So, you have been invited to sit EPSO´s MCQ (Multiple Choice test) but feel insecure about how to best tackle the “Numerical Reasoning” part of the test? ESPO Numerical reasoning tests use facts, tables, ratios, percentage and other data to test your ability to reason with numerical information. You’ll need to understand what is being asked of you and apply the appropriate operations to find the correct answer. In this article, we will explore what you will face when sitting such a numerical reasoning test and run through tips and examples designed to help you perform better.
Numerical data is data that is expressed with digits as opposed to letters or words so with numerical reasoning tests, the data is presented in various formats like tables, and raw data contained within sentences. Pie-charts and graphs are not common by other employers but are not commonly used in EPSO´s numerical reasoning tests. You will often have to perform several operations on that data to arrive at the correct answer. The key is to practise enough to quickly be able to identify what operations are needed, and then to perform them accurately. A key point to make here is that the answer is never just there staring at you. You do have to extract the data and apply some form of mathematical calculations. We’ll cover the type of calculations you may need to make in this article, so don’t worry if you haven’t used maths since school or college!
Unlike other psychometric tests, you will not expect to see abstract diagrams and data. There will be obvious headings at the top of the chart, so you know what is being represented. For example: “Number of Units Sold.”
They are not designed to test extremely complex mathematical operations, so you won’t be asked to work on highly-advanced formulae, such as parametric equations, complex matrices or angle calculations. Neither will they test your verbal reasoning and verbal critical reasoning skills.
Employers tend to use numerical reasoning tests and other psychometric tests (as part of their assessment methodology) because they are believed to better predict future job performance than traditional selection methods such as interviews and reading through CVs. As most tests now take place online, they are seen as a quick, accurate, fair, and low-cost way of sifting through the many applications received, particularly at graduate level.
Your numerical test results are compared against a large group of people who have taken the test before so the employer can review prospective candidates and understand if your core is high, typical or low. You may only get 5 out of 10 right, but when compared against the wider group, this may be a high score. Keep in mind that EPSO´s scoring throughout various competitions and years change. Sometimes you numerical reasoning score will be added to the total score while others it won’t and you will only be required to reach the pass mark which traditionally has been at 50% correct answers.
In the workplace, most roles involve dealing with numerical data. Those with higher levels of numerical reasoning ability are more likely to:
• quickly grasp numerical concepts; • effectively solve problems using numerical information; • make sound, logical decisions involving numbers.
Here are some examples of potential usage:
• In Human Resources, there will be calculations relating to attendance, turnover, cost of hires, bonus calculations, pay rates, percentiles to work out for performance gradings, etc. • Customer Service roles may need to calculate performance indicators, customer satisfaction indices, customer attrition rates, etc. • In Finance and Banking, financial and investment reports will need to be analysed, currency conversions carried out accurately, accounts prepared, and regulatory calculations submitted, and so on.
Watch our introduction video to numerical reasoning
• It’s important that you remember not to make assumptions. Everything you need to answer the question is on the page, and on the page alone. Don’t add your own knowledge, if you expect to see something but that fact/data/timeline isn’t included in the data you’re shown, then you can’t include it in your decision-making process for the question.
• Be careful of the use of numbers. Quite often longer numbers, e.g. hundreds of thousands are presented like this – ‘000’s or the text or headline might say that the number are in “thousands” or “millions”. Check dates and times carefully. Where a minimum number of units is requested in the question, you may need to round up a number you have calculated.
• Get familiar with the types of calculators that you will be given for the EPSO exam. Make sure to familiarize yourself with all the functions as they can save you precious time performing the necessary calculations.
• Before launching into a numerical question which involves lots of steps, have a quick look at the available answer options. Are any of them obviously wrong, and therefore able to be discounted? What units is the question expecting your answer to be in? Halfway through your calculation, is it apparent that there are only one or two possibilities? These techniques can save you time during your test.
• Ensure you understand the meaning of commonly-used words, for example, cumulative. This means that data is increasing by successive addition for every month, year, decade, or other time point highlighted. Financial terms used can include fixed costs, which are set expenses a company has which never change and variable costs, which are costs that vary depending on a company's production volume.
