Number Series Reasoning with Types, Tips & Examples
Tuhin Chakraborty
| Updated: Jan 9, 2023 20:01 IST
In Number Series reasoning, Series is a sequential order of letters, numbers, or both arranged in such a way that each term in the series is obtained according to some specific rules. These rules can be based on mathematical operations, place of letters in alphabetical order, and so on. In questions related to the number series logical reasoning section, a specified sequence or order of letters, numbers or a combination of both will be given in which one of terms such as letter/number/letter and number of the series will be missing either at the end of the series or in between the series. Candidates need to identify the pattern involved in the formation of series and accordingly find the missing term to complete the series.
What is Number Series Reasoning?
Number Series refers to a sequence of numbers following some pattern. Candidates need to find the missing or wrong number in the provided series. There may be some questions where one of the terms in the given series will be incorrect, and candidates need to find out the term of the series by identifying the pattern involved in the formation of the series.
There is no set pattern and each question may follow a different type of pattern or sequential arrangement of letters or digits, which candidates need to detect using their common sense and reasoning ability. On the basis of various types of questions that are asked in various competitive examinations, we have classified the number series reasoning section into several types, which are given below.
Types of Number Series
Let us see the various types of questions that may come one by one from below.
1. Addition Series: In this type of number series reasoning, specific numbers based on some pattern are added to get the next number.
2. Subtraction Series: In this type of number series reasoning, specific numbers based on some pattern are subtracted to get the next number.
3. Multiplication Series: In this type of number series reasoning, a particular type of number pattern is multiplied to get the next number.
4. Division Series: In this type of number series reasoning, a particular type of number pattern is divided to get the next number.
5. Square Series: In this type of number series reasoning, each number is a perfect square of a particular number pattern.
6. Cube Series: In this type of number series reasoning, each number is a perfect cube of a particular number pattern.
7. Fibonacci Series: In this type of number series reasoning, the next number is the addition of two previous numbers.
8. Alternating Series: In this type of number series reasoning, multiple number patterns are used alternatively to form a series.
9. Mixed Operator Series: In this type of number series reasoning, multiple operators are applied to get the next number in the series.
10. Arranging Number: In this type of number series reasoning, candidates need to rearrange numbers, as specified, and then answer the given questions.
Learn about Sequences and Series.
Tips and Tricks on Number Series Reasoning
Candidates can find various tips and tricks below for solving the questions related to the Number Series reasoning section.
Tip 1: Candidates need to find the process involved in the given series such as addition, subtraction, multiplication, division, and so on to find out the correct answer.
Tip 2: For arranging type number series, candidates need to rearrange the given series by using various processes to find out the correct answer.
Learn about Arithmetic Progression
Solved Examples on Number Series Reasoning
Example 1: 3, 6, 11, 18, 27, ?, 51 (based on addition series)
Solution: The solution of the series is as follows.
3 + 3 = 6
6 + 5 = 11
11 + 7 = 18
18 + 9 = 27
27 +11 = 38
38 + 13 = 51
Hence, the correct answer is 38.
Example 2: 50, 45, 40, 35, 30? (based on subtraction series)
Solution: The solution of the series is as follows.
50 – 5 = 45
45 – 5 = 40
40 – 5 = 35
35 – 5 = 30
30 – 5 = 25
Hence, the correct answer is 25.
Example 3: 5, 11, 24.2, 53.24, ?, 257.6816 (based on multiplication series)
Solution: The solution of the series is as follows.
5 x 2.2 = 11
11 x 2.2 = 24.2
24.2 x 2.2 = 53.24
53.24 x 2.2 = 117.128
117.128 x 2.2 = 257.6816
Hence, the correct answer is 117.128.
Learn about Decision Making Reasoning
Example 4: 4096, 1024, 256, ?, 16, 4 (based on division series)
Solution: The solution of the series is as follows.
4096 / 4 = 1024
1024 / 4 = 256
256 / 4 = 64
64 / 4 = 16
16 / 4 = 4
Hence, the correct answer is 64.
Example 5: 49, 121, 169, ?, 361 (based on square series)
Solution: The solution of the series is as follows.
7^ 2 = 49
11^ 2 = 121
13 ^ 2 = 169
17 ^ 2 = 289
19 ^ 2 = 361
Hence, the correct answer is 289.
Example 6: 8, 64, 216, ?, 1000 (based on cube series)
Solution: The solution of the series is as follows.
2 ^ 3 = 8
4 ^ 3 = 64
6 ^ 3 = 216
8 ^ 3 = 512
10 ^ 3 = 1000
Hence, the correct answer is 512.
Example 7: 12, 13, 25, 38, ?, 101, 164 (based on Fibonacci series)
Solution: The solution of the series is as follows.
12
13
25 = 12 + 13
38 = 13 + 25
63 = 25 + 38
101 = 38 + 63
164 = 101 + 63
Hence, the correct answer is 63.
Example 8: 2, 29, 4, 25, 6, ?, 8, 17 (based on alternating series)
Solution: The solution of the series is as follows.
2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
Similarly,
29 – 4 = 25
25 – 4 = 21
21 – 4 = 17
Hence, the correct answer is 21.
Example 9: 5, 7, 21, 55, ?, 215 (based on mixed operator series)
Solution: The solution of the series is as follows.
5 + ( 2 ^ 2 – 2) = 7
7 + ( 4 ^ 2 – 2) = 21
21 + ( 6 ^ 2 – 2) = 55
55 + ( 8 ^ 2 – 2) = 117
117 + ( 10 ^ 2 – 2) = 215
Hence, the correct answer is 117.
Example 10: The position of how many digit(s) in the number 381576 will remain the same after the number is arranged in ascending order?
Solution: Original number form is: 3 8 1 5 7 6
Ascending order form is: 1 3 5 6 7 8
If we check the number/s whose position will remain the same in both forms then we will see that the position of only number remains same or unchanged which is the number 7.
Hence, the correct answer is One.
Check out more details on other Reasoning Topics:
| Perfect Numbers | Cause & Effect |
| Blood Relations | Clocks |
| Calendars | Coding Decoding |
| Direction & Distance | Data Sufficiency |
We hope you found this article regarding the Number Series reasoning section was informative and helpful, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.
| If you are checking Number Series Reasoning article, also check related maths articles: | |
| Taylor Series | Missing Numbers in Series and Sequence |
| Number Arrangement Reasoning | Sequences and Series |
| Number System | Even Numbers |
FAQs on Number Series Reasoning
Q.1 What is the Number Series reasoning?
Ans.1
Number Series refers to a sequence of numbers following some pattern. Candidates need to find the missing or wrong number in the provided series.
Q.2 How many types of Number Series reasoning questions are there?
Ans.2
The types of Number Series reasoning-based questions that come up in various government exams are given above in the article. Kindly go through the article for the same.
Q.3 Where I will get the tips and tricks for the Number Series reasoning section?
Ans.3
Some of the tips and tricks regarding the Number Series reasoning section are given above in the article.
Q.4 Where I will find some of the sample questions related to the Number Series reasoning?
Ans.4
Various example questions along with their solutions are given above in the article. Kindly go through the article for the same.
Q.5 In which exam questions from Number Series reasoning come up?
Ans.5
Some of the prestigious exams where the Number Series reasoning-based questions are included in the Logical Reasoning syllabus are given above in the article.
Practice hundreds of questions on Testbook for FREE!
