**Important**::

Number Series shortcut tricks are very important thing to know for your exams. Time takes a huge part in competitive exams. If you manage your time then you can do well in those exams.

Most of us miss that part. Few examples on number series shortcuts is given in this page below. These shortcut tricks cover all sorts of tricks on Number Series. We request all visitors to read all examples carefully.

These examples will help you to understand shortcut tricks on Number Series.

First of all do a practice set on math of any exam. Choose any twenty math problems and write it down on a page. Solve first ten math problems according to basic math formula.

You also need to keep track of timing. After solving all ten math questions write down total time taken by you to solve those questions. Now practice our shortcut tricks on number series and read examples carefully. After finishing this do remaining questions using Number Series shortcut tricks.

Again keep track of the time. The timing will be surely improved this time. But this is not enough. If you need to improve your timing more then you need to practice more.

Math section in a competitive exam is the most important part of the exam. It doesn’t mean that other topics are not so important. But if you need a good score in exam then you have to score good in maths. You can get good score only by practicing more and more.

All you need to do is to do math problems correctly within time, and only shortcut tricks can give you that success. But it doesn’t mean that you can’t do math problems without using any shortcut tricks. You may have that potential to do maths within time without using any shortcut tricks.

But other peoples may not do the same. For those we prepared this number series shortcut tricks. Here in this page we try to put all types of shortcut tricks on Number Series. But it possible we miss any. We appreciate if you share that with us. Your little help will help so many need .

**What is Number Series ?**

Number series is a form of numbers in a certain sequence, where some numbers are mistakenly put into the series of numbers and some number is missing in that series, we need to observe first and then find the accurate number to that series of numbers.

Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks are comes into action.

In competitive exams number series are given and where you need to find missing numbers and mistakenly put into the series numbers. The number series are come in different types. At first you have to decided what type of series are given in papers then according with this you have to use shortcut tricks as fast as you can.

**Perfect Square Series**

Perfect square series is a arrangement of numbers in a certain order, where some numbers

**Series are based on square of a number which is in same order you need to place one square number that is missing in that given series,**we need to observe and find the accurate number to the series of numbers.This type of problem are given in Quantitative Aptitude which is a very essential in banking exam. It is simple to work on perfect square root numbers you can easily obtain the result of perfect square number. How you get easily by Perfect square numbers missing term by memorize square and square root numbers shortcut tricks .

The square of same number and the square result of a number which is equal to the square of another same element. In mathematical world, a square number or perfect square is number of an integer positive integer that is the square of an same integer number always and the numbers are non-negative.

In other words, we say it is the result of product of multiplication of some positive integer numbers with itself always. For example, we consider 4 is a result of square numbers, since it as 2 × 2 in normal way.

The normal representation of square numbers is n

^{2 }and that is similar with products of n × n, but it is similar with exponentiation of n^{2},In Square numbers are positive number. So we can explain it that a positive number is a square number, where its square roots are always integers positive numbers. so For example, √4 = ±2, so 4 is a square number.

**Perfect Square Series**

Here we see the some examples that how the perfect square are arranged how the missing square series are arranged.

**Example 1:**441, 484, 529, 576, ?,

**Answer:**441 = 21

^{2}, 484 = 22

^{2}, 529 = 23

^{2}, 576 = 24

^{2 },625 = 25

^{2}.

**Example 2:**121, 144, 169, ?, 225

**Answer:**121 = 11

^{2}, 144 = 12

^{2}, 169 = 13

^{2}, 196 = 14

^{2}, 225 = 15

^{2}.

**Example 3:**?, 2116, 2209, 2304, 2401, 2500

**Answer:**2025 = 45

^{2}, 2116 = 46

^{2}, 2304 = 48

^{2}, 2401 = 49

^{2}, 2500 = 50

^{2}

**Example 4:**961, 1024, ?, 1156, 1225

**Answer:**961 = 31

^{2}, 1024= 32

^{2}, 1089 = 33

^{2}, 1156 = 34

^{2}, 1225 = 35

^{2}.

**Example 5:**36, ?, 64, 81, 100, 121

**Answer:**36 = 6

^{2}, 49 = 7

^{2}, 64 = 8

^{2}, 81 = 9

^{2}, 100 = 10

^{2}, 121 = 11

^{2}.

**Example 6 :**121 , 169 , ? , 289 , 361

**Answer :**11

^{2}= 121 , 13

^{2}= 169 , 15

^{2}= 225 , 17

^{2}= 289 , 19

^{2}= 361.

**Example 7 :**121 , 484 , 1089 , 1936 , ? , 4356

**Answer :**11

^{2}= 121 , 22

^{2}= 484 , 33

^{2}= 1089 , 44

^{2}= 1936 , 55

^{2}= 3025 , 66

^{2}= 4356.

