Quantitative Aptitude – Number Series
Number series is a series of numbers arranging in a certain way. Every number in the series follow some rules. So, before answering the questions we need to understand those rules.
In Quantitative Aptitude part, chapter starts with Number series. Number series is an essential part of aptitude preparation. In every competitive exam you will get at least two questions on number series.
Number series questions is of two types-
- What is the next number in the series?
- Find the wrong number in the series.
What is the Next Number in the series?
This type of series generally came in the exam more. Here in this type of questions we need to observe the series carefully and find out the rules on which the series progress. Then according to that rules we need to find the next number in the series.
For example: 2, 4, 8, 16, ?
Here in this example we need to find the number which will come after 16. So, first of all we need to find the rule on which the series is progressed. Second number of the series is 4 which is double the first number 2. Third number 8 which is double the second number 4. Fourth number 16 which is double the third number 8.
So, the rule of the series is, it progress by double the previous number. So, the answer of the following series will be 16 x 2 = 32. Answer is 32.
Find the Wrong Number in the series
This is another type of number series. Here in this series we need to find the wrong number present in the series. It means we need to find the number which is not following the rule of the series.
For example: 24, 31, 38, 47, 52, 59
Here, in this example we need to find the wrong number present in the series. So, first of all we need to find the rule on which the series is progressed. As you can see that the second number of the series is 31 which came by adding 7 to the first number 24. And, third number of the series is 38 which came by adding 7 to the second number 31. Fourth number of the series is 47 which contradict the rule. It should be 38 + 7 = 45. Assume fourth number as 45. So, fifth number of the series is 52 which came by adding 7 to the fourth* number 45 and finally sixth number of the series is 59 which came by adding 7 to the fifth number 52.
So, the rule of the series is, it progress by adding 7 to the previous number. Here in this series only one number does not follow that rule which is fourth number 47. So, the answer of the following series will be 47.
Few Examples to Test your learnings:
Example #1
In the series below, Find the Wrong number in it.
2, 4, 8, 16, 30, 64
A. 4
B. 8
C. 16
D. 30
Correct Answer is: 30 [Option D].
How to Solve:
2, 4, 8, 16, 30, 64
In this series we need to find which number is wrong in the sequence. To do this we need to analyze that how the series is progressed?
In this example, the series is progressed by multiplying 2 with every numbers.
Like,
2 [First Number]
2 x 2 = 4 [Second Number]
4 x 2 = 8 [Third Number]
8 x 2 = 16 [Fourth Number]
Like this the next number should be,
16 x 2 = 32 [Fifth Number]
But, in the series we have 30 in fifth position. So, 30 is the wrong number here and must be replaced by 32.
Rough Workspace:
Example #2
In the series below, Find the Wrong number in it.
2, 10, 17, 26, 34, 42
A. 2
B. 10
C. 17
D. 34
Correct Answer is: 17 [Option C].
How to Solve:
2, 10, 17, 26, 34, 42
In this series we need to find which number is wrong in the sequence. To do this we need to analyze that how the series is progressed?
In this example, the series is progressed by adding 8 with every numbers.
Like,
2 [First Number]
2 + 8 = 10 [Second Number]
Like this the next number should be,
10 + 8 = 18 [Third Number]
But, in the series we have 17 in third position. So, 17 is the wrong number here and must be replaced by 18.
Rough Workspace:
Example #3
In the series below, which number should come next?
35, 40, 45, 50, 55, ..?..
A. 45
B. 53
C. 60
D. 61
Correct Answer is: 60 [Option C].
How to Solve:
35, 40, 45, 50, 55, ..?..
In this series we need to find which number will come next. To do this we need to analyze that how the series is progressed?
This is a very easy question to solve. In this example we just do simple Addition. Here we add 5 to every number as the series progressed.
Like,
35 [First Number]
35 + 5 = 40 [Second Number]
40 + 5 = 45 [Third Number]
45 + 5 = 50 [Fourth Number]
50 + 5 = 55 [Fifth Number]
Likewise, the next number of this series will be,
55 + 5 = 60.
So, the answer is 60.
Rough Workspace:
Example #4
In the series below, which number should come next?
32, 31, 33, 32, 34, 33, ..?..
A. 22
B. 35
C. 25
D. 26
Correct Answer is: 35 [Option B].
How to Solve:
32, 31, 33, 32, 34, 33, ..?..
In this series we need to find which number will come next. To do this we need to analyze that how the series is progressed?
In this example we just do simple alternating Subtraction and Addition.
In the first pattern, 1 is subtracted and in the second pattern, 2 is added.
Like,
32 [First Number]
32 - 1 = 31 [Second Number]
31 + 2 = 33 [Third Number]
33 - 1 = 32 [Fourth Number]
32 + 2 = 34 [Fifth Number]
34 - 1 = 33 [Sixth Number]
Likewise, the next number of this series will be,
33 + 2 = 35.
So, the answer is 35.
