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**Let's delve deep into numerical reasoning number series questions, so you could crush them on your coming assessment**

Number series aptitude questions present you with mathematical sequences that follow a logical rule, based on elementary arithmetic.

In these questions a sequence of numbers called ‘terms’ are presented, with 1 or more missing element(s).

You are then asked to **find the rule that connects them to each other**. After you have detected the rule, you can then deduce the missing number.

The difficulty level of these questions varies. For example, the logical rule behind the sequence(s) sticks out and is easy to recognise in a less trivial sequence.

Thus, the logical rule is less significant and much harder to recognise. When this occurs, the question demands more attention and creativity in deciphering the missing term.

Number sequences questions usually consist of four to seven visible numbers along with a single missing number or, depending on the sequence's complexity level, 2 or 3 missing numbers.

All term in the sequence meet a specific logical rule which needs to be recognised in order to find the missing terms.

The difficulty level of number sequence questions may increase in several ways:

- The rule behind the sequence becomes less significant.
**Loger sequence:**usually, the longer the sequence, the more complex the question is.**The missing term appears early early in the sequence rather than a later:**

This give you less initial information to discern the hidden rule behind the sequence.**More then 1 number missing in a sequence:**if true, this adds a layer of difficulty to your examination – again, less information (i.e. less known items in the sequence) makes it harder for you to recognise the sequence’s rule.**A combination of two alternating series****A logical rule that hides in the difference between items:**when the rule is not hidden directly within the visible sequence, rather it is formed between the difference of each adjacent number it is usualy less apparent to most people.

Number series questions are an integral part of almost all numerical reasoning tests. Many companies deal with processing and analysing numerical data in daily work.

A few examples of tests that use number series questions as part of their assessment process:

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Ready for some hands-on practice? Great.

My advice is that you go slow through the sample questions below and the answer breakdown that follows each one.

The objective of this section is to help you learn some solving tips and techniques in an active and memorable way, not to simulate your test conditions.

This is why, our solving tips are integrated into the explanations. Pay close attention.

Also, if you still hadn't taken your free test you might as well take it after you finish this section.

The free test *is* meant to simulate your actual test, and it's a good opportunity for you to get some more practice and also start implementing what you've learned here.

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1) Arithmetic Sequences

2) Geometric Sequences

3) Exponent Sequences

a. Perfect Squares

b. Perfect Cube Sequences

4) Two-Stage Sequences

5) Mixed Sequences

6) Alternating Sequences

7) Fibonacci Sequences

8) A Combination of Sequences' Types

In arithmetic sequence questions, you will find that the differences between the numbers are obtained by adding, subtracting or performing both operations to the previous term.

**Example:**

Please choose one correct answer:

1 | ** ?** | 5 | **? ** | 9 | 11

**A)** 2, 6

**B)** 3, 7

**C) **2, 8

**D) **3, 6

✔️ **The correct answer is B**

There are two items missing. The only two visible adjacent items are 9 & 11.

The difference between them is 2.

In addition, the difference between 5 and 9 is 4 as well as between 1 and 5.

That is, in both cases the difference between the 1st and 3rd item and the 3rd and 5th item is 4.

We can conclude that the missing numbers in the series should have a difference of 2 between the items adjacent to them on either side.

The numbers 3 & 7 complete the series.

**The answer is 3,7**

Geometric sequence questions address the ascent or descent of moving numbers.

Here, each term is obtained by multiplying, dividing or using both operations, to the previous term by a specific number or order of numbers.

**Example: **

Please choose one correct answer:

0 | 3/4 | 8/9 | 15/16 | 24/25 | ** ?**

**A)** 29/28

**B) **33/32

**C) **35/36

**D) **37/38

✔️ **The correct answer is C**

The series in this question follows the pattern:

1-n2, n= 1/1, 1/2, 1/3, 1/4…

Exponent sequences display all terms as exponent numbers, moving in a specific order.

They can be broken down into 2 groups: 1) perfect square and 2) perfect cube sequences. Below is a breakdown of each group.

**a. Perfect Squares**

In perfect square sequences, all terms are perfect square numbers (*x*^{2}) moving in a specific order.

**Example:**

What is the following number in the series?

720 | 720 | 360 | **?** | 30 | 6

**A)** 180

**B)** 120

**C)** 90

**D)** 60

✔️ **The correct answer is B**

**Solving tip:** A good way to tackle this question would be to examine it backwards- starting from the last term, working your way up to the first term.

This tip can be useful especially in questions where you are required to find a term that is in the middle of the series.

**b. Perfect Cube Sequences**

In a perfect cube sequences, all terms are cubed numbers (*x*^{3}), also moving in a specific order.

**Example:**

0 | 3/4 | 8/9 | 15/16 | 24/25 | ** ?**

**A)** 29/28

**B)** 33/32

**C)** 35/36

**D)** 37/38

✔️ The correct answer is 35/36 **(C)**

The series in this question follows the pattern:

1-n2, n= 1/1, 1/2, 1/3, 1/4…

In Two-stage sequences you will find that the differences between consecutive terms form an arithmetic or a geometric sequence. Thus the logical rule needs to be discovered.

**Example:**

1 | **?** | 5 | **?** | 9 | 11

**A) **2, 6

**B) **3, 7

**C) **2, 8

**D)** 3, 6

✔️ The correct answer is 3, 7 **(B)**

There are 2 items missing.

The only 2 visible adjacent items are 9 & 11.

The difference between them is 2.

In addition, the difference between 5 and 9 is 4 as well as between 1 and 5.

That is, in both cases the difference between the 1st and 3rd item and the 3rd and 5th item is 4.

We can conclude that the missing numbers in the series should have a difference of 2 between the items adjacent to them on either side.

The numbers 3 & 7 complete the series.

The answer is 3, 7

Mixed sequences cover a single sequence with more than 1 arithmetic rule characterising it.

**Example:**

0 | 3/4 | 8/9 | 15/16 | 24/25 | **?**

**A)** 29/28

**B) **33/32

**C) **35/36

**D) **37/38

✔️ **The correct answer is C**

The series in this question follows the pattern:

1-n2, n= 1/1, 1/2, 1/3, 1/4…

Here, a single sequence made of alternating terms form two independent sub-sequences and combine them.

**Example:**

3 | 8 | 15 | 24 | 35 | **?**

**A) **42

**B) **36

**C) **48

**D) **46

✔️ The correct answer is 48 **(C)**

The value of the differences increases by 2 each time.

Therefore 13 (11 + 2) should be added to the last term in the series.

35 + 13 = **48**

That's our answer.

Each term known as a Fibonacci number is the sum of the 2 preceding numbers in a sequence. The simplest Fibonacci sequence is: 1, 1, 2, 3, 5, 8, etc.

**Example:**

Z2 | Y4 | X8 | W16 | ** ?**

**A)** V32

**B)** S32

**C)** V24

**D)** S24

✔️ The correct answer is V32 **(A)**

The series in this question follows 2 sets of rules:

1) The letters decrease by -1.

2) The numbers double each time.

This sample question follows both set of rules found in two-stage sequences and exponent sequences.

**Example:**

3 | 3 | 3 | 6 | 3 | 9 | 3 | ** ?**

**A)** 3

**B)** 27

**C)** 12

**D)** 6

✔️ The correct answer is 12 **(C)**.

**There are 2 ways to look at this series: **

I) There are 2 inner series. each following a different rule: Odd terms- remain constant: 3. Even terms- increase by 3:

3+3=6

6+3=9, 9+3=12

II) Another point of view:

**The series in this question follows 2 rules: **

I) The mathematical operations between the terms change in a specific order, x, : and so forth.

II) Every two steps the number by which the terms are multiplied or divided increases by 1.

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**1) There may be more than one way to solve a number sequence question** [example]

Consider the data between each term: As mentioned above, a sequence can be made up of two alternating sequences or take from several combined operations.

**2) Look at the difference between terms:** when you can't find a rule look for for a difference between consecutive terms - it may create an independent sequence.

Use the multiple-choices options to determine the correct answer quicker.

**3) Don’t shy away from estimation**. Sometimes you do not need to use full calculations to determine the correct answer.

**4) develop your calculator skills** (in case of calculator usage): Aside from basic arithmetic operations, learn how to use various, more advanced, formulas and operations such as exponents, square roots, factorial, memory etc.

Need additional help? Check out how to use a calculator webpage.

**5) Familiarise yourself with maths operations:** such as basic arithmetic, fractions, decimals, exponents etc.

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