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What is Number Series?

Number series aptitude tests present numerical sequences that follow a logical rule based on elementary arithmetic. An initial sequence is presented from which the rule must be deduced. You are then asked to predict the next number that obeys the rule. The difficulty level of these questions can increase in two ways: the logic behind the sequence test becomes less trivial, thereby demanding attention and creativity, or the missing number is positioned at an early stage, thus preventing you from deciphering the hidden rule by looking only at the previous numbers in the sequence.


Number Series Examples Questions

If you do not fully understand what is meant by number series questions, the following sample questions will give you a better idea. Below you will find different methods used for number series reasoning tests. 

Traditional Number Series Questions

  • Question One:

In a simple series, the difference between two consecutive numbers is constant. For example: 

27 | 24 | 21 | 18 | ? 

 

There is a difference of (-3) between each item. The missing number in this case is 15. 

  • Question Two: 

In a more complex series, the differences between numbers may be dynamic rather than fixed, yet there is still a clear logical rule. Example: 

3 | 4 | 6 | 9 | 13 | 18 | ? 

Add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2, and after the third number add 3, etc. In this case, the missing number is 24. 


Advanced Number Series Questions

  • Question One: 

The Fibonacci sequence is a common principle seen in advanced number series questions. In the following question, you will find that the difference between every two terms created in a sequence is onto its own:

36 | 30 | 28 | 20 | 10 | ?

A. 8

B. -8

C. 12

D. -6

 

The correct answer is B (-8)

The differences between the terms in this series follow the Fibonacci sequence principle. The difference between two terms equals the sum of the two previous differences.

-6 + (-2) = -8

-2 + (-8)= -10

-8+ (-10) = -18 → 10-18 = -18

  • Question Two:

Here, you will find that each adjacent term creates a new sequence, different from the next term in the line. When this is seen, typically two methods can be used: 1. basic mathematical functions (+, -,  ÷, x) are repeated and/or 2. the terms themselves increase or decrease in an orderly fashion. Read the question sample below for a further grasp of the concept:

50 | 57 | 49 | 53 | 41 | 49 | ?

A. 59

B. 53

C. 47

D. 36

The correct answer is D (36)

In this question, you need to explore a series within a series. The intervals between the original terms create a series of their own. 
Consider the intervals as a separate series, given in absolute value:
|7| |8| |4| |12| |8| |13|
You will notice that the differences between the numbers follow two rules:
(1) The mathematical operations between the intervals alternate in a specific order, +, /, x, -
(2) In each step the value of the number by which the previous interval is divided/subtracted/multiplied/added- increases by 1.
You can use this understanding in order to go back to the original series and find the missing term (i.e., work backwards): 
8+5 = 13
49+13 = 62.


Multiplication or Division Patterns 

See whether there is a multiplication or division pattern between two adjacent numbers. For example:  

64 | 32 | 16 | 8 | ? 

Divide each number by 2 to get the next number in the series. The missing number is 4. 


Logical Patterns 

Check whether adjacent numbers in the series change based on a logical pattern as seen below: 

2 | 4 | 12 | 48 | ? 

Multiply the first number by 2, the second number by 3 and the third number by 4, etc. The missing item is 240.


Using More than one Numerical Sign – Two Versions 

  • Question One: 

See if you can find a rule that involves using two or more basic arithmetic functions (+, -, ÷, x). In the series below, the functions alternate in an orderly fashion. 

5 |  7 | 14 | 16 | 32 | 34 | ? 

Add 2, multiply by 2, add 2, multiply by 2, etc. The missing item is 68. 

Tip: Series in this category are easy to identify. Just look for numbers that do not appear to have a set pattern.

  • Question Two: 

In a series that involves two or more basic arithmetic functions, it is important to look for the difference between adjacent items effectively creating their own series. We recommend that you try to identify each pattern separately. For example: 

4 | 6 | 2 | 8 | 3 | ?

In this series, the differences themselves create a series: +2, ÷3, x4, -5. The numbers advance by intervals of 1, and the arithmetic functions change in an orderly sequence. The next arithmetic function in the series should be +6, and so the next item in the series is 9 (3+6 = 9). 

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What’s Inside this Pack 

Inside this exclusive PrepPack™ you will find 12 number series tests along with comprehensive explanations and tips to further help improve your overall score. You will find everything from basic number series tests and decimal practice to advanced number series questions. Each of these tests has been carefully designed together to give you a full taste of what you should expect come testing day. 


How to Improve Your Overall Score

Many top British companies have incorporated numerical reasoning tests into their recruitment process. While it is unlikely the test will only consist of number series questions, you will find many of these questions within many numerical reasoning tests. To further help you succeed, it is important to be prepared for commonly used numerical question types. 

Here we provide tailored preparations for specific companies, such as the Macquarie psychometric assessment, preparation for specific test providers, such as Cubiks test preparation, as well as comprehensive and all-inclusive numerical reasoning preparation kits. 

Remember that preparing for the commonly used numerical sequence questions should be part of any preparation as it will likely appear on your test. Furthermore, our practice pack teaches you how to quickly spot patterns and understand the reasoning behind them using video tutorials, study guides and practice questions. 


Number Series Test Tips 

The best method of tackling number series questions is to become familiar with the different question types. In this way, you will be able to quickly identify the patterns and know if you are working with a multiplication pattern, addition/subtraction, etc. If you haven’t read it, check out the section above which covers the number series sample questions.  

Are you ready to implement these tips while practising the real thing? Access your complete number series bundle pack by clicking the button below.

 

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