What is Number Series ?
Number series is a arrangement of numbers in a certain order,where some numbers are wrongly put into the series of numbers and some number is missing in that series,we need to observe and find the accurate number to the 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. 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.
Different types of Number Series There are some format of series which are given in Exams.
Perfect Square Series:
This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.
Ex: 441, 484, 529, 576, ?
Sol:Here, 21*21=441
22*22=484....
So,missing number is 25*25=625
Perfect Cube Series:
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
Ex: 1331, 1728, 2197, ?
Sol:Here, the answer is 13^3=
Prime Series :
In which the terms are the prime numbers in Order
Ex : 2, 3, 5, 7, 11, 13, _ , 19
Sol: Here,missing term is 17.
Geometric Series:
This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.
Ex: 5, 45, 405, 3645, ?
Sol:Here,5*9=45,
45*9=405,
405*9=3645
3645*9=32805
missing term is 32805
Two stage Type Series:
A two stage Arithmetic series is one in which the differences of successive numbers themselves form an arithmetic series.
Ex: i. 3, 9, 18, 35, 58,——
ii. 6, 9, 17, 23,——
Mixed Series:
This type of series are more then one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule.
Wrong Number Series:
Sometimes, a question is asked to find out the wrong number in a series. This is a bit difficult task. This is because from the point where you get a wrong number, all other succeeding numbers would also be look wrong. You can only solve such a question comfortably only if you have expertise in handling the questions on series very well.
Ex: Find the wrong number in the following series.
10 21 43 85 175
Sol: Here, the logic involved is (previous number*2) + 1 only.But the error lies where instead of
(43*2) + 1 = 87, 85 has been given. So 85 is the wrong number.
Twin Series:
This is a newly included type of series in which two series are given, and below that the starting point of another series is given. Now you are supposed to analyze the logic from the first series and apply the same logic to form the second series.
Ex: 5 8 12 17 23 30
9 a b c d e
Which number should come in place of c?
Sol:In this question, it canbe analyzed that the difference between the numbers is 3, 4, 5, 6 and 7.
So youhave to apply the same logic and start the series with 9.
The first numberafter 9 would be
9 + 3 = 12 (this would replace letter a),
the second numberwould be
12 + 4 = 16 (this would replace letter b)
and the third number wouldbe 16 + 5 = 21 (this would replace the letter c).
Some other common types of number series involve the following types of logic
Type-1:
Alternate Primes :
Ex: 2, 5, 11, 17, 23, _, 41
Type-2:
Every Third number can be the sum of the preceding two numbers:
Ex : 3, 5, 8, 13, ?
Sol:Here, 3+5=8,
5+8=13
The next term is 13+8=21
Type-3:
Every Third number can be the product of the preceeding two numbers
Ex : 1, 2, 2, 4, 8, 32. _
Sol:Here,1*2=2,
2*2=4,
2*4=8,
4*8=32,
Next term is 32*8=256
Type-4:
The difference of any term from its succeding term is constant (either increasing series or decreasing series )
Ex : 4, 7, 10, 13, 16, 19, _, 25
Sol:Here, 7-4=3,
10-7=3,
13-10=3.... Similarly
Missing term is 19+3=22
Type-5:
The difference between two consecutive terms will be either increasing or decreasing by a constant number :
Ex : 2, 10, 26, 50, 82, _
Sol: Here, 10-2=8, (8*1=8)
26-10=16, (8*2=16)
50-26=24, (8*3=24)
82-50=32, (8*4=32)
Next number is 82+(8*5=40)=122
Type-6:
The difference between two numbers is power of constant number where power will increases continuously
Ex : 15, 16, 19, 28,
Sol:Here,16-15=1, (3^0)
19-16=3, (3^1)
28-19=9, (3^2)
Next term is 28+(3^3)=55
Type-7:
The difference can be multiplied by numbers which will be increasing by a constant number :
Ex : 2, 3, 5, 11, 35, _
Sol: The difference between two numbers are
3 - 2 = 1
5 - 3 = 2
11 - 5 = 6
35 -11 = 24
Here, the differences are multiplied by numbers which are in increasing order .
Differences are
1 x 2 = 2
2 x 3 = 6
6 x 4 = 2 4
So, the next difference wil be
24 x 5 = 120.
So , the answer is 35 + 120 = 155 .
Type-8:
Every succeeding term is got by multiplying the previous term by a constant number or numbers which follow a special pattern.
Ex : 5, 15, 45, 135, _
Sol: Here, 5 x 3 = 15
15 x 3 = 45
45 x 3 = 135
So, the answer is 135 x 3 = 405 .
Type-9:
In certain series the terms are formed by various rule (miscellaneous rules). By keen observation you have to find out the rule and the appropriate answer.
Ex : 4, 11, 31, 90, _
Sol:Terms are,
4 x 3 -1 = 1 1
11 x 3 -2 = 3 1
31 x 3 -3 = 9 0
So, the answer is (90 x 3) -4 = 2 6 6
Ex : 3, 7, 23, 95, _
Sol:Terms are,
(3 x 2) + 1 = 7
(7 x 3) + 2 = 23
(23 x 4),+ 3 = 95
So, the answer will be
(95 x 5)+ 4 = 479
Number series is a arrangement of numbers in a certain order,where some numbers are wrongly put into the series of numbers and some number is missing in that series,we need to observe and find the accurate number to the 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. 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.
