Numerical Reasoning Test Guide: Our Top Tips
This guide will help you develop your skills, knowledge and strategies in tackling numerical reasoning tests.
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How a numerical reasoning test works
The great thing about numerical tests is that they are not the same as a maths test. Of course, they involve numbers and calculations but they are not trying to measure your maths ability in the same way as a school exam. This is great news for those of us with dark memories of impenetrable maths questions requiring skills like algebra, trigonometry and probabilities. Numerical tests do not require you to write out longhand answers and they do not require knowledge of uncommon formulae and theories.
So what are 'Numerical Tests'?
Numerical tests are fundamentally different from maths tests because of what they are built to measure. Rather than assess your understanding and application of a maths syllabus (such as GCSE or A-Level) they are designed to measure your ability to correctly interpret numerical information and use it to solve problems and make decisions. Modern tests base the information on real-life numerical data you would find in the workplace. So numerical tests only really require you to perform the kinds of analysis with numbers you'd be expected to perform at work.
This difference between maths exams and numerical tests means that sometimes people's scores from both are different. Employers often see candidates with great maths qualifications who demonstrate poor numerical test results. This is generally the result of the maths qualifications being pushed up by good exam technique, lots of revision and effective memory ability. The numerical test score is lower because it is not affected by exam technique, revision and memory; the numerical test relies on effective analysis, problem-solving and good test-taking technique, of which you will learn more later in this guide.
This is great news for those test-takers who have traditionally struggled with maths exams. Numerical tests are different - they measure different skills in a different way. Employers often see candidates with low or mediocre maths qualifications who can perform very well on the much more job-relevant numerical test.
As well a being different from maths exams, numerical tests tend to share a number of common characteristics, so you will always know what to expect.
Common characteristics of numerical tests include:
- Multiple choice answers - no longhand answers or showing your working-out.
- Use of calculators permitted - no mental arithmetic required
- Strict time limits - some are generous while some are very short (we cover this later)
- Example questions before you start the test - these are not timed or scored
- No prior knowledge required - no equations to memorise (or surreptitiously write on your arm)
- Relevant to the workplace - modern tests are based on the kind of numerical information you would deal with in the job
Understanding how numerical tests work, how they are different from maths exams and their common characteristics should begin to dispel the fear of the unknown. Any remaining anxiety about your performance can be countered by developing a deeper understanding of the inner-workings of tests and, in section 2 of this guide the most effective test taking techniques to develop based on this understanding.
What maths do I need to know
Numerical tests are not the same as maths exams but you will still need some maths skills - you will be dealing with problems based on numbers after all. Fortunately, the skills you need are far simpler than those expected by maths GCSE.
Maths for numerical tests
Here's a list of the most widely used maths calculations in numerical tests:
If you are unfamiliar or unconfident with any of these maths skills you should focus on your time on test practice questions that require the forms of calculation that trouble you. You could also look to use basic maths study aids to supplement your development through the practice questions.
Remember that you will be allowed to use a calculator during the numerical test to complete these calculations.
High-level critical reasoning in numerical tests
Graduate and professional tests are at the top of the numerical-test tree as far as difficulty is concerned. These top-level tests measure the advanced skill of numerical critical-reasoning to reflect the demands of the jobs for which they are used to help recruit and the calibre of candidates who apply.
The difficulty of these tests does not lie in the types of calculations you are required to perform; numerical critical-reasoning tests are still based around the seven basic maths skills described above. Their difficulty is the result of the complexity of the numerical data the questions are based upon and the nature of the problems you are required to solve.
What is critical reasoning?
Numerical critical reasoning is the ability to analyse and manipulate numerical information in order to draw inferences, determine underlying relationships and make decisions. These high-level tests are different from those you might be expected to complete for entry-level or mid-level roles because you are expected to demonstrate abilities that are above and beyond simply understanding numerical data and answering questions about it. Instead you will need to work in a more complex way to arrive at correct answers.
