Author Archives: Numerical Reasoning

Employers use numerical reasoning tests to help them predict who has the required numerical abiltiy to perform well in the job, so naturally they have to have a point at which they say ‘yes you’re in’ or ‘no, sorry’. In real life, most employers are not this black and white when it comes to your numerical test score; they will look at everyone’s score and compare them against a set of other competencies and success factors. So for example if you scored highly in a partner interview and you have relevant work experience, but were not the highest performer in your numerical test, the recruiting organisation may well decide that you are sill the best person for the job. It’s all relative, as they say.

Very large organisations (such as large professional services firms or firms with large graduate schemes) cannot afford to study each separate applicant in this pragmatic way. Instead they may use an online numerical test as an online sifting tool. The computer will automatically highlight candidates achieving a certain score and put them forward to the next stage of the selection process. If you don’t make this automatic cut, you will be rejected by that company. Often in this situation the company says that you are not allowed to re-apply for another minimum period of time, usually 12 months.

If you don’t make the cut, the truth is that you would probably have found the job frustrating, demoralising  or stressful. The whole point in psychometric testing is that it is the best tool we have for predicting who will be suited to the role. Psychometric testing (including numerical tests) are based on years of research and development. So if the test says you are not suitable, the chances are the test is right and you should be please that you did not get put in a job for which you were not suitable.

When you are preparing for your numerical reasoning test, you should think carefully about where and when you practice. The best environment for practising, it goes without saying, is one which is quiet, comfortable and familiar.

In addition you should consider the following:

Interruptions: put a sign on your door to let your housemates know that you are not to be disturbed.
Same desk: if your real test is online, and therefore can be taken wherever you like, try to make it the same place as where you have practised (e.g. your room or study). This repetition and familiarity will help replicate your performance.
Noise or disturbances: pay attention to your surroundings; is there an annoying draft, humming, or do you have a wobbly desk?


Should you get your clever friend to help with your online (unsupervised) test? Or rather, if you do, will anyone find out?!

This is one of the more common questions I get asked by candidates, because they want to know how easy it would be to cheat.

The short answer is: no; you should not get anyone else to help you with your online test and yes, they probably will find out.

The longer answer, and the reason why, is that modern numerical test technology detects subtle pattern behavior in the way you respond to each question. Some companies then ask candidate to take a follow-up test at their offices. If the ‘fingerprints’ of your test-taking style don’t match, they can ask some pertinent questions about why the results differ.

Another reason not to cheat is that the tests are there to assess whether you will be a good fit for the role. If don’t have the numerical ability to perform, you will spend the rest of your career being passed over for promotion, struggling, and more likely to leave. So whilst this doesn’t sound a valid reason whilst you’re unemployed, the truth is that you will being selected for a job to which you are not suited.





Another frequently-asked question by candidates is what is the pass mark? How many questions should they be aiming to get right?

The answer to this depends on knowing what a percentile score is. Because employers will have a ‘select in / sift out’ percentile score in mind when deciding the cut-off percentile score. The cut-off percentile score can be whatever the employer decides they are looking for, but typically speaking companies such as the big graduate recruiters will use the 40th-50th percentile as a benchmark. Some elite institutions may go as far as stipulating the 90th percentile (i.e. they will take only the top 10%), but this is rare.

What is a percentile? It is the percent of the comparison group who have a score lower than yours. So for example, scoring in the 4oth percentile means that 40% of the comparison group (referred to as the norm group) had a score below yours, and 60% had a score higher than yours.

The norm group is a group of people who have taken the test before, against whom your score is compared. Test publishers will have many different norm groups depending on what the employer wants to benchmark you against. So there are graduate norm groups, senior manager norm groups, international administrative workers norm groups, bespoke norm groups for a specific company, and even a specific role…just about any group of test takers can generate score data against which your score can be comaped.

The reason percentile scores and norm groups are used is that this is the best way to make comparisons. If you score 19/24, is that good? Average? Who knows, until you know what other people got. It may be that the test was really easy and that the average score from other participants is 22/24. The only way to capture your relative performance is to use percentile scoring against a norm group, which is what employers do.

You can read more about percentile scores in our page here: percentiles.


If it can be proved that you cheated in any of your tests, you will be ejected from the selection process. This is because almost certainly you will have agreed to the conditions attached to taking a numerical test for selection, which will have contained a declaration that you have attempted the test on your own without help, without distorting the results  without deceitful intentions etc. And in the unlikely event that you didn’t have to agree to such terms, let’s face it; very few companies would want to  employ a conniving candidate.

So, how do they detect cheating? Various means. Test publishers spend multiple thousands of pounds and many man-hours ensuring their tests are cheat-proof. The most common practice is to give (or pose the prospect of) a re-test under supervised conditions. So if you get a friend to help, or you employ some other deceitful means to distort your score on your online (unsupervised) test, you will probably be found out when you take a re-test in the employer’s office where you are unable to employ such tactics. At this point, if there are significant variations between your supervised and unsupervised test scores, serious suspicions of misconduct will arise.

So don’t cheat!

Almost always yes. The reason for this is that most numerical reasoning tests used in employment selection are trying to measure your numerical ability in a work setting, where there is usually a calculator available. Very few roles nowadays require employees to perform complex mental calculations, so as such very few selection tests assess this ability. If you are given a test where calculators are not permitted, you will be supervised (which is more expensive than an online unsupervised test for the employer) and the maths involved will be more straightforward.

