## 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: Take 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 practicing 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. This will determine whether the correct calculation is A ÷ B or A x (1-B). Let’s consider two examples.

"In 2009 sales were £1,000, which was an increase of 10% from sales the previous year. What were the sales in 2008?"

Essentially we need to solve the following problem: ? x 110% = £1,000. So the calculation is ? = (£1,000 ÷ 1.1) = 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 2009 sales were £1,000. If in 2010, sales decrease by 10%, what would be the sales in 2010?"

Since this is a decrease of 10% from one number to another, we start with the reference number and multiply by (100 - 10)%. 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 number is and understand what the end number 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.

## 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.