By practising these tests, you will become familiar with how the information is presented to you. You will develop your own style of approaching them and importantly you will increase your confidence. In all cases, work quickly and accurately is the best advice during the test, and when practising, start out by not timing yourself. Time yourself when you feel ready to add the element of typical pressure, that you’ll feel in a test environment.
There are different ways to tackle these questions. I suggest strongly to read the question first. Find out what it is exploring. You already know you will be required to answer questions by interpreting figures/data that’s presented in statistical tables, so don’t be tempted to try to analyse those first. This is why.
You may not need to analyse all of the chart or graph. It is as simple as that.
Test designers may add in a column that isn’t needed, or a pie-chart that is superfluous to the question. This is done as a red herring as your data-selection skills are being measured as well as your mathematical reasoning ability. Once you know that, you can narrow the information down to the part of the chart or data point you need to explore.
If the question consists of three or four parts. Firstly, read the end part of the question. This is your goal, to work out this part. If you are to reach that answer, you can often work backwards. Combine the information from two or three different parts.
Focus upon the detail. The answers may be similar numerically, and numbers may be transposed in the choice of answer options. Double-check your calculator and your answer. Only ONE of the answers will be correct. Don’t let a misplaced digit cost you a point due to an inaccurate response.
Don’t allow yourself to be confused by some of the more basic calculations. You are bound to come across the use of percentages as a starter. Some of these are straightforward, some are more complex, such as reverse percentages and ratios. You may need to use basic algebra to solve questions that involve rate problems (work/ speed/ distance/ time) as well as financial-oriented problems.z Basic calculations will include one or more of the following:
• Addition • Subtraction • Multiplication • Division • Averages • Ratios
So, how do you work these out?
With reverse percentages, look at this example. If I bought an item in 2018 and the price had increased the next year by 20% to £600, what price did I pay in 2019?
You don’t take 20% off £600. That would be a mistake, giving you a price of £480.
You would need to add the 20% onto 100% and use that as the basis for calculating the accurate figure.
The higher 2019 figure is divided by 120, as that is the figure with the increase and you multiply by 100. The calculation looks like this:
£600/120 x 100 = £500
A shorter way of writing this would be
£600/1,2 = £500 where the 2 in “1,2” represents the 20%
You may find reverse percentages being used with VAT calculations. Don’t forget to use this method and use the after-sales tax figure to calculate prices before VAT is added!
Percentage points refer to an increase or decrease of a percentage. This is an absolute term (in contrast to percentage change/difference). If you are asked to find a percentage point difference, you have to perform the following: New percentage – old percentage = Point difference. We cover percentages extensively in our video lessons on EPSOprep.com. There you can find lessons below packed with valuable tips and examples. You can also find the solutions to EPSOs sample questions found on their website.
• Percentage increase and decrease • Percentage and Percentage points • Reverse percentages • Learn to solve percentages mentally
Ratios require you to work out the relative size of two or more values.
a:b is usually how the ratio is presented, so using the formula, if I stated that there are 30 red and black playing cards on the table and the ratio of black to red cards is 2:3, how many cards are black?
Therefore, there are 12 black playing cards on the table.
In a recent survey, 1600 participants were asked about their preference for a new cola, compared against a well-known brand. 22% preferred the new cola, 32% were indifferent, and the rest disliked the new cola. How many people disliked the new cola?
A: 836 B: 750 C: 736 D: 724
Addition: 22% + 32% = 54% Subtraction: 100% – 54% = 46% Final Calculation: 46% of 1600 = 736 (Tip: using the calculator, 1600 x 46 followed by the % sign)
The correct answer is C.
Exchange Rate Calculation Example Exchange Rates for Sterling (£)
If you changed 500 US dollars into Euros on the 1st April, how many euros would you receive?
A: 446.43 B: 438.60 C: 332.58 D: 361.29
Process Even though there is no direct relationship between Euros and dollars, the table shows the value of £1 against both currencies. Therefore, you can establish a relationship.
You can create an equation from this. More simply you multiply 500 x 1.12 and divide by 1.55 500 x 1.12 / 1.55 = 361.29 Euros.
The correct answer is D.
A car washing company hires a unit for £1600 per month and employment costs are £5100 per month. Each car wash costs £0.75 in materials/maintenance. If the car wash services 3200 car washes this month, what are the total costs for this month?