**Example 8 :**961 , 1024 , 1089 , ? 1225

**Answer :**31

^{2}, 32

^{2}, 33

^{2}, 34

^{2}, 35

^{2}

**Example 9 :**1849 , ? , 2025 , 2116 , 2209

**Answer :**43

^{2}, 44

^{2}, 45

^{2}, 46

^{2}, 47

^{2}

**Example 10 :**2500 , 2401 , 2304 , ? , 2116 , 2025

**Answer :**50

^{2}, 49

^{2}, 48

^{2}, 47

^{2}, 46

^{2}, 45

^{2}

## Perfect Cube Series

Perfect cube series is a arrangement of numbers in a certain order,where some numbers

**this Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series.**we need to observe and find the accurate number to the series of numbers. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.

All numbers are arranged in sequent order. we need to observe and find the accurate number to this type series of numbers. Here we learn the perfect cube series of Example.

This type of problem are given in Quantitative Aptitude which is a very essential in banking exam. Under below given some more example for your better practice.

In perfect cube series number is a combination of cube number are arranged. In example 1) 1331, 1728, 2197, ? where you need to count them in a one step or two step calculation for obtain the difference common result according with the series of ratio numbers .

At first you can calculate missing number in ratio series and that you place the actual missing number in the ? or missing place. Be prepared when you calculate differences because it is either one or two step calculation. So when you calculate and get result of two difference numbers you need follow some step wise.

At first calculate the first number cube value and second number cube value if all number are maintain a sequential order cube value then follow same steps which is carry up to last and after that you get actual missing number by finding the common value when you put the missing number you have noticed that all series numbers are common difference in between them.

This kind of missing series calculation you go thorough some common calculation shortcut tricks using cube and cube shortcut tricks, or you memorize the 1 to 30 cube series number value.

In this type series example questions, it is sounds hard, but it really isn’t. Get it? Once you have done this, by practice with more example then you just easily can do in your way as well competitive and as in bank exam also . So, each of our examples are given below.

**Perfect Cube Series:**

**Example 1 :**1331 , ? , 35937 , 85184 , 166375

**Answer :**11

^{3}, 22

^{3}, 33

^{3}, 44

^{3}, 55

^{3}

**Example 2 :**125, ?, 343, 512, 729, 1000

**Answer :**125 = 5

^{3}, 216 = 6

^{3}, 343 = 7

^{3}, 512 = 8

^{3}, 729 = 9

^{3}, 1000 = 10

^{3}.

**Example 3 :**1 , 9 , 125 , 343 , ? , 729

**Answer :**1

^{3}, 3

^{3}, 5

^{3}, 7

^{3}, 8

^{3}, 9

^{3}

**Example 4 :**125, ?, 343, 512, 729, 1000

**Answer:**125 = 5

^{3}, 216 = 6

^{3}, 343 = 7

^{3}, 512 = 8

^{3}, 729 = 9

^{3}, 1000 = 10

^{3}.

**Example 5 :**8 , 64 , ? , 512 , 1000 , 1728

**Answer :**2

^{3}, 4

^{3}, 6

^{3}, 8

^{3}, 10

^{3}, 12

^{3}

**Example 6 :**4096, 4913, 5832, ?, 8000

**Answer:**4096 = 16

^{3}, 4913 = 17

^{3}, 5832 = 18

^{3}, 6859 = 19

^{3}, 8000 = 20

^{3}.

**Example 7 :**1331 , ? , 29791 , 68921 132651

**Answer :**11

^{3}, 21

^{3}, 31

^{3}, 41

^{3}, 51

^{3}

**Example 8 :**1331, 1728, 2197, ?

**Answer:**1331 = 11

^{3}, 1728 = 12

^{3}, 2197 = 13

^{3}, 2744 = 14

^{3}.

**Example 9:**1728, 1331, ?, 729, 512

**Answer:**1728 = 12

^{3}, 1331 = 11

^{3}, 1000 = 10

^{3}, 729 = 9

^{3}, 512 = 8

^{3}.

**Example 10 :**1000 , 8000 , ? ,64000 , 125000

**Answer :**10

^{3}, 20

^{3}, 30

^{3}, 40

^{3}, 50

^{3}

**Example 11 :**125000 , 64000 , ? , 8000 , 1000

**Answer :**50

^{3}, 40

^{3}, 30

^{3}, 20

^{3}, 10

^{3}

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## Ratio and Proportion Methods Shortcut Tricks

You all know that math portion is very much important in competitive exams. That doesn’t mean that other sections are not so important. But only math portion can leads you to a good score. A good score comes with practice and practice. All you need to do is to do math problems correctly within time, and only shortcut tricks can give you that success. But it doesn’t mean that without using shortcut tricks you can’t do any math problems.

You may have that potential that you may do maths within time without using any shortcut tricks. But so many people can’t do this. Here we prepared ratio and proportion shortcut tricks for those people. Here in this page we try to put all types of shortcut tricks on Ratio and Proportion. But we may miss few of them. If you know anything else rather than this please do share with us. Your little help will help so many needy.