What this means in reality is that to answer a numerical critical-reasoning test you are often required to perform multiple calculations. In other words there may be several stages of calculation you need to complete to reach an answer. Sometimes this even involves a degree of estimation or dealing with ambiguities, as you sometimes would at work.
If this sounds a little daunting, don't worry. The calculations are still based on basic maths skills. You can maximise your score by developing effective test-taking technique. You can complete some practice questions to get a preview of the demands presented by critical reasoning questions; they may not be as bad as you think!
Become a test-taking black belt
How strategies make the difference to your score
Differences we see in people's test scores are often down to factors unrelated to their numerical ability, such as:
- Lack of familiarity with test taking
- Poor timing
- Silly mistakes
- Nerves and anxiety
Candidates with high scores tend to posses high levels of numerical ability combined with effective test-taking strategies. These test-taking black belts know that when you're taking a numerical test, it's not all about maximum effort; it's about theright kind of effort in the right places.
This section introduces you to the advanced test-taking strategies you will develop to ensure that your test score is not dragged down by errors, slips and poor technique. Test-taking black-belts achieve their high scores by applying the numerical abilities they have developed through practice using the sharpest strategies. You can learn the winning strategies that can make a real difference to your numerical test performance.
Focus, nerves and concentration
For many of us the worse part of taking a numerical test is the waiting beforehand. The nerves and anxiety we can experience before the test session can spill into the early stages of the test itself, affecting your focus and concentration. You need to maintain maximum concentration during the test session in order to perform at your best. Nerves and anxiety must be minimised before they cause mistakes and a dip in performance.
Here are some tips for combating nerves and building focus prior to the test session:
1. And breathe...
If you're feeling nervous then move your attention to your breathing. Ensure you are taking long, slow breaths and focus your mind on counting slowly down from 10 with each breath. Each time your mind wanders from breathing this countdown you should gently move the distracting thought to one side and begin the count again from 10. This focusing exercise reduces your stress levels and enables the parts of your mind devoted to concentration and reasoning to marshal its energies ready for the test itself.
2. Feel the fear and do it anyway
Sometimes our nerves and anxiety can cause distracting physical and mental symptoms of stress. A racing heart, sweaty palms and a mind full of chattering monkeys are common stress-related sensations, which make concentration and peak performance much harder to achieve. Rather than try to fight against these feelings you should use the 'acceptance and commitment technique' to move past them. Quiet your mind by moving around your body to notice, label and accept each of the stress related sensation you identify. Do not try to counteract them; simply acknowledge that they are there. Next you must work on your commitment; remind yourself of your objectives and then rehearse exactly what you are going to do when the test session begins. Acceptance and commitment technique helps you to feel the fear and do it anyway.
Ensuring that you are focused and calm will help you to employ the effective test-taking strategies during the test session itself that will give you the edge.
Our final top numerical reasoning test tips
Now that you've gathered a better understanding of numerical reasoning tests and the key things to consider, it's time to move onto our final tips.
Watch the following video, or read through the list below, and absorb our final advice on numerical reasoning tests. Once you've taken in all our advice, it's time to start practising!
Numerical Test Tip 1: Understand the questions
If you practise some psychometric aptitude tests, you will see for yourself how easy it is to be caught out by not reading the question properly. This includes not recognising the units, not seeing the applicability of a graph or table (e.g. dates), and making assumptions about implied meaning. It is worth re-reading the question after you have answered it to check you have understood it since this will take a split second but will prevent you from throwing away the time spent on that question.
Numerical Test Tip 2: Bring your own calculator
If you are sitting your numerical reasoning test at an assessment centre, the chances are you will be told you have to use the calculator they provide to you. However take your own just in case. You will be familiar with the functions of yours and the locations of buttons will be instinctive, enabling you to save a few vital seconds over the other candidates. If your psychometric test is online, obviously you can use your own calculator.
