Sample Free Numerical Tests with Questions Broken Down Into All Numerical Test Types
✓ Learn what to expect from your fastapproaching Numerical Reasoning test
✓ Improve your abilities with our expert breakdown of example questions & answers
✓ Start your preparation with insider tips and techniques and much more
Numerical reasoning tests reflect your ability to use numbers quickly and accurately.
These tests assess your knowledge on various maths reasoning topics such as financial analysis and data interpretation, currency conversion, percentages, ratios, number sequences and more.
Between stress and the unconventional question structure, numerical reasoning tests are often considered more challenging than other tests types.
Therefore, numerical tests can be a good indicator for the employer to better understand how you cope in stressful situations.
Remember, since numerical reasoning tests are used in multiple professions and levels, from graduates to senior management, the subject matter is quite diverse in topic.
Content Table:
1) Question Types
2) Free Tests
3) Free Tests by Testing Company
4) Sample Questions
5) FAQs
6) Unique Test Types
7) Useful Resources
There are many psychometric maths tests with subtle differences in the type of maths reasoning questions presented to you, as most tests include a mix of more than one question type (for a test with specific question types see here).
We set this page to cover the 5 major question types commonly used that you will most likely encounter on your actual test.
We feel you have a good shot at passing your test with the score you need, if you cover the topics listed below (the links lead to example questions).
1. Graphs and Tables
2. Currency and Unit Conversions
3. Percentages
4. Ratios
5. Number Series
Below the free numerical psychometric tests is a walkthrough of each example broken down to give you a better understanding of each one, you can press the links above to jump ahead.
A Samples for Each of the 5 Major Question Types. Complete each test to get your predicted score, then review your answers.
Tables & Graphs 


Test Time  5 min 
Questions  6 
Pass Score  8 
Currency & Unit Conversion 


Test Time  8 min 
Questions  6 
Pass Score  8 
Percentages 


Test Time  3 min 
Questions  6 
Pass Score  8 
Ratios 


Test Time  3 min 
Questions  6 
Pass Score  8 
Number Series 


Test Time  5 min 
Questions  10 
Pass Score  8 
Practice 1,000s of Numerical Reasoning Questions 


Access 1,000s more questions that simulate your actual test. Just a few days of practice can get you to your assessment knowing just what to expect. 
Numerical test are hardly the same across the board and we know different companies use different tests. So, unless you have to, you shouldn't waste your time practising a nameless generic test.
The list below is planned to grow every time we publish a new free tailored numerical test. Don't be discouraged if your test isn't in the list yet, we're adding new ones all the time.
One of the hardest parts of your preparation process is finding the right numerical reasoning practice.
As noted, practice tests that come with answers are a big help, but these questions should be appropriate for the test you're about to take.
Below is a list of the various numeracy questions you likely will encounter. By understanding what each question's goal you prepare yourself for the test and for the job as well.
Stay with us and we'll give you a taste of each question type and walk you through its solving process.
We've also laid the examples starting with the most important to the least. Keep in mind that you should come to grips with all maths reasoning questions types and put the most time and effort into any question you personally find the most difficult.
The numerical reasoning test introduces a large family of table and graphs that represent maths data.
Tables and graphs questions assess your understanding of numerical data presented in them, along with your ability to extract relevant data and use it correctly.
From these questions, your future employer wants to ascertain how you form logical deductions.
What to expect?
Example Question 1:
How many more employed graduates were there in 1990 than in 2000?
A. 75
B. 360
C. 485
D. 100
E. 135
The correct answer is C (485)
Example Question 2:
What businesses combined contribute 50% of the annual income?
A. Restaurants, Bars & Clubs
B. Clubs & Coffee shops
C. Restaurants, Bars & Coffee shops
D. Restaurants & Cinemas
E. Clubs & Cinemas
The correct answer is D (Restaurants & Cinemas)
50% of the annual income is half of the annual income. The annual income is: 46 + 70 + 104 + 20 + 60 = £300 million (the sum of incomes of all businesses. Therefore, half of the annual income is £300/2 = £150 million. Looking at the answeroptions and summing the annual incomes distribution of the businesses accordingly, one can see that the annual income distribution by
Restaurants, Bars & Clubs = 46 + 20 + 60 = £126
Clubs & Coffee shops = 60 + 70 = £130
Restaurants, Bars & Coffee shops = 46 + 70 = £116
Restaurants & Cinemas = 46 + 104 = £150
The businesses that contributed £150 million combined are: Restaurants (£46 million) and Cinemas (£104 million).
