Number Series – Logical Reasoning Questions, Tips, and Tricks

Number Series is a fundamental and frequently tested topic in competitive exams such as SSC (Staff Selection Commission) and bank recruitment examinations. It forms a crucial part of the quantitative aptitude or numerical ability section in these exams. A number series consists of a sequence of numbers arranged in a specific pattern or order, and the task is to identify and understand this pattern to predict the next number or missing number in the series.

Below are some practice Number Series Logical Reasoning Questions that can help applicants do well on such exams by giving them practice. The article also includes many approaches to answering a question on number series. Candidates are advised to review the questions to prepare for competitive examinations.

Number Series

Types of Number Series Problems

A series is a predetermined arrangement of symbols or numbers in a particular order. Candidates must either identify a term that is erroneous or absent from the list. The number series, alphabet series, alphanumeric series, and symbol or character series are some examples of series types. The types of number series problems are as follows:

• Arithmetic Series: In this type of series, the difference between consecutive terms remains constant. For example, 2, 4, 6, 8, 10, where the common difference is 2.
• Geometric Series: In a geometric series, each term is obtained by multiplying the previous term by a fixed common ratio. For example: 2, 4, 8, 16, 32, where the common ratio is 2.
• Mixed Series: Mixed series combine elements of both arithmetic and geometric progressions. They may involve alternating patterns or a mix of addition and multiplication.
• Square, Cube, and Power Series: These series involve terms that are squares, cubes, or raised to some power. For example: 1, 4, 9, 16, 25 (squares), or 1, 8, 27, 64, 125 (cubes).
• Fraction and Decimal Series: Some series involve fractions or decimals, and you need to identify the underlying pattern in these cases.
• Prime Number Series: These series are composed of prime numbers, and you need to determine the logic behind the selection of prime numbers.
• Alternate Number Series: In this type, certain numbers may be skipped in the series, and you must identify the pattern for the missing numbers.
• Pattern-Based Series: These series are designed with unique patterns that may not follow conventional mathematical rules. You need to observe and identify the pattern.
• Number Reversal Series: In this type of series, numbers are presented in reverse order or with their digits reversed, and you need to decipher the pattern.

Tips and Tricks to Solve Number Series Problems

The foundation for learning algebra and geometry is having a working grasp of different number series. Additionally, it aids in the development of students’ problem-solving abilities, which are crucial during the formative years. The following are the tips and tricks to solve number series problem in competitive exam:

• Before attempting to find the next number, identify the type of series you are dealing with (arithmetic, geometric, mixed, etc.). This will give you a clue about the underlying pattern.
• Check if the differences or ratios are consistent throughout the series. If they are not, it might be a mixed series or involve a more complex pattern.
• Analyze if there are any mathematical operations (addition, subtraction, multiplication, division) applied to the numbers. Try to identify these operations and apply them consistently.
• If you can’t immediately identify the pattern, use the process of elimination. Substitute each answer choice into the series and see if it fits the pattern. This can quickly narrow down your options.

Sample Number Series Reasoning Questions

1. In the following question find the missing term: 3,8,5,27,8,64,12,125,17,? [SSC CGL Tier 1 2017]

a) 216

b) 361

c) 625

d) 441

Solution: If we check the series we can see that the difference between first, third, fifth, seventh, ninth term is increasing by 1. Lets see 5-3=2, 8-5=3, 12-8=4, and 17-12=5. Now to solve this type of problem you have to remember the square and cube of numbers.

If we check the series again we can see that there is 8 which is the cube of 2 (difference of third and first number), 27 which is the cube of 3 (difference of fifth and third number), similarly if we observe we can see that there is 64 which is the cube of 4 (difference of seventh and fifth number), 125 which is the cube of 5 (difference of ninth and seventh number), so the correct answer will be cube of 6 means 216 which is option a.

2. Which number will replace the question mark (?) in the following series? 1331, 2197, ?, 6859. [SSC CGL Tier 1 2022]

a) 4913

b) 5832

c) 4096

d) 3375

Solution: If we observe the series we can see that every number present in the series is a cube of a particular number. 1331 is the cube of 11, and 2197 is the cube of 13, also, 6859 is the cube of 19. So the correct option will be a perfect cube and also it would be the cube of the next prime number between 13 and 17. We know that 17 is the only prime number between 13 and 19. So the correct option will be cube of 17 means 4913 which is option a.

3. Find the next number in the series: 12, 7, 21, 16, 30, ?

a) 35

b) 40

c) 25

d) 45

Solution: The series follows the pattern of alternately subtracting 5 and adding 14:

12 – 5 = 7

7 + 14 = 21

21 – 5 = 16

16 + 14 = 30

So, the next number will be 30 – 5 = 25.
4. Find the next number in the series: 0, 1, 1, 2, 3, 5, ?

a) 6

b) 7

c) 8

d) 9

Solution: The series follows the pattern of adding the two previous numbers to get the next number:

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

So, the next number will be 3 + 5 = 8.

FAQs on Number Series Logical Reasoning Questions

What is the Number Series?

The term “Number Series” refers to a sequence of numbers that has been established, and the questions that may be based on these themes will require us to identify the laws that lead to the construction of a number series.

How to solve Number Series Logical Reasoning questions?

Candidates should thoroughly study the question before proceeding. Candidates should try to determine the series’ trend by examining the pattern of the series. Determine whether the series has a rising or declining tendency. They should also determine the rate at which the terms are increasing or dropping using that information.

What is the purpose of Number Series?

Number Series aptitude questions expose you to logically consistent mathematical sequences built on the foundation of first-grade arithmetic. ‘Terms’ a list of numbers are offered in these questions with one or more missing elements. The next step is for you to identify the rule linking them.

What is Number Series questions?

Number Series questions will present a list of numbers along with a blank that needs to be filled in. You must determine the pattern between the numbers, their predecessor, and their successor in order to fill in the blank.