In this post we will understand the concept of number series which is important part of logical reasoning syllabus for competition exams like GMAT, CAT , SSC, IBPS, SBI, NDA and other notable exams.
we have tried to cover the basic details of number series along with the types of series which are frequently asked in the exams.
Number series is a form of series in which numbers or are arranged in particular order in different ways
Generally two types of questions are asked in number series
- To find the missing number
- To find an error in number
Types of number series –
Prime number series
This type of series contain prime numbers in a consecutive way , alternate way or in a different way
7, 11, 13, 17, 19,?
This is a continues series of prime number
So our next number of the series should be 23
3, 7, 13, 19, ?
This is an alternate series of prime numbers
Here we see that we get a gap of one prime number in between each element
3, 7, 17, 31, ?
In this type of series we get a gap of one, two or more than two prime numbers
In above series we get a gap of one prime number in between first and second element
Then gap of two prime number between second and third element and so on.
In this type of series the difference of each consecutive elements is same
For example difference of first and second element is same as difference of second and third element and so on
2, 12,22, 32, ?
Here we take a difference of two consecutive elements
Here 42 is the right answer
3, 20, 63, 144, 275, ?
Here we apply Difference of difference method
So our next element should be a difference of +12
In multiplication series the multiplication factor is same or may be different in consecutive elements
2, 4, 8, 16, 32, ?
6, 12, 36, 144, ?
Here we get a multiplication series of 2,3,4,5
So our next element should be 144×5=720
-in division series the consecutive elements are in decreasing order with large difference. This series follow the same concept of multiplication series but in opposite way here the gap decreases rapidly
1000, 500, 250, 125, ?
Here second element is half of first element and third element is half of second element and so on
Here we get the last element as 125÷2=62.5
15120, 2160, 360, 72, 18, ?
Here second element is seven times the first element
And third element is six times the first element and so on
In this type of series the consecutive elements are in square form either in ascending order or descending other
1, 4,9, 16, 25,?
Here all the elements are in square form so our last element should be 62 =36
196, 169, 144, ?
Here all elements are in squares of decreasing order
So our last element should be 112=121
when there is an addition of 1 in N2 series we get N2+1 series
10, 17, 26, 37, 50, ?
By taking difference of each consecutive element
This difference can be written as
So it is N2+1 series and our last element should be 82+1=65
122, 145, 170, ?
Our last element should be 142+1=197
when there is an subtraction of 1 in N2 series we get N2-1 series
195, 168, 143, 120, ?
Here we get N2-1 series and our last element should be 102-1=99
3, 8, 15, 24, ?
Here we get N2-1 series and our last element should be 62-1=35
here we add same number to the square of that number
20, 30, 42, 56, ?
Here we get N2+N series and our last element should be 82+8=72
here we subtract same number to the square of that number
56, 42, 30, 20, ?
Here we get N2-N series and our last element should be 42-4=12
here the elements are in cubic form ascending or descending order
8, 27, 64, 125, ?
Here we get N3 series and our last element should be 63=216
here we are at the same number to the cube of that number
126, 217, 344, ?
Here we get N3+1 series and our last element should be 83+1=513
here we subtract the same number to the cube of that number
7, 26, 63, 124, ?
Here we get N3-1 series and our last element should be 63-1=215
It is a special type of series. Here we get a particular series in an alternate elements either addition subtraction multiplication or division
In this type of series our consecutive element are not continuously increases or decreases that is they are not arranged in a particular order
18, 24, 21, 27, ?, 30
Here we get an alternate series of +3 so our fifth element should be 24
15, 14, 19, 11, 23, ?
Here we get an alternate series of -3 and +4
So our last element should be 8
50, 200, 100, 100, 200, 50, 400, ?
It is alternate multiplication and division series
Here we get an alternate series of ×2 and ÷2
So our last element should be 25
This is a mixture of all type of series
1, 2, 2, 4, 3, 8, 7, 10, ?
Here we get a alternate different type of addition series
2, 7, 27, 107, ?
Here taking the difference of each consecutive element
Here arranging the difference we get following series
So our last element should be 107×4-1=427
Some important points
- If there is a small gap of numbers between the consecutive elements then it may be difference series
- If there is a large gap of numbers between the consecutive elements then it may be division or multiplication series
- If there is not continuously increasing or decreasing order then it may be in alternate series
- If the elements of the series are near to the square or cube of any numbers then we do some addition or subtraction to get the required elements of the series.