Example Question 3:
If Chinese Insurance Stocks comprise 3.5% of all Insurance securities (globally), approximately how many Insurance bonds are Chinese?
A. 9,200,000
B. 9,500,000
C. 10,800,000
D. 910,000
E. 1,080,000
The correct answer is B (9,500,000)
Looking at the left chart’s title and key, you can infer it presents data about the number of securities (in thousands), which are comprised of bonds and stocks. You should note that the question considers only the insurance securities.
According to the left chart, the total number of insurance securities (insurance stocks + insurance bonds) is: 33,000,000 + 3,000,000 = 36,000,000.
According to the right chart, Chinese Insurance securities are 30% of total securities. Thus, the total number of Chinese insurance securities is: 36,000,000 x 0.3 = 10,800,000
The question states that Chinese insurance stocks comprise 3.5% of the global insurance securities. Thus, the number of Chinese insurance stocks is: 36,000,000 x 0.035 = 1,260,000
As the total number of Chinese insurance securities is comprised of Chinese insurance stocks and Chinese insurance bonds, to find the number of Chinese insurance bonds you simply need to calculate:
Chinese insurance securities  Chinese insurance stocks = 10,800,800 – 1,260,000 = 9,540,000
This equals approximately 9,500,000.
Another possible, slightly shorter, way of resolution is to calculate the percentage of Chinese insurance bonds out of the total insurance securities and multiply it by the total number of insurance securities (which, according to the calculation is 36,000,000):
% of Chinese insurance bonds = % of Chinese insurance securities – % of Chinese insurance stocks = 30% – 3.5% = 26.5%
26.5% of 36,000,000 = 36,000,000 x 0.265 = 9,540,000
Since you are asked for approximation and 9,540,000 is not one of the answer options, you need to find the closest number to 9,540,000. Therefore, 9,500,000 would be the correct answer.
Solving these questions with speed and confidence will be super important for you to get a high score on your test. To dive deeper checkout our full Graphs & Tables
The most commonly used conversion tests are currency and unit conversion tests. Currency and unit conversion questions involve calculating one or more currency or unit values in terms of another.
Many of these types of questions deal with the finance and business world and appear mostly in tables and graphs format.
Example Question 1:
THB (Thai Baht) Exchanges Rates
*% changes refer to THB.
Approximately how many USD can be purchased for 2550 CHF at the end of 2012?
A. 3187
B. 250,952
C. 3230
D. 3209
E. 2231
The correct answer is A (3187)
The table lists exchange rates from THB to other currencies. Since we do not know the exchange rate from CHF to USD, we will have to calculate it ourselves.
First, we need to calculate the exchange rates to CHF and USD in 2012, using the percentage changes in the right column:
THB to CHF in 2012: 0.14% = 0.0014, hence 0.027*(10.0014) = 0.02696
THB to USD in 2012: 0.07% = 0.0007, hence (0.0337*1.0007) = 0.03372
Now we need to find the exchange rate from CHF to USD, so we can calculate how many USD can be purchased for 2550 CHF:
1 CHF is worth (THB to USD/THB to CHF) =
(0.03372/0.02696) = 1.25 USD
Therefore, with 2550 CHF, one can purchase:
2550*1.25 = 3187.5 USD
Since you are asked for approximation and the closest answer option to 3187.5 is 3187, then 3187 is to be chosen as correct.
Example Question 2:
In percentages, how much more USD will one get when exchanging 1,223,500 JPY compared to exchanging 9,750 EUR?
A. 13.3%
B. 88.3%
C. 117.7%
D. 35.5%
E. 90.2%
The correct answer is A (13.3%)
First, convert 1,223,500 JPY to USD using the relevant exchange rate (1 JPY = 0.013 USD):
1,223,500 x 0.013 = 15,905.5 USD
Then, convert 9,750 Euro to USD using the relevant exchange rate (1 EUR = 1.4401 USD):
9,750 x 1.4401 = 14,040.975 USD
Now, calculate how much more 15,905.5 is than 14,040.975. Since the result should be in percentages, and the order of the numbers matters, you should use the formula for percentage change with 14,040.975 as the reference value:
(Difference between Values / Reference Value) x 100
[(15,905.5  14,040.975) / 14,040.975] x 100 =
Since the expression on the numerator is divided by 14,040.975 (the denominator) one can simplify it by dividing each one of the numbers on the numerator by 14,040.75 as follows:
[(15,905.5 / 14,040.975) – (14,040.975 / 14,040.975)] x 100 =
[(15,905.5 / 14,040.975) – 1] x 100 = 13.3%
Note that the order of wording in the question dictates the calculation; when asked how much more X is than Y, you should always regard Y as the reference value and X as the value relating to it. In that respect, comparing numbers in percentages is similar to finding the ratio of two numbers.
