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numerical reasoning tests

Numerical Reasoning Tests

  • 45 tests
  • 900 questions
numerical reasoning tests

Numerical reasoning tests demonstrate your ability to deal with numbers quickly and accurately. These tests contain questions that assess your knowledge of ratios, percentages, number sequences, data interpretation, financial analysis and currency conversion.

What is a numerical reasoning test?

A numerical reasoning test is a form of psychometric assessment commonly used in the application stages of the recruitment process. It is specifically designed to measure a candidate’s numerical aptitude and their ability to interpret, analyse and draw conclusions from sets of data.

They’re often used in conjunction with other psychometric tests, including verbal reasoning tests, personality tests and situational judgement tests.

Unlike standardised maths tests, which demonstrate a student’s ability to learn and apply mathematical techniques based on a set syllabus, numerical reasoning tests reflect how successfully a candidate can apply numerical understanding in a realistic context.

General arithmetic, percentages, fractions and averages are all common elements of a numerical reasoning test, but its main focus is statistical information. Candidates are required to work with graphs, tables and charts to identify key facts and figures, and apply the correct logic to form an answer in response to a worded question.

You may be required to sit a numerical reasoning test if you’re applying for a job in a numeracy-based sector, such as finance or insurance. That said, they are increasingly common for any role that involves a level of data interpretation or numerical analysis, including marketing and HR.

Why do employers use numerical tests?

In a competitive job market, employers of all shapes and sizes use a range of methods to narrow down their pool of candidates for any given opening. Numerical reasoning tests are one such method.

The questions posed in these tests are based on the particulars of a given job function, such as determining profit margin or estimating material quantities. As such, they give employers a good indication of how an applicant would perform in the role in question, allowing them to separate those with promise from those who would struggle with their daily tasks.

Numerical reasoning tests are also a good measure of how well an individual works under pressure. Employers want to know that you can perform well in any given circumstance, and since these assessments are timed, they demonstrate your ability to interpret data and draw accurate conclusions at speed.

How numerical reasoning tests work

Numerical reasoning tests are not standardised. They can vary in duration, complexity and format depending on a number of factors, including:

  • The test provider – there are several publishers of numerical reasoning tests, each with its own slight variation on the assessment, so the exact nature of your test will depend on which provider the employer uses.
  • The occupation in question – since numerical reasoning tests are used to predict your workplace performance, they vary in relation to the role for which you’ve applied. For example, the questions posed to an aspiring engineer will differ from those presented for a financial post.
  • The level of the position – typically, the higher up the ladder you climb, the more complex the numerical reasoning test, so the difficulty rating of your assessment will increase as you progress from graduate, to professional, to managerial level.

That said, there are commonalities across the board which can help you prepare for your numerical reasoning test.

Typical Structure

Generally speaking, numerical reasoning tests are short, timed assessments presented in a multiple choice format. Their exact length can vary from roughly 10 to 45 minutes, and the number of questions will be relevant to their duration. As a guide, one question for every minute is a reasonable expectation, but some of the more difficult tests require more speed.

If you have the right skill set, the questions themselves would not be too difficult to answer under normal circumstances. However, these tests aren’t designed to be straightforward, and the time limit isn’t the only added complication.

Many test publishers use what are known as distractors – answer options purposefully similar to the correct answer, or that could be achieved if a common mistake was made.

In addition, numerical reasoning tests for graduate level positions can be quite complex in their nature. The data given may include information that’s not relevant to the question posed but is there to distract you. It’s also likely that you’ll need to apply a number of processes to draw the right conclusion, not just a single action.

Common Question Types

You can expect a range of questions that cover various aspects of numerical understanding.

These are likely to include general arithmetic, or numerical computation, where you’ll work with addition, subtraction, division and multiplication, as well as dealing with things like percentage change and simplified ratios.

Currency conversion questions are also a common occurrence.

Numerical reasoning questions often take the form of a number series, where your numerical logic will be tested, rather than your ability to perform basic calculations.

You’ll also encounter numerical estimation questions. Here, you’ll be asked to give an approximation as opposed to an exact answer, usually through graph interpretation.

The last common question type is data interpretation. With these, you may be presented with numerical data in the form of graphs, charts and tables, or in a paragraph of written text, and asked to make an inference based on the information provided.

Scoring

How well you’ve performed in your numerical reasoning test will usually be assessed comparatively. Your prospective employer will receive your raw score, that is the number of correct answers, which will then be measured against a benchmark score.