Rough Workspace:
Example #5
In the series below, which number should come next?
26, 24, 20, 18, 14, ..?..
A. 14
B. 13
C. 12
D. 16
Correct Answer is: 12 [Option C].
How to Solve:
26, 24, 20, 18, 14, ..?..
In this series we need to find which number will come next. To do this we need to analyze that how the series is progressed?
In this example we just do simple alternating Subtraction.
In the first pattern, 2 is subtracted and in the second pattern, 4 is subtracted.
Like,
26 [First Number]
26 - 2 = 24 [Second Number]
24 - 4 = 20 [Third Number]
20 - 2 = 18 [Fourth Number]
18 - 4 = 14 [Fifth Number]
Likewise, the next number of this series will be,
14 - 2 = 12.
So, the answer is 12.
Rough Workspace:
Example #6
In the series below, Find the Wrong number in it.
18, 27, 36, 47, 54, 63, 72
A. 27
B. 47
C. 54
D. 72
Correct Answer is: 47 [Option B].
How to Solve:
18, 27, 36, 47, 54, 63, 72
In this series we need to find which number is wrong in the sequence. To do this we need to analyze that how the series is progressed?
In this example, each number is the multiple of 9 except the number 47.
So, the wrong number in this series is 47 and must be replaced by 45.
Rough Workspace:
Example #7
In the series below, which number should come next?
5, 7, 11, 19, 35, ..?..
A. 47
B. 57
C. 67
D. 77
Correct Answer is: 67 [Option C].
How to Solve:
5, 7, 11, 19, 35, ..?..
In this series we need to find which number will come next. To do this we need to analyze that how the series is progressed?
In this example we just do simple Multiplication and Addition with every number.
In the pattern we multiply the number with 2 and then subtract 3 from the resulting number.
Like,
5 [First Number]
( 5 x 2 ) - 3
= 10 - 3
= 7 [Second Number]
( 7 x 2 ) - 3
= 14 - 3
= 11 [Third Number]
( 11 x 2 ) - 3
= 22 - 3
= 19 [Fourth Number]
( 19 x 2 ) - 3
= 38 - 3
= 35 [Fifth Number]
Likewise, the next number of this series will be,
( 35 x 2 ) - 3
= 70 - 3
=67.
So, the answer is 67.
Rough Workspace:
Example #8
In the series below, Find the Wrong number in it.
2, 3, 4, 6, 8, 11, 14, 18, 20
A. 4
B. 8
C. 11
D. 18
Correct Answer is: 11 [Option C].
How to Solve:
2, 3, 4, 6, 8, 11, 14, 18, 20
In this series we need to find which number is wrong in the sequence. To do this we need to analyze that how the series is progressed?
In this example, we add 1 with every number in a Prime number series.
Like,
1 + 1 = 2 [First Number]
2 + 1 = 3 [Second Number]
3 + 1 = 4 [Third Number]
5 + 1 = 6 [Fourth Number]
7 + 1 = 8 [Fifth Number]
Like this the next number should be,
11 + 1 = 12 [Sixth Number]
But, in the series we have 11 in sixth position. So, 11 is the wrong number here and must be replaced by 12.
Rough Workspace:
Example #9
In the series below, Find the Wrong number in it.
5, 15, 30, 80, 180
A. 15
B. 30
C. 80
D. 180
Correct Answer is: 80 [Option C].
How to Solve:
5, 15, 30, 80, 180
In this series we need to find which number is wrong in the sequence. To do this we need to analyze that how the series is progressed?
In this example, the series is progressed by multiplying 3 with odd places numbers and 2 with even places numbers.
Like,
5 [First Number]
5 x 3 = 15 [Second Number]
15 x 2 = 30 [Third Number]
Like this the next number should be,
30 x 3 = 90 [Fourth Number]
But, in the series we have 80 in fourth position. So, 80 is the wrong number here and must be replaced by 90.
Rough Workspace:
Example #10
In the series below, Find the Wrong number in it.
12, 10, 13, 11, 15
A. 12
B. 10
C. 11
D. 15
Correct Answer is: 15 [Option D].
How to Solve:
12, 10, 13, 11, 15
In this series we need to find which number is wrong in the sequence. To do this we need to analyze that how the series is progressed?
In this example, the series is progressed by subtracting 2 with odd places numbers and adding 3 with even places numbers.
Like,
12 [First Number]
12 - 2 = 10 [Second Number]
10 + 3 = 13 [Third Number]
13 - 2 = 11 [Fourth Number]
Like this the next number should be,
11 + 3 = 14 [Fifth Number]
But, in the series we have 15 in fifth position. So, 15 is the wrong number here and must be replaced by 14.
Rough Workspace:
So, if you need any farther help on Number Series, then let us know. We will discuss on those problems here in www.AptitudeTricks.com. Feel free to ask your questions.
Chain rule is a very important topic in Quantitative Aptitude. Questions from chain rule will surely come in competitive exams which have aptitude section.