Example Question 3:
Approximately, how much did Company X pay for twofifths of June's available storage volume, in GBP?
A. £181,635
B. £408,678
C. £363,269
D. £479,720
E. Cannot say
The correct answer is B (£408,678)
In June, the rent price was $75 per ft^3 while 600 cubic metres(m^{3}) were available for storage. Twofifths of the space is: 600*2/5 = 240 cubic metres.
Converting to ft^3: 240*35.31 = 8474.4.
The total rent would have been: 8474.4*75 = $635,580.
Converting to GBP: 635,580*0.643 = £408,677.94
Note: Always make sure you use the correct axis:
() The left axis presents the available storage volume (corresponds to the grey columns).
() The right axis presents the rent price per ft^3 (corresponds to the blue squares).
() Each axis contributes different values, even for the same line. For example, while the first horizontal line denotes a value of 100 on the left axis, it denotes a value of 50 on the right axis.
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As percentage questions are a fundamental part of numerical assessment tests, it is important to have a good grasp on them.
Percentages are an effective way of measuring an individual’s ability to solve problems from the everyday business and financial world. Thus, the tests are designated to evaluate a candidates' ability to make accurate judgements.
Oftentimes, you will need to find a quantity and quantify percentage problems, express numerical increase or decrease between two numbers using percentage change etc.
It is unlikely you will encounter a test that focuses on percentages alone; rather, many different concepts will be combined to answer a single question. Thus, mastering percentages is extremely important for succeeding on numerical reasoning tests.
Example Question 1:
Due to an increase in taxes on electronic devices, the price of a 46” LED flat TV screen has increased to £845, which is 30% increase of the original price.
What was the original price of the TV prior to the increase?
A. £515.45
B. £591.50
C. £650
D. £676
E. £768.95
The correct answer is C (£650)
In this question the 100% is the original price.
A good way to tackle this type of questions is by writing down the information you have in a table:
%  Value 
You can use the 'triangle trick' in order to calculate the missing data: Multiply along the diagonal and then divide by the remaining number.
Applying this method to this question:
In order to find the missing data we will multiply the numbers connected by the diagonal (the hypotenuse) and then divide by the number located on the remaining vertex: X = (845*100)/130 = £650.
Another approach to this type of questions requires an understanding of the relation between a given percentage and the proportion it represents (and vice versa). This relation is represented by the following formula:
total = the value of the 100%.
We can isolate the part we are interested in: Total = (Value*100)/%
And insert the data: Value = (£845*100)/130 = £650.
Another way to tackle this question: If you start with 130%, divide the number by 130 to get 1%. Then, simply multiply the value you have received by 100.
Example Question 2:
A cell phone company offers insurance that covers cases of theft and accidental water damage. According to its policy, the insurance pays 60% or 50%, respectively, of the value of the phone after a $30 deductible. This means the client pays the first $30, after which the insurance pays 60% of the remaining amount in the case of a theft and 50% in the case of accidental water damage.
How much will a client pay to get an identical new phone, if her cell phone, worth $1,080, was stolen?
A.$420
B. $450
C. $464
D. $660
E. $678
The correct answer is B ($450)
The total price of the phone is $1,080. The client will pay the first $30, which leaves another $1,050 out of which 60% is covered by her insurance.
You can either calculate 60% the insurance covers and then deduct it from $1,050 in order to receive the client’s share, or you can realise that if the insurance covers 60% then the client’s share equals 40%.
We will demonstrate the second option:
40% of $1,050 = 40/100 * $1,050 = $420
Thus, the total amount the client will pay is: $30 + $420 = $450.
Solving Tip: you can use the ‘10% method’ in this question:
10% of $1050 =$105
40% = 4*10% = 4*$105 = $420
$420 + $30 = $450.
Ratios are essentially a different way of expressing a fraction. Using fractions and decimals is a useful method of evaluating ratios in numerical tests.
Ratio and proportion problems are incorporated into numerical reasoning aptitude tests to measure quantitative aptitudes of the candidates.
Example Question 1:
Scott and Rachel are enthusiastic car collectors. The cars they own are either German or Japanese made cars.
