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Content Table:

  1. What to Expect from Your Numerical Test
  2. Question Types
  3. Free Tests
  4. Free Tests by Testing Company
  5. Sample Questions
  6. FAQs
  7. Unique Test Types

 

Top Numerical Reasoning Tips Video Tutorial

 

What Is a Numerical Reasoning Test?

Numerical reasoning is the most used type of aptitude or psychometric tests. Numerical reasoning tests assess your ability to use numbers quickly and accurately.

They 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.

 

Read on to:

✓ Learn what to expect from your fast-approaching 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 Question Types: Try Each Type to Locate Your Weak Points

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 below lead to example questions and solution walk-through. We broke-down the whole solving process for you so you could get a better understanding of question type.

  1. Graphs and Tables
  2. Currency and Unit Conversions
  3. Percentages
  4. Ratios
  5. Number Series

 

note  Note:  Most psychometric maths tests include a mix of more than one question type - with different tests having many subtle differences in the way each type of questions is presented to you.

For tests with only a specific question type - see here

 

Free Numerical Reasoning Practice Tests 

1 Sample 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.

 

Tailored Numerical Tests - Practice Questions You'll See on Your Specific Test

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.

 

note  Note:  This list 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.

 

Numerical Reasoning Test Sample Questions & Answers:
a Walk-Through by Our Experts

  1. Graphs and Tables
  2. Currency and Unit Conversions
  3. Percentages
  4. Ratios
  5. Number Series

 

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.

note  Note:  One of the hardest parts of your preparation process is finding numerical reasoning practice that emulates your real exam.

Generic Practice questions can be a big help, but you're always taking a risk of putting in time and effort only to face completely different questions when you finally take the test.


1) Tables & Graphs

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?

  • Tables display data in rows and columns, containing a lot of information in a small space. You will need to learn how to extract only what is needed to come up with an answer.
  • Graphs mostly show the relation between a number of different items or variables. To solve them efficiently you will have to get to know the relationship types and learn how to spot them.

 

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)

 

The number of employed in 2000 =

Private + State = 1250 + 1350 = 2600.

The number of employed in 1990 =

Private + State = 1475 + 1610 = 3085

The difference in the number of employed in 1990 and 2000 =

3085 - 2600 = 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 answer-options 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 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 ≈ 9,500,000

Solving these questions with speed and confidence will be super important for you to get a high score on your test. To dive deeper check-out our full Graphs & Tables 


2) Currency & Units Conversion

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*(1-0.0014) = 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 thr correct answer.

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 two-fifths 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(m3) were available for storage.

Two-fifths 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.

You can get access to full length mock tests and many more practice drills tailored to your exact test, by employer or test name. 

don't waste time practising generic materials that may or may not look anything like your real test. We research, compile and verify practice questions based on actual tests.

Don't Lose Time! Continue the Practice You Started

Don't Lose Time. Complete the Preparation You Started.

 

3) Percentages

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 (£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).

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  ($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.

Alternatively you can realise that if the insurance covers 60% then the client’s share equals 40%.

 

Let's 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


4) Ratios

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

Remember, you are told that the number of Scott's Japanese cars equals to the number of Rachel's Japanese cars.

So, 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:

One-tenth of one bag of toys weighs the same as one-seventh 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.


5) Number Series

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 (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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FAQs

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.

 

Non-Calculator 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, non-calculator 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 non-calculator 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 job-specific 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 word-problems 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.


Numerical Test Types: There are More than You May Think

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.

 

Non-Calculator 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, non-calculator 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 non-calculator 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, cut-e and Talent-Q.

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.

tailored test prep for numerical reasoning tests

For a deeper dive into the rabbit hole, we've compiled some of our more advanced resources.

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