Fixed costs = £1600 (unit rental) + £5100 (Monthly cost for employees) = £6700 Variable costs = £0.75 x 3200 = £2400 Fixed + Variable Costs = Total Costs £6700 + £2400 = £9100
Typically, these questions involve something moving at a constant speed. From the three variables (speed, time or distance) you will be given two and required to calculate the third.
The Three Formulas • Speed = Distance /Time • Time = Distance/Speed • Distance = Speed x Time
Quick Way of Calculating Average Speed
What is your average speed in mph if you travel 45 miles in 1 hour 10 minutes? A: 32.4 mph B: 36.8 mph C: 38.6 mph D: 41.5 mph
Speed = Distance/Time
The first step is to convert the time into minutes: 1 hours and 10 minutes is 70 minutes. 45/70 = 0.624 0.624 x 60 minutes = 38.6mph (Correct answer C)
If I cycled to a friend’s house at a speed of 8km/hr and the journey took 1 hour and 15 minutes, how far did I cycle? A: 7km B: 10km C: 11km D: 13 km
This would be calculated as: 8km = 60 minutes (turn 1 hour into minutes) The quickest way is to divide 8 by 60 and multiply by 75 (1 hour 15 minutes) Distance = 8 x 75 = 9.99km recurring, so seek the answer that states the nearest rounded whole figure, which is 10km. The correct answer is B.
A coach travels at 32 mph while moving but after accounting for stopping time, to let passengers on and off the coach, it averages a speed of 26mph. How many minutes does the coach stop for each hour? A: 9 minutes 30 seconds B: 10 minutes 45 seconds C: 11 minutes 15 seconds D: 12 minutes
In one hour without stopping, the coach would have travelled 32 miles. Once stopping is factored in, the coach actually travels 26 miles. So, it travels 6 miles less far as a result.
Distance/Speed = Time 6miles/32mph = 0.1875 hours 0.1875 x 60 = 11.25 minutes, which is 11 minutes 15 seconds So, the coach stops for 11 minutes, 15 seconds, in every hour on average.
Put you numerical reasoning skills to a test with these two paractice questions that are followed up with an solution to the question.
The calculator can provide some further shortcuts, but only use these if you know how the shortcuts work.
• For example, any decimal can be converted into a percentage by multiplying it with 100 and adding a % sign at the end. To convert a percentage back into a decimal, divide it by 100.
• If you need to store a number for further use within the same calculation, use the M+ button, you can then recall it, using the MR button. This will save you time as you will not have to waist time writing down the number and then punching it in again in the calculator when needed. Remember, these tests are highly time critical.
• If you have a figure you need to type in anything less than 1, type in the decimal point then the number. E.g. 0.95 – type in .95 instead.
• If you use a scientific calculator, you can use brackets and indices. For example, with indices, you can work out compound amounts. I earn £2 a day interest which is multiplied by the same amount each day, how much interest would I earn after 7 days? 2, press the button, followed by 7 (number of days) = 256. Alternatively, 2% interest daily compounded over a 7-day period would be 2.00033%, so double-check what you are being asked to compound. The calculators provided by EPSO do not have this function but it can be useful to remember should you sit other tests.
If the word “million” is used consistently, you do not have to convert it into numbers. E.g. 125 “million” passengers and 110 “million” pieces of luggage.
Always remember to convert decimal points into minutes when using a time calculation. 10.5 means 10 minutes 30 seconds.
Know where you can save time by knowing basic fractions. 3/4 is less than 2/3 and 5/6 is greater than both. If you have to estimate an answer, and you are using fractions to work out a greater or lesser amount, this can help.
Practice you mental calculus. Many calculations are rather simple and can be performed mentally. You should for example be able to calculate how much something that cost 500 EUR and increased in price with 10% costs now without using the calculator.
Finally, identify which bits of information are relevant and needed to answer the question. Advanced questions will contain ‘distractors’ which you will get used to identifying and navigating around through question practice. Practice really does help to improve your performance. Work through as many questions as possible prior to sitting your assessment to maximise your chances of success and your test performance. You can always study the Financial Times and Economist to review tables and charts to familiarise yourself with similar content.
If you want to get a better understanding of numerical reasoning you can sign up for free on EPSOprep.com and view our free introduction lesson. There you can also find video lessons that more in-depth cover the topics discussed in this article.
Remember you can find free questions and video introductions to EPSO test abstract reasoning tests by logging in