Different types of Number Series There are some format of series which are given in Exams.
Perfect Square Series:
This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.
Ex: 441, 484, 529, 576, ?
Sol:Here, 21*21=441
22*22=484....
So,missing number is 25*25=625
Perfect Cube Series:
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
Ex: 1331, 1728, 2197, ?
Sol:Here, the answer is 13^3=
Prime Series :
In which the terms are the prime numbers in Order
Ex : 2, 3, 5, 7, 11, 13, _ , 19
Sol: Here,missing term is 17.
Geometric Series:
This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.
Ex: 5, 45, 405, 3645, ?
Sol:Here,5*9=45,
45*9=405,
405*9=3645
3645*9=32805
missing term is 32805
Two stage Type Series:
A two stage Arithmetic series is one in which the differences of successive numbers themselves form an arithmetic series.
Ex: i. 3, 9, 18, 35, 58,——
ii. 6, 9, 17, 23,——
Mixed Series:
This type of series are more then one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule.
Wrong Number Series:
Sometimes, a question is asked to find out the wrong number in a series. This is a bit difficult task. This is because from the point where you get a wrong number, all other succeeding numbers would also be look wrong. You can only solve such a question comfortably only if you have expertise in handling the questions on series very well.
Ex: Find the wrong number in the following series.
10 21 43 85 175
Sol: Here, the logic involved is (previous number*2) + 1 only.But the error lies where instead of
(43*2) + 1 = 87, 85 has been given. So 85 is the wrong number.
Twin Series:
This is a newly included type of series in which two series are given, and below that the starting point of another series is given. Now you are supposed to analyze the logic from the first series and apply the same logic to form the second series.
Ex: 5 8 12 17 23 30
9 a b c d e
Which number should come in place of c?
Sol:In this question, it canbe analyzed that the difference between the numbers is 3, 4, 5, 6 and 7.
So youhave to apply the same logic and start the series with 9.
The first numberafter 9 would be
9 + 3 = 12 (this would replace letter a),
the second numberwould be
12 + 4 = 16 (this would replace letter b)
and the third number wouldbe 16 + 5 = 21 (this would replace the letter c).
Some other common types of number series involve the following types of logic
Type-1:
Alternate Primes :
Ex: 2, 5, 11, 17, 23, _, 41
Type-2:
Every Third number can be the sum of the preceding two numbers:
Ex : 3, 5, 8, 13, ?
Sol:Here, 3+5=8,
5+8=13
The next term is 13+8=21
Type-3:
Every Third number can be the product of the preceeding two numbers
Ex : 1, 2, 2, 4, 8, 32. _
Sol:Here,1*2=2,
2*2=4,
2*4=8,
4*8=32,
Next term is 32*8=256
Type-4:
The difference of any term from its succeding term is constant (either increasing series or decreasing series )
Ex : 4, 7, 10, 13, 16, 19, _, 25
Sol:Here, 7-4=3,
10-7=3,
13-10=3.... Similarly
Missing term is 19+3=22
Type-5:
The difference between two consecutive terms will be either increasing or decreasing by a constant number :
Ex : 2, 10, 26, 50, 82, _
Sol: Here, 10-2=8, (8*1=8)
26-10=16, (8*2=16)
50-26=24, (8*3=24)
82-50=32, (8*4=32)
Next number is 82+(8*5=40)=122
Type-6:
The difference between two numbers is power of constant number where power will increases continuously
Ex : 15, 16, 19, 28,
Sol:Here,16-15=1, (3^0)
19-16=3, (3^1)
28-19=9, (3^2)
Next term is 28+(3^3)=55
Type-7:
The difference can be multiplied by numbers which will be increasing by a constant number :
Ex : 2, 3, 5, 11, 35, _
Sol: The difference between two numbers are
3 - 2 = 1
5 - 3 = 2
11 - 5 = 6
35 -11 = 24
Here, the differences are multiplied by numbers which are in increasing order .
Differences are
1 x 2 = 2
2 x 3 = 6
6 x 4 = 2 4
So, the next difference wil be
24 x 5 = 120.
So , the answer is 35 + 120 = 155 .
Type-8:
Every succeeding term is got by multiplying the previous term by a constant number or numbers which follow a special pattern.
Ex : 5, 15, 45, 135, _
Sol: Here, 5 x 3 = 15
15 x 3 = 45
45 x 3 = 135
So, the answer is 135 x 3 = 405 .
Type-9:
In certain series the terms are formed by various rule (miscellaneous rules). By keen observation you have to find out the rule and the appropriate answer.
Ex : 4, 11, 31, 90, _
Sol:Terms are,
4 x 3 -1 = 1 1
11 x 3 -2 = 3 1
31 x 3 -3 = 9 0
So, the answer is (90 x 3) -4 = 2 6 6
Ex : 3, 7, 23, 95, _
Sol:Terms are,
(3 x 2) + 1 = 7
(7 x 3) + 2 = 23
(23 x 4),+ 3 = 95
So, the answer will be
(95 x 5)+ 4 = 479
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