The German to Japanese ratio in Scott's collection is 5:2 in favour of the Germans.
The German to Japanese ratio in Rachel's collection is 4:3 in favour of the Germans
The number of Japanese cars Scott owns is identical to the number of Japanese cars Rachel owns.
What is the ratio between the total amount of cars (German and Japanese) Scott has and the total amount of cars Rachel has?
A. 15:8
B. 9:7
C. 1:1
D. 3:2
The correct answer is D (3:2)
A good way to tackle this question will be to use a ratio table:
German  Japanese  
Scott  5  2 
Rachel  4  3 
In the question we are given 2 sets of ratios between German and Japanese cars in each collection. Each collection has its own row in the table.
Since we know the number of Japanese cars is identical in both collections we will modify the table so it will indicate this equality in a manner that is easier to manipulate and preferably using the minimum common product. We will expand Scott's ratio by 3 and Rachel's ratio by 2:
German  Japanese  
Scott  15  6 
Rachel  8  6 
Thus, we can see that the ratio between Scott's total amount of cars and Rachel's total amount of cars is 21:14, simplify the ratio, dividing it by 7 → 3:2.
Shortcut:
Rachel =R
Scott = S
For Japanese cars: 2S=3R
Since you are told that the number of Scott's Japanese cars equals to the number of Rachel's Japanese cars, then the Scott to Rachel Japanese cars ratio also represents the ratio between Scott's total number of cars and Rachel's total number of cars:
Therefore: S/R=3/2
Example Question 2:
Onetenth of one bag of toys weighs the same as oneseventh of one bag of marbles.
What is the ratio of the weight of 2 bags of toys to 3 bags of marbles?
A. 7:15
B. 20:21
C. 21:20
D. 3:2
E. 15:7
The correct answer is B (20:21)
Let T represent the weight of one bag of toys, while M represents the weight of one bag of marbles. According to the question:
Therefore:
The ratio of the weight of 2 bags of toys to 3 bags of marbles is, thus, 20:21.
Number series questions present sequences of numbers called ‘terms’, each following logical arithmetic operation rules.
Your task is to find the missing number in the sequence. The difficulty level of these questions tends to increase as the logic behind the sequences becomes less trivial, thereby demanding attention and creativity.
Example Question 1:
3  8  15  24  35  ?
A. 42
B. 36
C. 48
D. 46
The correct answer is C (48)
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
The answer is 48.
Example Question 2:
3  3  3  6  3  9  3  ?
A. 3
B. 27
C. 12
D. 6
The correct answer is A (3)
There are two ways to look at this series:
(1) There are two 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.
(2) Another point of view:
The series in this question follows two rules:
(1) The mathematical operations between the terms change in a specific order, x, : and so forth.
(2) Every two steps the number by which the terms are multiplied or divided increases by 1.
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Below are commonly asked numerical reasoning questions asked by people just like you. Read on to learn what you need before sitting the test.
A: Some numerical tests allow calculators while others do not. The latter is a technique done to further assess your mental mathematical ability. Finding out if calculator are permitted or not will affect your test preparation:
Calculator Use Forbidden: Practice required math techniques such as basic arithmetic's operations, averages, percentages, ratios, exponents, square roots etc. Our pages and free tests can further help you refresh your math skills. Strengthen your skills further by checking out our mental arithmetic page.
Calculator Allowance: Master your calculator skills. Aside from basic arithmetic's operations, learn how to use various, more advanced, formulas and operations such as exponents, square roots, factorial, memory etc. Feel prepared by reading more on our page, how to use a calculator.
NonCalculator Tests:
Some numerical tests do not allow the use of a calculator as they are an assessment of your mental mathematical ability. While it is, in general, common for there to be a time limit on aptitude tests, noncalculator tests move particularly quickly.
The questions on these tests can be made up of the concepts in the regular numerical reasoning tests seen above.
However, the numbers you are asked to work with are easier to calculate. Learn more about noncalculator tests and how to train yourself today.
A: A good score on a numerical psychometric test varies depending on the position you are applying for.
So, it’s a good idea to look into your chosen company, find the average score and attempt to score higher to shine above other candidates.
upon completion of our test sample, find a score report that breaks down how many questions you answered correctly and incorrectly.
Furthermore, you can go back to any question that you may have scored incorrect and see how our experts answered it.
A: Many large companies such as Pearson, Hewlett Packard and P&G use psychometric maths test. Taking the numerical aptitude test is also true depending on your entrée level.
For example, this exam is used to test incoming management and other supervisor jobs.
