 (7*7*7)

729 (9*9*9)

1331 (11*11*11)

2197 (13*13*13)

3375 (15*15*15)

**Correct option: A**

**Question 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**

**Options:**

**A. 12168**

**B. 2197**

**C. 21952**

**D. 35973**

**Solution: **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….

**Correct option: A**

**Question 3. ****Find the missing numbers from the series?**

**9261, 32768,——– , 157464, 274625,———**

**Options:**

**A. 79507, 438976**

**B. 81454, 398676**

**C. 68921, 45887 6**

**D. None of the above.**

**Solution: **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.

**Correct option: A**

**Type 3. 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.
- This is explained with a couple of examples mentioned below:

**Question 1. ****Find the missing numbers from the series?**

**12, 24, —, 96, —, 384**

**Options:**

**A. 48, 192**

**B. 36, 108**

**C. 72, 288**

**D. None of the above.**

**Solution: **In this series, it is evident that 2 is multiplied to each consecutive number to get the next number. Which is mentioned below:

6*6= 12

112*2= 24

24*2= 48

48*2= 96

96*2= 192

192*2= 384

Therefore option A is the correct one.

**Correct option: A**

**Question 2. ****Which one is/are the wrong number which is not following the series trend?**

**12, 24, 48, 816, 16214, 32424**

**Options:**

**A. 16214**

**B. 12, 24**

**C. 48, 816**

**D. 32424**

**Solution **If we separate each 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.

**Correct option: A**

**Question 3. Find the missing numbers from the series below?**

**3, 21, 147, —, 7203, —-**

**Options:**

**A. 2209**

**B. 1029**

**C. 6172**

**D. None of the above**

**Solution: **This series consists of a sequence where each number is multiplied by 7:

3

3*7= 21

21*7= 147

147*7= 1029

1029*7= 7203

7203*7= 50421

**Correct option: B**

**Type 4. 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.

**Question 1. ****Find the missing numbers from the below-mentioned series?**

**1, 3, 9, –, 243, —**

**Options:**

**A. 81, 729**

**B. 27, 729**

**C. 81, 486**

**D. None of the above**

**Solution: **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

1*3

1*3^{2 }= 9

1*3^{3} = 27

1*3^{4} = 81

1*3^{5} = 243

1*3^{6} = 729

**Correct option: A**

**Question 2. ****Find the wrong number which does not follow the series pattern?**

**5, 7, 15, 35, 112, 455**

**Options:**

**A. 15**

**B. 5**

**C. 7**

**D. 35**

**E. 112**

**F. 455**

**Solution: **5*0+7= 7

7*1+7= 14

14*2+7= 35

35*2+7= 112

112*2+7= 231

**Correct option: A**

**Question 3. ****Find the missing number from the below series?**

**9, 81, —, 6561, 59049**

**Options:**

**A. 648**

**B. 729**

**C. 3281**

**D. None of the above**

**Solution: **9

9*9= 81

81*9= 729

729*9= 6561

6561*9= 59049

**Correct option: B**

**Type 5. Mixed series**

- Here the series is formulated by using more than one arithmetic logic.

**Question 1. ****Find out the missing numbers from the below series?**

**81, 80, 84, –, 91, 66, —, 53**

**Options:**

**A.) 88, 76**

**B.) 75, 102**

**C.) 76, 95**

**D.) None of the above**

**Solution: **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

**Correct option: B**

**Question 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**

**Options:**

**A. 39**

**B. 365**

**C. 120**

**D. 1092**

**Solution: **12

12*3+3= 39

39*3+3= 120

120*3+3= 363

**Correct option: B**

**Question 3. ****Below series contains a wrong number, find the one which does not follow the series trend?**

**12, 61, 307, 7656, 38281**

**Options:**

**A. 12**

**B. 307**

**C. 61**

**D. 7656**

**E. 38281**

**Solution: **12+12*5+1= 61

61*5+1= 306

306*5+1= 1531

1531*5+1= 7656

7656*5+1= 38281

**Correct Option: B**

**Read Also: Formula for Number Series Question**

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