# What are the first series of numbers

## Recruitment test Logical thinking Series of numbers

**Probably the most feared test is the recruitment test Logical Thinking Number Series. It is now our goal for you to revise this opinion after this post, because we would like to explain approaches to you to unlock the logic behind series of numbers - and to be able to solve the test. For those who are now wondering what this form of logical thinking ability is needed for, let me tell you: In your professional life, too, you will be given tasks that follow a certain pattern. If you learn how to recognize these patterns, you will also learn how to apply them again, and this is ultimately what every efficient and structured way of working is based on: the basic idea of recognizing patterns and being able to apply them again. So you need your logical thinking skills not only once for the recruitment test logical thinking number series - but also for your professional life. We explain to you what logic can be behind series of numbers.**

### Recruitment test Logical thinking Series of numbers

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Basically, series of numbers always look confusing at first glance and some people ask themselves: What pattern should be behind it? First, try to identify the groups that you can form. This means that there are different groups that correlate with each other. In the next table you can see some examples:

No group | 5 – 15 – 25 – 35 – 45 – 55 – … | With this series of numbers, it becomes clear at first glance that it is a very classic development of the numbers. From number to number, ten points are jumped further. |

Group of two | 3 – 75 – 13 – 70 – 23 – 65 – 33 – 60 – … | A group of two means that every other number is related. This means that from 3 to 13 to 23 to 33 the number 10 was always added. This is number group 1 in our example. In the number group 2, the number 5 is always subtracted from 75 to 70 to 65 to 60. |

Group of three | 21 – 8 – 36 – 14 – 16 – 40 – 7 – 24 – 44 – … | A group of three means that every third number is related. Number group 1 jumps from 21 to 14 to 7, so always subtracts the number 7.Number group 2 jumps from 8 to 16 to 24 and therefore always adds the number 8.Number group 3 jumps from 36 to 40 to 44 and therefore always adds the number 4 . |

Once you have identified the groups, there are various possible relationships between the numbers. Addition and subtraction, which have already been indicated, are only two arithmetic variants that would be possible in the recruitment test logical thinking series of numbers. Learning tip: Anyone who now feels reminded of the multiplication table is absolutely right, because whoever has mastered this will sometimes be able to recognize more easily which groups belong together and which numbers are added or subtracted.

**Case 1: sums and differences**

The simplest and most common form in the recruitment test logical thinking number series is the formation of sums and differences. This means that the numbers in their number groups are either added or subtracted, or in another way: the numbers are added or subtracted in thought. After two examples including an explanation, we have listed some exercises for you:

__Example 1:__ 7 - 72 - 14 - 64 - 21 - 56 - 28 - 48 - X - Y.

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__Result and explanation:__ This is a group of two. Group 1 (7-14-21-28-X) always adds the number 7. Group 2 (72-64-56-48-Y) always subtracts the number 8. So the result is for X = 35 and Y = 40.

__Example 2:__ 13 - 96 - 35 - 18 - 90 - 42 - 23 - 84 - 49 - X - Y - Z.

__Result and explanation:__ This is a group of three. Group 1 (13-18-23-X) always adds the number 5. Group 2 (96-90-84-Y) always subtracts the number 6. Group 3 (35-42-49-Z) always adds the number 7. So the result is: X = 28, Y = 78, Z = 56.

__Exercises: __

- 37 - 2 - 38 - 4 - 39 - 6 - 49 - 8 - 50 - 10 - 51 - 12 - X - Y.
*(Solution: X = 61, Y = 14)* - 88 - 6 - 77 - 12 - 66 - 18 - 55 - 12 - 44 - 6 - X - Y.
*(Solution: X = 33, Y = 12)* - 17 - 6 - 37 - 26 - 57 - 46 - 77 - 66 - X - Y.
*(Solution: X = 97, Y = 86)*

**Case 2: multiplications and divisions**

It becomes a little more difficult when not only numbers are added together or subtracted from one another, but also when working with multiplications and divisions, i.e. when numbers are multiplied (taken) or divided (divided). This shows once again who has a good knowledge of multiplication tables, because this knowledge helps enormously at this point. After two examples including solutions and explanations, exercises follow.

__Example 1:__ 2 - 7 - 4 - 49 - 16 - 2401 - X - Y.

__Result and explanation:__ This is a group of two. Group 1 (2-4-16-X) always multiplies by itself. 2 times 2 makes 4, 4 times 4 makes 16, 16 times 16 makes X = 256. Group 2 (7-49-2401-Y) multiplies always also always with itself. 7 times 7 makes 49, 49 times 49 makes 2401, 2401 times 2401 makes Y = 5,764,801.

__Example 2:__ 250 - 3 - 50 - 6 - 10 - 12 - X - Y.

__Result and explanation:__ This is a group of two. Group 1 (250-50-10-X) is divided by the number 5. Hence X = 2. For group 2 (3-6-12-Y) the respective result is always multiplied by 2. That is, Y = 24.

__Exercises:__

- 6 - 72 - 36 - 9 - 9 - 18 - 54 - 3 - X - Y.
*(Solution: X = 54, Y = 3)* - 21 - 4 - 3 - 20 -15 - 140 - X - Y.
*(Solution: X = 30, Y = 1260)* - 35-36-7-4-49-32-7-8-X-Y.
*(Solution: X = 35, Y = 36)*

**Attention: Mathematical special cases**

In addition to the math classics, special mathematical rules may also be hidden in the series of numbers. Pay attention when you see the numbers 2, 3, 5, 7, 11, 13, 17 and 19. Although these are not related to an arithmetic symbol, they belong to a very specific group of numbers, namely to the prime numbers, which are only divisible by themselves and the number 1. You can access an overview of all prime numbers here. Basically, it makes sense to combine the preparation for the recruitment test logical thinking series of numbers with the preparation for the math test, as, as you have already seen yourself, there are various parallels. In addition, the series of numbers were only part of the logical thinking recruitment test, which is also available for domino series, graphic analogies or series of figures.

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