Numerical Reasoning Tests Formulas ▷ Complete Guide 2022

Content Table:

  1. Introduction
  2. Averages
  3. Percentages
  4. Ratios
  5. Rate Formulas
  6. Finance Formulas



In order to succeed on the Numerical Reasoning Test you are scheduled for, no matter it's type, you will need to have first mastered some basic maths skills.

Numerical aptitude tests usually target the following mathematic skills: 1) Addition 2) Subtraction 3) Multiplication 4) Division 5) Averages 6) Percentages 7) Ratios.

More advanced calculations, such as averages, percentages and ratios can become simpler with the use of specific formulas.

Such is the case with algebraic questions that involve rate problems (work/ speed/ distance/ time) as well as financial-oriented problems. 

For your benefit, we assembled here a short guide to basic as well as advanced formulas that you are expected to be able to apply in your numerical test.

Let's Get Started!



Definition: A calculated “central” value of a set of numbers.

The formula to calculate this looks like this:


numerical formulas 1

 in a more mathematical form it would look like this:

averages formula



Xi = An item in the set; X1, X2, X3 ...

= Sum

N = The number of items in the set

X̅ = The average of set X



Weighted average

Definition: A calculated “central” value of a set of numbers, in which each value or set of values is assigned a different weight.

The formula to calculate this looks like this:


weighted average formula 1

 and in mathematical form:

weighted average formula 2



Xi = An item in the set; X1, X2, X3 ...

wi = The weight of item i in the set

= Sum

N = The amount of the items in the set

X̅ = The weighted average of set X

In a simplified form, it can be put as:


For example: the heights of students in a classroom were measured. There are 2 children at 1.20 m, 3 children at 1.25 m and 3 children at 1:30 m.

What is the average height of a student in the classroom?


weighted average formula 3


Percentages & Fractions

Definition: A percentage is a part of a whole, where the whole is defined as 100. A fraction is a part of a whole, where the whole can be any number.

The formula to calculate this looks like this:


% = (fraction) x 100


Note that when dealing with percentages it is sometimes easier to convert them into decimals and use the decimals in percentages calculations.

For example: 50% = 0.5; 120% = 1.2; 11% = 0.11 etc.


Calculating a percentage

The formula:


% = (Value/Total) x 100


For example: if you own 20 company shares and the total number of shares is 400, this means you own: 20/400= 5% of the shares.


Percentage Increase/Decrease

The formulas:


% Increase:
New value = (1+ Increase) × (Original amount)

% Decrease:
New value = (1 − Decrease) × (Original amount)


For example: if a shirt cost £30 and a week later was offered at a 15% discount, how much does the shirt cost? 91 − 0.15) × 30 = 0.85 × 30 = £25.5


Calculating Percentage Change

Definition: Percentage change refers to the relative percent change of an increase or decrease in the original amount.

% Increase: 

percent increase formula


% Decrease:

percent decrease formula numerical test

For example: if a shirt cost £30 and a week later was offered for the price of £24, what was the discount on that shirt? (30-24/30) x 100 = 20%

Note: Percentage change is different from absolute change. While percentage change is calculated in relation to the original amount, absolute change is calculated as an absolute amount.

In other words, it is not divided by the original amount.



Calculating Percentage Difference

Definition: Percentage difference refers to the relative percentage change in a certain amount, when you are not able to determine which amount is the original one.


percentage difference formula numerical  test


For example: “Molly's designs” gets 200 customers a week while “Best wear” gets 240 customers. What is the percentage difference in customers between the two stores?

percentage difference numerical test



Reversed Percentages:

% Increase:

reversed percentage numerical test


% Decrease:

reversed percentage decrease analytical test


For example: if a shirt costs £33 after a 20% increase in price, how much did it cost prior to the price change? 

reversed percentage example numerical


Percentage Points

Definition: Percentage points refer to an increase or decrease of a percentage. This is an absolute term (in contrast to percentage change/difference).

The formula looks like this:


Percentage points difference = New percent − Old percent


Now use what you learned in practice in your free numerical percentages test


Definition: The relative size of two or more values. The values are usually separated by a colon sign.

a:b is a given ratio. N is the total sum of items.


The number of a items = 

ratios formula numerical test


For example: there are 70 red and blue marbles in a jar. The ratio of red to blue marbles is 3:4. How many red marbles are there?

ratios example numerical test

Now use it to solve your free numerical ratios test

Rate Formulas

What are rate problems?
A rate is a mathematical way of relating two quantities, which are usually measured in different units.

Rate problems usually involve three variables such as speed/distance/time or product/time/number of workers etc.

You are usually given 2 variables and are required to find the missing variable according to the data given in the question.


Speed: S = V × T 

S = distance

V= velocity

T = time


Work: W = P × T

= work

P = power

T = time


For example: Jill drove across a 0.3 mile long bridge. The time it took her car to travel from one side to the other was 20 seconds. How fast was Jill driving?

0.3 = V x 20 ⇾ 0.3/20 ⇾ V = 0.015 Miles per second (or 0.9 miles per minute).


Fixed and variable costs:

Fixed costs are set expenses a company has which never change and variable costs are costs that vary depending on a company's production volume.


Total cost = Fixed costs + Variable costs


For example: if the rent a pencil company pays for its offices is £100 per month, each pencil costs them £0.10 to make, and they make 100 pencils each month.

What is the company's total monthly cost?

Total cost = 100 + (0.10 x 100) = 100 + 10 = £100


Return on Investment (ROI):

Measures the profitability of an investment expressed as a percentage.


ROI calculation formula


Profit margin:

Measures how much out of every dollar of sales a company actually keeps in earnings.


profit margin formula numerical test


Good luck!


numerical test preparation


Not what you were looking for?