This benchmark score will either be based on the performance of other candidates for the role, or the historical scores of employees in a similar position of comparative level.

There is no differential or negative scoring in a numerical reasoning test. You’ll get one point for every correct response and won’t be marked down for an incorrect answer.

You can easily improve your score with practice, and by mastering some key formulas for success.

Key maths skills you'll need – and how to improve

Although numerical reasoning tests focus more on your interpretation and analytical abilities, rather than your mathematical skills, there are a few key areas you’ll need to be confident in.

Addition, subtraction, multiplication and division should be revised as the very basics. Generally speaking, GCSE level understanding is sufficient.

You’ll also need to be able to work with percentages, fractions, ratios and averages. Here are a few key formulas to get you started.

Percentage Increase

To calculate a percentage increase, subtract the original number from the new number, divide this difference by the original number, and multiply by 100.

Example: find the percentage increase of 200 to 300

300 - 200 = 100

100 ÷ 200 = 0.5

0.5 x 100 = 50

Answer: 50%

Percentage Decrease

To find a percentage decrease, subtract the new number from the original number, divide this difference by the original number, and multiply by 100.

Example: find the percentage decrease of 500 to 240

500 - 240 = 260

260 ÷ 500 = 0.52

0.52 x 100 = 52

Answer: 52%

Adding Percentages

To add two percentage increases together, first add 100 to each given percentage and convert into decimals. Multiply the base figure by the first decimal, and then multiply the resulting value by the second decimal.

Example: your phone bill is £42. It increases by 10% after 12 months, and a further 20% increase is applied six months later. What’s the price of your phone bill after 18 months?

10 + 100 = 110, expressed as 1.10 as a decimal

20 + 100 = 120, expressed as 1.20 as a decimal

42 x 1.10 = 46.2

46.2 x 1.20 = 55.44

Answer: £55.44

Converting Percentages into Fractions

To convert a percentage into a fraction, simply write down the percentage as a proportion of 100, and simplify if necessary.

Example: Convert 75% into a fraction

75/100 simplified to 3/4

Answer: 3/4  

Mean Averages

To find the mean average of a series of numbers, add them all together and divide the answer by the total amount of numbers present.

Example: find the mean average of 3, 15, 8 and 22

3 + 15 + 8 + 22 = 48

48 ÷ 4 = 12

Answer: 12

Adding Fractions

To add two fractions together, first make sure the denominators are the same, then add the two numerators together and place over the denominator. Simplify the fraction if needed.

Example: 1/5 + 3/5

The denominators are the same, so 1 + 3 = 4

Answer: 4/5

If your denominators are not the same, multiply one fraction by the required amount to get two equal denominators. You must multiply both the denominator and numerator to keep the value of the fraction.

Example: work out 2/3 + 1/6

To get a common denominator, multiply 2/3 by 2

2 x 2 = 4

3 x 2 = 6

Now work out 4/6 + 1/6

4 + 1 = 5

Answer: 5/6

Subtracting Fractions

To subtract fractions, simply deduct one numerator from the other and place over the denominator.

Example: work out 3/7 - 2/7

3 – 2 = 1

Answer: 1/7

If the denominators are not the same, follow the steps as above to first achieve a common denominator.

Multiplying Fractions

For multiplication, multiply the numerators, then multiply the denominators and write as your new fraction.

Example: 1/3 x 2/5

1 x 2 = 2

3 x 5 = 15

Answer: 2/15

Dividing Fractions

To divide fractions, find the reciprocal of the dividing fraction by turning it upside down, then multiply the first fraction by this reciprocal.

Example: 2/3 ÷ 1/4

1/4 becomes 4/1

2 x 4 = 8

3 x 1 = 3

Answer: 8/3 

Expressing Mixed Fractions as Improper Fractions

First take the whole number of the mixed fraction and multiply it by the denominator of the fractional part. Add this result to the numerator and write above the existing denominator.

Example: convert 3 2/4 into an improper fraction

3 x 4 = 12

12 + 2 = 14

Answer: 14/4, simplified to 7/2

How best to prepare for a numerical test

Numerical reasoning tests aren’t easy. Even if you have an excellent grasp of basic arithmetic and years of experience working with data in its various forms, exam nerves, time constraints and intentional decoys can all impact your performance.

The good news is that with a bit of effort, and some tips to pass your numerical reasoning assessment, you can greatly improve your chances of a better than average score.

Make sure to take plenty of practice tests and time yourself as you do. Analyse your results, and if there’s an area you’re struggling with, make this a priority.