Given that calculators are almost always permitted, what one do you choose to use? If you get the choice (for example you are taking the test remotely from home) try to use a calculator with which you are familiar. Knowing instinctively where the buttons are and how it works will save  a few vital seconds during your test. Also try to use one which displays your keystrokes on the screen (all scientific calculators do this) because this will help you see where you got to in a  calculation involving several input steps. We’ve all had the feeling whilst inputting numbers to a calculator that we’ve miss-keyed something, or forgotten where we got to, so being able to see this on-screen is a big help.

Percentile Scores

The most important result employers will be looking at when you complete your numerical test is your percentile score. The concept of a percentile score is quite important to understand, because it is quite different from a percentage score.

Let’s say you score 18 out of 24 in a numerical reasoning test. Is that good? It sounds quite good; better than average you might speculate. But what if most other people who took the same test scored 22-24? Suddenly your 18 looks low. A percentile score encapsulates the scores of other people, so that your score is directly meaningful in the context of what everyone else scored.

Lets look at some examples, with interpretations to help illustrate the concept.
1st percentile  –  your score was in the bottom 1% of the scores achieved by everyone else
20th percentile  –  20% of people scored lower than your score and 80% scored higher than your score
50th percentile  –  your score was the mean score achieved by everyone who took the test – that is to say exactly half the scores were above yours and half were below yours.
90th percentile  –  your score was higher than 90% of the scores achieved by the people who took the test.

 percentile scores



Classic Question 1: What was the difference in value of Central Pacific’s holding between October and November 2010?

This is  a classic data interpretation question where you need to look between different sources of information. It also includes some typical unit anomalies to try to catch you out. Let’s work through it.


Step 1: Find the information you need

Whilst the pie chart and histogram titles are different, it should be apparent that they both show monetary values of a fund for different regions within the Pacific. The pie chart shows data for Oct 2010 and the histogram shows data for Oct and Dec 2010. The question asks that we look at the difference between Oct and Nov for the Central Pacific element.

For Oct (the pie chart) we have to work out the number because we are told simply that the Central Pacific element is 15% of £37.5 million. That is 0.15 x 37.5 = 5.625 (£million).

For Nov we can take the figure straight from the histogram as 90.6 (£100,000s)

Step 2: Calcualte the difference

The difficult part is now done but don’t forget we need to pay attention to the units.

90.6 (£100,000s) – 5.625 (£million)

£9,060,000 – £5,625,000 = £3,435,000

Ans = £3.435 million



Essentials Lessons:

   Look out for dates, and recognise their different format. Test questions deliberately try to emulate the interpretation required to read numerical data in the real world. So dates are not always straightforward. Sometimes data will be for two seperate periods and it would be a mistake to compare their data like-for-like.




   It is common for different units to be used within the same question, to test whether you pay attention to detail. Dropping the units during a calculation is a good time-saving technique, but make sure you keep everything in the same units and put them back at the end of the calculation. Some numerical questions include in the multiple choice options answers which look similar to the correct answer but with the wrong units, so be careful.


    Some axes do not start at zero, some are truncated, some have no units at all and you have to use the data labels on each data point entry.  Again, this is deliberately done to test whether candidates can interpret the data correctly.


Rebased data
    Some charts are presented as ‘rebased’. This is a useful way of representing comparisons from a reference point and is often used to compare financial performance over time.  The important thing with rebased data is that every data point is entirely relative to the rebased point; no not take the values as absolute.



Keys    Pay attention to the colour coding or shading of keys and their corresponding data. Different fills and patterns can be used to differentiate between data groups and if you’re not concentrating you could mix them up. It is important to note that colours will be used which avoid disadvantaging colour blind candidates; patterns or single colour palates will be used.

Classic Question 1: Add these two fractions and express the answer as a fraction

Adding fractions is something which doesn’t come up very often in numerical reasoning tests, however being confident in knowing how to do it will help with some calculations. How do you work out:



The key is to find a common denominator.  This means a factor which is common to both of the numbers on the bottom of the fraction. You can’t add (or subtract) two fractions if they have different denominators. This is usually best done by manual inspection.

Step 1: see if the larger denominator can divide into the smaller denominator; i.e. can 27 be divided down into multiples of 9. In this case yes! Since 9 x 3 is 27. At this stage we can happily recast the fractions into the same denominator, 9. To express a fraction in a different denominator you must multiply both the top and bottom by the same number to keep the fraction expressing the same value. So…


Which is equivalent to


Which we can now easily compute as

Ans = 14 / 27

At this stage we could look to express the fraction in smaller numbers, but there are no common factors to 14 and 27 so this is as neat as this fraction gets.

In the above example we divided one denominator into the other. But what if there is no common fraction? We have to multiply both fractions by separate numbers to get them into a common denominator. Let’s look at the following example.

fractions 4

So now we have (30 / 78) + (13 / 78) = 13 / 78

Ans = 13 / 78

Classic Question 1: How many Canadian Dollars (CAD) can a trader buy with 400 Indian Rupees (IRP)?

currency exchange

Step 1: Analyse the problem

We cannot convert directly from CAD to IRP, so we are going to have to use an intermediary currency. In this case, GBP. This technique is called cross multiplication/division.

Step 2: Cross multiply/divide

(400 ÷ 82.821) x 1.566

Ans = 7.56 CAD


So why did I do that combination of division and multiplication? Let’s look at the full process:

We need to convert 400 IRP into the base currency we have data for (GBP in this case). So 400 ÷ 82.821 = 4.8297 GBP. Then we need to know how many IRP our 4.8297 GBP is equivalent to. We can use the table again: 4.8297 x 1.566 = 7.56 CAD.