**What is Ratio?**

A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a : b = a / b, In ratio a : b, we can say that a as the**first term**or**antecedent**and b the**second term**or**consequent**.

**Example :**The ratio 4 : 9 we can represent as 4 / 9 after this 4 is a antecedent and, consequent = 9

**Rule of ration :**In ratio multiplication or division of each an every term of a ratio by the same non- zero number does not affect the ratio.

Different type of ratio problem are given in Quantitative Aptitude which is a very essential topic in banking exam. Under below given some more example for your better practice.

Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks and formula are comes into action.

**What is Proportion?**

The idea of proportions is that two ratios are like equal.

If a : b = c : d, we write a : b : : c : d,**Ex.**3 / 15 = 1 / 5**a**and**d**called**extremes,**where as**b**and**c**called**mean terms**.

**Proportion of quantities**

the four quantities like a, b, c, d we can say proportion then we can express it**a : b = c : d**

Then**a : b : : c : d <–> ( a x d ) = ( b x c )****product of means = product of extremes.**If there is given three quantities like

**a, d, c**of same like then we can say it proportion of continued.**a : d = d : c**, d is called**mean term.****a**and**c**are called**extremes.**

## Geometric Series

**Examples 1:**5, 45, 405, 3645, ?

**Answer:**5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.

**Examples 2:**73205, 6655, 605, 55, ?

**Answer:**5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205.

**Examples 3: **25, 100, ?, 1600, 6400**Answer: **25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.

**Examples 4:** 9, 54, ?, 1944, 11664**Answer: **9 x 6 = 54, 54 x 6 = 324, 324 x 6 = 1944, 1944 x 6 = 11664.

## Mixed Series

**Examples 1:**

**Problem :**111, 220, 438, ?, 1746

**Answer:**

from 111 to 220 we get using this 111 x 2 = 222 – 2 = 220,similarly we follow next steps

from 220 to 438 we get using this 220 x 2 = 440 – 2 = 438,

from 438 to ? we get using this 438 x 2 = 876 – 2 = 874,

from 874 to 1746 we get using this 874 x 2 = 1748 – 2 = 1746.

So the missing number is 874

**Examples 2:**

**Problem :**24, ?, 208, 622, 1864

**Answer:**

from 24 to ? we get using this 24 x 3 = 72 – 2 = 70, Similarly we follow next steps

from 70 to 208 we get using this 70 x 3 = 210 – 2 = 208,

from 208 to 622 we get using this 208 x 3 = 624 – 2= 622,

from 622 to 1864 we get using this 622 x 3 = 1866 – 2 = 1864.

So the missing number is 70

**Examples 3:**

**Problem :**11, 24, 50, 102, 206, ?

**Answer:**

11 x 2 = 22 +2 = 24,

24 x 2 = 48 + 2 = 50,

50 x 2 = 100 + 2 = 102,

102 x 2 = 204 + 2 = 206,

206 x 2 = 412 + 2 = 414.

So the missing number is 414.

**Example 4:**

**Problem :**0, 6, 24, 60, 120, 210, ?

**Answer :**The given series is : 1

^{3}– 1, 2

^{3}– 2, 3

^{3}– 3, 4

^{3}– 4, 5

^{3}– 5, 6

^{3}– 6,

So the missing term = 7

^{3}– 7 = 343 – 7 = 336 .

**Example 5:**

**Problem :**11, 14, 19, 22, 27, 30, ?

**Answer :**

The pattern is + 3, + 5, + 3, + 5, …………

So the missing term is = 30 + 5 = 35 .

**Example 6:**

**Problem :**6, 12, 21, ? , 48

**Answer :**

The pattern is + 6, + 9, + 12, +15 ………..

So the missing term is = 21 + 12 = 33 .

**Example 7:**

**Problem :**18, 22, 30, ? ,78, 142

**Answer :**

The pattern is +4, +8, +16, +32, +64

So the missing term is = 30 + 16 = 46 .

**Example 8:**

**Problem :**589245773, 89245773, 8924577, 924577, ?

**Answer :**

The pattern is The digits are removed one by one from the beginning and the end in order alternately, So to obtain the subsequent terms of the missing series is = 92457 .

**Example 9:**

**Problem :**8, 35, ? , 143, 224, 323

**Answer :**

The pattern is (3

^{2}– 1), (6

^{2}– 1),………., (12

^{2}– 1), (15

^{2}– 1), (18

^{2}– 1)

So the missing term is = (9

^{2}– 1 ) = 81 – 1 = 80 .

**Example 10:**

**Problem :**3, 7, 23, 95, ?

**Answer :**

The pattern is ( x 2 + 1 ),( x 3 + 2) , ( x 4 + 3 ) , ……….

So the missing term is = 95 x 5 + 4 = 479 .

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