Don’t just push a test aside once completed. Read through the answer explanations in detail, regardless of whether you got it right or wrong. The more you do this, the better you’ll understand relevant processes and when to apply them.

If they’re willing to divulge the information, find out what test provider your prospective employer uses. It’s likely the publisher has practice tests of its own that you can take for a more realistic representation of what’s in store.

Finally, brush up on your mental arithmetic. The skills you need here are easily improved with practice, and the quicker you are at basic calculations, the more time you’ll have to interpret complex data.

Common numerical test publishers

There are many companies that design and administer numerical reasoning tests. We’ve given a brief overview of six of the most popular below.

SHL

SHL is one of the better known publishers of numerical reasoning tests. It offers employers tailored assessments to suit specific job roles, which generally last between 17 and 25 minutes depending on the level of the position applied for.

Cubiks

Cubiks provides a range of psychometric tests including personality and situational judgement tests, as well as ability tests under its Logiks banner. The Logiks Numerical Reasoning Test is used by many big name employers including KPMG and Shell. It’s a 25-minute assessment consisting of 20 questions.

Talent Q

The Talent Q numerical reasoning test is slightly different in that it’s a computer adaptive assessment. Basically, this means the questions are generated based on your previous answers and adjust in difficulty accordingly, so the better you perform, the harder it gets.

cut-e

Acquired by AON in 2017, cut-e offers a range of numerical reasoning tests that are a little different from the norm. The most complex, the scales numerical ability test, works solely on inference, where you’ll be given a statement relating to particular data, and asked to answer true, false, or cannot say.

IBM Kenexa

Another provider popular with big name employers, including Amazon and GSK, IBM Kenexa’s numerical reasoning test is typical in its structure, but since it draws from an extensive question pool, no two tests are ever the same.

Revelian

This is perhaps one of the toughest numerical reasoning tests in terms of time pressure. You’ll have just 12 minutes to work through as many of the 25 questions as you can, including word problems, number matrices and number series.

Saville

Saville offers a range of numerical reasoning tests suited to different occupations and professional levels. They’re heavily focused on numerical interpretation, with several data sets presented, and three minutes to answer four questions on each one.

Pearson

Pearson administers psychometric tests through its assessment platform, TalentLens. As one of the most established providers, its numerical reasoning test is widely used in recruitment across both the public and private sectors.

Prepare yourself for leading employers

Free example numerical reasoning questions

Try out these 4 example numerical reasoning questions. Answers to each are below the questions, with full explanations.

1. Percentages

numerical reasoning practice question

What was the average total percentage decrease in the number of homes sold by Bradfield Homes and Thompson Homes from May to June?

  • A) 18.18%
  • B) 13.26%
  • C) 13.04%
  • D) 8.33%

2. Ratios and fractions

numerical reasoning practice question

If there were 50,000 people employed in Blackpool in 2021 what is the ratio of employed to unemployed people in that year?

  • A) 25:1
  • B) 12.5:1
  • C) 10:1
  • D) 8.33:1

3. Tables and graphs

numerical reasoning practice question

If Heathrow Airport pledged in January to reduce cancelled flights by 80% by March, by how many cancelled flights have they failed to reach this target?

  • A) 4
  • B) 0
  • C) 14
  • D) 18

4. Conversions

numerical reasoning practice question

2,000 CHF was used to purchase USD in Q2 and then sold in Q4. How much will the amount be worth in CHF?

  • A) 2,117.65
  • B) 2,098.03
  • C) 2,077.67
  • D) 1,981.48

Answers

1) May = 110 + 120 = 230 June = 90 + 110 = 200 230 - 200 = 30

30 / 230 x 100 = 13.04%, so the answer is C)

2) 50k : 5k

50 / 5 = 10

10:1, so the answer is C)

3) Step 1: Take the number of flights cancelled in January and calculate an 80% reduction:

30 × (1-0.8) = 6

Step 2: Subtract this figure from the March figure:

10 - 6 = 4, so the answer is A)

4) Step 1: Calculate how many USD you can buy with CHF 2,000 in Q2:

2,000 × 1.08 = USD 2,160

Step 2: Calculate how many CHF you can purchase with USD 2,160 in Q4:

2,160 ÷ 1.02 = CHF 2,117.65, so the answer is A)

For more example questions and explanations, try our free practice test questions, or download our numerical reasoning questions and answers PDF.

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How are numerical reasoning tests scored?