The purpose behind using numerical tests is to ensure management is recruiting the best and brightest individuals.
A: If you feel weak in other areas that you could be tested on, we have over 20 free aptitude tests that you shold check out. You can find a generic aptitude test, psychometric, verbal reasoning, Excel, inductive reasoning, and more.
You also have jobspecific free tests that include prison officer examples, a test for pilots and more. Navigate our website and discover additional exams that are most relevant to you.
A: Numerical tests change depending on the position or field they are intended for. In this way, employers can check specific numerical knowledge.
For instance, many healthcare providers such as nurses, paramedics, midwives and healthcare assistants are required to know how to calculate and administer the right amount of different medications.
Thus, drug calculations tests are used to examine how quickly and accurately candidates can make calculations.
Leading banks and investment banking companies meanwhile present their candidates with statistical data in the form of graphs and/or charts to relate to the business world.
The questions better display the candidate's skills in calculating and usage of critical reasoning. Topics can also include basic financial concepts and simplistic mathematical functions such as percentages, ratios, arithmetic, basic algebra, etc.
Typically, the test allows a calculator and consists of 15–30 questions to be completed within a 15–35 minutes timeframe.
Our graduate and senior mgmt numerical packs offer an array of tests known to appear in the selection processes of numerous top investment banks, you can use these materials to prepare for more than one assessment.
You are also welcome to explore some of our investment banking employer pages: JPMorgan Chase, Goldman Sachs, Merrill Lynch Bank of America, Morgan Stanley, Citigroup, Deutsche Bank and Credit Suisse.
A: Time limits for numerical reasoning tests differ depending on the test provider and specific test you are working on.
The best policy is to find out which provider and types of tests you will experience. After you can backtrack and work on speedily getting through the questions.
A: The difficulty of numerical reasoning tests differs from person to person. One person may struggle with fractions while the same person cannot solve wordproblems or graphs.
We recommend that you take a general test and personally figure out which areas you struggle with then focus your energy on those specific areas.
There are too many numerical assessment tests to give you an introduction that covers it all.
The following tests are specific types that
Basic numeracy Tests:
Basic numeracy tests, also known as numerical literacy tests or basic maths tests, are all about the foundations of maths.
Having a good grasp of how to use the four basic operations, fractions, decimals, rounding numbers, averages, and basic geometry is important for many jobs.
In fact, companies often test their candidates to make sure they possess these key skills. The questions are often simple and must be solved in limited time frames.
For each type of question, you may encounter a variety of mathematical concepts, such as the four functions, ratios, percentages, statistics, decimals, and fractions.
It is unlikely you will encounter a test that focuses on just one concept; rather, many different concepts will be needed to answer the questions.
NonCalculator Tests:
Some numerical tests do not allow the use of a calculator as they are an assessment of your mental mathematical ability. While it is, in general, common for there to be a time limit on aptitude tests, noncalculator tests move particularly quickly.
The questions on these tests can be made up of the concepts in the regular numerical reasoning tests seen above.
However, the numbers you are asked to work with are easier to calculate. Learn more about noncalculator tests and how to train yourself today.
Charts in numerical reasoning questions are used to easily present data for the question and are a visual aid to help you understand the data under discussion. There are two types of charts used on numeracy tests: graphs and tables.
A graph shows the relation between a number of different things or variables, which are each measured along a pair of axes at right angles.
Tables, on the other hand, display a set of facts and figures according to a system designed to fit a lot of information into a small space.
This type of test is provided by SHL, cute and TalentQ.
These are difficult types of questions commonly seen on the GMAT and the Rust Advanced Numerical Reasoning Appraisal (RANRA). Before presenting the question, there are two statements, each offering a specific data set.
Your task is to determine how sufficient these statements are to helping you answer the question:
Do you need the information from both statements? Is just one of them enough? Does neither of them help you? Does each statement have enough information on its own?
Advanced numerical reasoning tests are used when advanced maths reasoning questions, analysis and data interpretation skills are required for the job.
These numerical psychometric tests include similar maths concepts to the numerical questions seen above and are simply considered more difficult as they include numerous charts to read and more calculations to perform.
You may also need to use information beyond the question, such as formulas that may or may not be provided on the test.
Numerical critical reasoning tests are a type of advanced numerical test, but these tests are difficult to characterise as each assessment company sets its own standards. One thing common to these tests is that they have very accurate and precise calculations are needed to solve the math problems.
For a deeper dive into the rabbit hole, we've compiled some of our more advanced resources.
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