Numerical Test Tip 3: Know your calculator
If you are allowed to use your own calculator (often not the case at assessment centres), or you are sitting your numerical reasoning tests online, make sure your calculator is both familiar to you and has large buttons and a clear screen. Don’t use the calculator on your mobile phone for example! This will all help save time and will reduce the chances of calculator entry mistakes.
Also, make sure you are familiar with all the useful features of your calculator. The numerical reasoning tests you will have to face probably won’t involve lengthy statistical analysis and complex functions. But as a minimum make sure you know:
- How to use the bracket function to deal with calculations involving multiple stages
- How to enter values to multiple memories and recall them
- Powers. This is useful, for example, in calculating compound interest over multiple years.
Numerical Test Tip 4: Use the rough paper
In most psychometric aptitude tests you will be allowed to use rough paper for your working. Sensible use of this will cut down mistakes and save you time if you have to go back to a mid-point in a calculation. The extent to which you write down your working obviously has to be balanced with taking too long on each question; you will get a feel for how much you need to write down when practising some aptitude tests for yourself. Writing things down also helps you spot mistakes with units, which are all too common if you do all the work on your calculator. Sometimes, the working for one question will be required in the working for the next question, so if you already have it written down, you don’t have to repeat that part of the calculation.
Numerical Test Tip 5: Consider only the options available
This applies to numerical reasoning tests only, since the most common form of verbal reasoning tests only ever have three options; True, False and Cannot say. In some numerical questions you can immediately discount some of the available options using deduction or common sense. In ratio questions particularly (e.g. what is the ratio of A:B:C:D) you might not have to calculate all of A, B, C and D. If you've calculated A and B and you can see that only one of the options available is your answer for A:B then click that one and move on! This is a good time-saving technique.
Numerical Test Tip 6: Time allocation for numerical reasoning question
For numerical reasoning questions, have a quick look ahead at the next few questions to see how many questions a figure applies to. It is common for one figure to apply to three or four questions, in which case it is worth investing time to absorb what the data is telling you before launching into the first question. Then on each question, you can refer back to the data but at least you know where to look and what you are looking at. A typical example of time allocation for a set of three questions might be:
- 3 seconds scanning ahead to see how many questions the figure relates to;
- 15 seconds studying and absorbing the graph/table/data;
- 10 seconds reading and understanding the first question;
- 60 seconds answering the question and quickly referring back to the data;
- 10 seconds reading and understanding the second question;
- 60 seconds answering the question and quickly referring back to the data;
- 10 seconds reading and understanding the third question;
- 60 seconds answering the question and quickly referring back to the data.
That’s about three and a half minutes to answer three questions, which is about right for a typical set of three numerical reasoning questions.
Numerical Test Tip 7: Financial Times graphs
It's important to be able to quickly digest and interpret presented data such as graphs, histograms and tables. One of the ways you can improve your speed in an aptitude test is by reducing the time it takes you to take in the information presented in the numerical reasoning questions. You will soon find it second nature to check what the axes are and in what scale, check if the graph has been rebased or not, check if numbers are given in different units, and check what is an estimated projection compared with what are recorded values.
All these things help you to quickly answer numerical reasoning questions, and you can improve your data interpretation skills by reading figure-based news in for example The Economist or the Financial Times. You can also use the data in the pages of these publications to practice converting from one currency to another, which is commonly comes up.
Numerical Test Tip 8: Human error
When performing calculations in your calculator, for example summing a long list of numbers, read the numbers directly from the monitor screen/test paper instead of your rough working. It is easy to misread your scribbles. Also it cuts out one opportunity for human error (the incorrect writing down of numbers onto paper).
Numerical Test Tip 9: Check units and bases
A commonly used technique to test candidates is to present a table of numbers in a thousands for example. A sloppy test taker will miss this and give the wrong answer. The wrong answer is usually one of the options, so make sure you register all the information presented in tables and graphs. Practice will help train you into looking for these details.
