**How to Pass Numerical Reasoning Tests – First Time!**

It appears that nowadays, just about every selection process or assessment centre consists of a numerical reasoning test. It is important that you score very high during your test which is why we have created a 168 page workbook that is full of numerical reasoning test questions and explanations.

Learn how to pass your Numerical Reasoning assessment with this ultimate NEW testing guide. Packed full of sample questions for BASIC, INTERMEDIATE and ADVANCED levels, this comprehensive guide will guarantee to improve your chances and enhance your performance.

**BASIC – INTERMEDIATE – ADVANCED**

In this direct, but easy to follow guide, you will be taught the basics of maths through to intermediate numerical questions and then followed by advanced numerical reasoning. Broken down into detailed examples for every numerical reasoning question type, this guide then includes 100s of sample questions for you to practice your numerical reasoning – each with its own detailed answer.

Focused on primarily on helping people like you to pass any form of numerical reasoning test, including GCSE mathematics, 11-plus, career assessment centres, A-level mathematics and also advanced numeracy tests.

**PREPARATION, PRACTICE, AND PERSEVERANCE!**

Amidst the education system, children will have to partake in several assessments in which to monitor their progress.

Here at How2become, we believe the three KEY things to remember in regards to SATs and examinations is Preparation, Practice, and Perseverance!

By preparing for every eventuality in which you will encounter, will allow you to be confident enough to tackle these assessments head on; the only way this can be achieved is through practice and persevering!

The more practice you encounter, the better you will score! Persevering through practice papers and sample questions will guarantee to improve your knowledge and ability, and, therefore, will prepare you for your assessment!

**To help you get started in your preparation, let us take a look at a couple of sample numerical reasoning test questions and answers.**

## Sample Numerical Reasoning Practice Questions

A farm is split into 3 sections, A, B and C. If the area of all 3 sections combined is 250m2 and the area of section A is 80m2, work out the area of section B using the diagram below.

Diagram not to scale

a) 32m2

b) 76m2

c) 74m2

d) 96m2

A builder needs 5 pieces of wood and has a plank of wood measuring 45 metres in length. If the builder chops the plank into 5 equal pieces what length would each of the 5 pieces be?

a) 5 m

b) 4 m

c) 8 m

d) 9 m

e) 40 m

**Answer to numerical reasoning question 1**

The combined area of all 3 sections A, B and C is given as 250m2 in the question and the area of section A only is given as 80m2. This means that the area of sections B and C combined must be:

250-80=170m2

It is possible to find the area of section C alone from the diagram and is calculated by multiplying the two sides together:

Area of section C is 12×8=96m2

The area of sections B and C combined is 170m2 so the area of section B alone can be calculated by subtraction the area of C from the area of sections B and C combined as shown below:

Area of section B = Area of sections B and C combined – Area of section C

=170-96

=74m2

**The answer to question 1 is c) 74m2**

**Answer to numerical reasoning question 2**

If a 45 m length plank is chopped into 5 equal pieces the calculation is 45÷5 = 9m

Each piece is 9m long.

**The answer to question 2 is d) 9m**

**BASIC SAMPLE NUMERICAL REASONING TEST QUESTIONS**

## Percentage Increase |

To work out the percentage increase of a set of data, you need to remember this formula: Percent Increase % = Increase ÷ original number x 100 If your answer is a negative number, then this is a percentage decrease. |

### Mass / Density / Volume

To work out the Mass:

- Mass = Density x Volume

To work out the Volume:

- Volume = Mass ÷ Density

To work out the Density:

- Density = Mass ÷ Volume

**INTERMEDIATE SAMPLE NUMERICAL REASONING TEST QUESTIONS**

### Simplifying Equations

Simplify 5w – 6x – 2w – 1x

(5w) (- 6x) (- 2w) (- 1x)

(5w – 2w) = 3w

(-6x – 1x) = -7x

3w -7x

- The important thing to remember for simplifying equations is to break up the equation (like above).
- The ‘-‘ signs and the ‘+’ signs should also be grouped and be on the left side of the number.

### Velocity Graphs

How to work it out:

Step 1 = Car A = change in velocity = 16 – 5 = 11 11 ÷ 20 = 0.55

Step 2 = Car B = change in velocity = 15 – 0 = 15 15 ÷ 20 = 0.75

Step 3 = difference from Car B to Car A = 0.75 – 0.55 = 0.2

**ADVANCED SAMPLE NUMERICAL REASONING TEST QUESTION**

### Solving Simultaneous Equations

**x = 0.5 and y = -4**

EXPLANATION =

- (Equation 1) = -6x + 8y = -35 (Equation 2) = 2x + 3y = -11
- -6x + 8y = -35 6x + 9y = -33
- -6z + 6x + 8y + 9y = (-35) + (-33)
- 17y = -68 y = -4

Substitute y = -4 into equation 1 = -6(x) + 8(-4) = -35 - -6x – 32 = -35 -6x = -35 + 32 -6x = -3
- x = 0.5

### Show that, in the diagram below, cos α = 65

Your working out should be as follows:

Using the two right-angled triangles we can determine the following

Now since ? = ∠??? − ∠???, we can use the angle subtraction formula for

cosine to find cos ?:

## PASS ANY MATHS ASSESSMENT WITH THE HELP OF OUR ULTIMATE NUMERICAL REASONING TESTING GUIDE!

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