Numerical reasoning tests use various scoring systems, but the two most common are raw and comparative. Raw score is when all your correct answers are summarized and displayed in percentage ratio. Comparative score is when your results are compared to the results of other people who took the test in your group.

Where will I take my numerical reasoning test?

Depending on the employer, you may be asked to take your numerical reasoning test online, or in person at an assessment centre. If online, it may also be the case that you’re required to sit a second test in person as an anti-cheat precaution.

When should I expect my results?

Unfortunately, there’s no answer to this. It will vary between employers. If you’re unsuccessful in progressing to the next stage, you may not even receive your results at all. Where this is the case, you can always try contacting the HR department for feedback on your assessment. This can help you improve in future tests.

What's more important – speed or accuracy?

Ideally you want a fine balance between the two. The more questions you answer, the higher your score, but only if you get them right. Don’t take chances, and don’t let the time pressure get to you. Ultimately, practice is more important than either, since this is the best way to ensure you can work both quickly and correctly. 

Can you use a calculator in numerical reasoning tests?

In most cases, yes, you’ll be able to use a calculator, and we recommend using one that you’re familiar with. However, this might not always be possible. There are some numerical assessment tests that don’t allow them at all, and others where, if taking the test in person, you’ll be given a standard issue calculator at the assessment centre. Every test will have different rules, so if you can, check this information beforehand.

Why are numerical reasoning tests so hard?

Numerical reasoning tests are hard to ensure that there’s a nice spread of results for employers to gain a strong understanding of their candidates’ analytical abilities. On top of this, some numerical reasoning tests are purposefully written to be difficult to reveal how candidates perform under pressure.

Where can I practice numerical reasoning tests?

There are many general practice tests available online, as well as publisher specific tests from the providers themselves, including those mentioned above. Some of these are free to use, some are paid for services that offer additional support. You can also use our own resources. We have a range of free aptitude tests to help you prepare for whatever type of assessment you may be facing.

Can I get help if taking my test online?

Having someone to help you with your numerical reasoning test is not a good idea and getting someone to take it for you should be avoided at all costs. You’re taking the test as an indicator of how well suited you are for the role in question. Cheating is not only disrespectful to the employer, it will be of no benefit to you in the long run.

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Numerical Reasoning Tests Tips

1Be prepared

If taking your test at an assessment centre, make sure you know exactly where you’re going, and arrive early to avoid panic. If taking your test online, make sure you’ll have no interruptions, and double-check your internet connection for stability.

2Digest the practice questions in the real test

Most numerical reasoning tests start with a couple of practice questions to get you warmed up. Study these carefully and make note of structure, content and style. They’ll give you a good indication of what’s to come and get you in the right frame of mind.

3Pay close attention to detail

The easiest way to slip up on your test is to misinterpret the question. You may be working against the clock but don’t let that stop you from taking the time to understand what is being asked. Read each question carefully to avoid silly mistakes.

4Work with what you've been given

Each question will include all the information you need to draw the right conclusion, so don’t make assumptions about the data. Just work with what’s in front of you.

5Don't dwell on difficult questions

Remember, you’re working on a time limit, so if you find yourself stuck, move on. Often, the more you struggle with a complex problem, the more confused you become. You can always come back for another go if you have time to spare at the end.

6Take an educated guess

Where you are unsure of the answer, use a process of elimination to narrow down your options. An unanswered question will score you nothing. An educated guess may well prove correct.

7Beware of red herrings

As mentioned, multiple-choice options in numerical reasoning tests can often include distractors, and questions can include irrelevant information designed to put you off track. Keep your wits about you, double-check your answers for accuracy, and focus only on the information you need.

8Double-check what you're working with

Some questions may require you to work with varying units of measurement, multiple currencies, or different number representations. Make sure you’re using the right information in the right way to draw your conclusions.

9Pace yourself

Although it’s important not to let it become a distraction, you need to be aware of timing. As a rule of thumb, one question every minute is a steady pace, though some tests will allow more, and some less. Practice is essential here, so be sure to include pacing as part of your test preparation.

10Stay calm and focused

Numerical reasoning tests require fixed concentration, so shut yourself off from whatever surrounds you. Though it’s easier said than done for some, try not to let the pressure get to you, and keep a cool head that’s zoned in on the task at hand.

Numerical Reasoning Video Tutorials

Simplified Ratios

2 mins

Data Interpretation

2 mins

Number Series

3 mins

Percentage Change

2 mins

Currency Conversion

2 mins

Graph Interpretation

2 mins

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