Numerical Test Tip 10: Percentage increases and decreases
One of the most common areas of confusion and sources of mistakes in numerical reasoning questions is understanding how to apply percentage calculations to information given in a question. It is essential to understand whether you are being asked to work out a percentage change from A to B or if it’s from B to A. Below are some formulas which describe 4 common situations:
For percentage decreases we can use the formula:A x (1 - percentage decrease expressed as a decimal) = B
For percentage increases we can use the formula:A x (1 + percentage increase expressed as a decimal) = B
However, when calculating from B to A, we must rearrange these formulas.
For percentage decreases when we know the final result, but not the starting result:
B = A / (1 - percentage decrease expressed as a decimal)
And, similarly for percentage increases:
B = A / (1 + percentage increase expressed as a decimal)
Let's consider an example:
Sales this year were £200, which was a drop of 50% from the previous year. Calculate the sales last year?
Our unknown is A, the sales number for last year. Our end result is B, £200. The percentage decrease of 50% expressed as a decimal is 0.5.
Putting these numbers into the formula:
200 = A / (1 - 0.5)
Rearranging to solve for A:
200 / 0.5 = A
200 / 0.5 = 400
A quick eyeball check 200 is 50% of 400, and we're ready to move on to the next question!
Let’s consider another two examples:
"In Year 2 sales were £1,000, which was an increase of 10% from sales the previous year. What were the sales in Year 1?"
Essentially we need to solve the following problem:
? x 110% = £1,000.
So the calculation is ? = (£1,000 ÷ 1.1). So ? = 909.091.
Why is it not £1,000 x 0.9? Because that would be a decrease of 10% applied to £1,000, not an increase of 10% applied to an unknown number.
Let’s consider a second similar question:
"In Year 3 sales were £1,000. If in Year 4, sales decrease by 10%, what would be the sales in Year 4?"
Since this is a decrease of 10% from one number to another, we start with the reference number and multiply by (100 - 10)% expressed as a decimal. So, in this second example, the correct working is £1,000 x 0.9 = £900.
Remember: it is all in the wording of the question. Understand what the starting value is and understand what the end result is.
NOTE: You will see in our solutions a short-hand way of calculating percentage changes. Let's say we want to find the percentage change from 500 to 600. The long-hand way is to find the absolute difference (600 - 500 = 100) and then divide by the starting number. So we would have (100 ÷ 500) x 100 = 20%. This calculation actually simplifies down to 600 ÷ 500 = 1.2, which we know is a 20% increase.
Check out our Numerical Reasoning Test Formula Sheet for more information on the formulas you will need to know.
Numerical Test Tip 11: Do sanity checks
After spending valuable minutes understanding a graph or table, it would be foolish not to spend a couple of seconds checking you answer. This does not mean going through all the working again (that would be a waste of time), but you should spend a few seconds re-reading the question to make sure you have indeed calculated what is being asked, and have a go at estimating a range for where a sensible answer should lie. This serves a quick check to ensure you haven’t done anything silly, or got your units wrong. And hopefully you will move onto the next question with a positive confidence.
Still do a sense-check if your answer matches one of the multiple choice options. Distractors are often generated from common mistakes.
Numerical Test Tip 12: Use a calculator which displays the last entry
With data interpretation questions it is inevitable that you will have to at some point add up (or subtract, or similar) a large list of entries from a table or graph. It is very easy in this type of calculator-entry work to miss out an entry or accidentally take an entry from an adjacent column. If you use a calculator which displays your last calculation or entry (all scientific calculators do this) you can use this feature to check where you go up to and also check that your last entry was correct. Basic calculators do not do this.
This tip only really applies to online psychometric tests because for those conducted at an assessment centre, you will usually be told you have to use the calculator provided.
Additional psychometric test resources
We have lots of specialised and specific psychometric test advice waiting for you. Simply navigate over to our resources section where you can find all of our test advice, or click on one of the following links you may find useful: