Numerical Reasoning Test: Question Types, Worked Examples and How to Prepare

What numerical reasoning tests are for, the question types you will meet, how they are timed and scored, and six worked examples with full working to help you prepare.

By Tony Musso on Sun Oct 18 2026

A numerical reasoning test checks how well you can pull the right figures out of a table or chart and work with them quickly: percentages, ratios, conversions and changes over time. It is not a maths exam. You will not need algebra or anything beyond GCSE-level arithmetic, but you will need to read carefully and keep calm against the clock.

If an employer has invited you to sit one, this guide explains what the test is for, the question types you will meet, how it is scored, and how to prepare. It also includes worked examples with full working, so you can see exactly how each type is solved.

Why employers use numerical reasoning tests

Numerical tests are most common early in a recruitment process, often straight after the online application. You are likely to meet one if you apply for:

Graduate schemes, especially in finance, retail management, engineering and professional services
Banks, insurers and accountancy firms, for both graduate and experienced hires
The Civil Service, where online tests are used for many vacancies and on the Fast Stream
Consultancies, where working with data is a daily part of the job

Employers use them because they are a quick, consistent way to compare large numbers of applicants on the same task. Many use the result as a sift before the interview or assessment centre, and some look at it alongside other online tests such as a situational judgement test.

What the questions look like

Most questions follow the same pattern: a table, bar chart, line graph or pie chart, then a question with four or five multiple-choice answers. The data is usually business-flavoured: sales by region, staff numbers, budgets, survey results or exchange rates.

The skills tested come down to a handful of types:

Reading tables and charts: finding the right row, column or bar, and noticing units such as "£000s" or "millions".
Percentages: finding a percentage of a number, or what percentage one number is of another.
Percentage change: the increase or decrease from one figure to another, always calculated against the starting figure.
Ratios: splitting an amount in a given ratio, or simplifying a ratio.
Currency conversion: converting between pounds and another currency at a given rate.
Reverse percentages: working back to an original figure after an increase or decrease.

How the tests are timed and scored

Numerical tests are tightly timed on purpose. Many people do not finish, and that is expected. The instructions on the first screen will tell you how many questions there are and how long you have. Divide one by the other so you know your pace, and do not let one hard question eat several minutes.

Your result is not usually judged as a simple mark out of a total. Your raw score is compared with a comparison group (sometimes called a norm group), such as other graduates or other applicants for similar roles. That gives a percentile: how you performed relative to that group. Each employer then decides its own cut-off, and it can vary by role and by how many people applied.

Two practical points:

If the instructions do not say that wrong answers lose marks, an educated guess is usually better than a blank.
Some employers ask you to resit a shorter version at the assessment centre to confirm your result, so it pays to sit the online test yourself, honestly.

Calculators and rough work

Calculator rules vary. Many online tests allow a calculator and expect you to use one, but some do not. Check the instructions in your invitation email and on the test screen before you start. Have pen and paper ready either way; writing down the figures you are using cuts careless errors.

Worked example questions

These examples were written for this guide. They are typical of the style you will see.

Example 1: Percentage change from a table

Region	2024 sales (£000s)	2025 sales (£000s)
North	240	276
Midlands	180	171
South	320	360
Scotland	150	165

Question: By what percentage did North sales change from 2024 to 2025?

Working: Change = 276 − 240 = 36. Divide by the starting figure: 36 ÷ 240 = 0.15. Multiply by 100.

Answer: a 15% increase.

Follow-up: Which region had the largest percentage increase?

North: 36 ÷ 240 = 15%
Midlands: (171 − 180) ÷ 180 = −9 ÷ 180 = −5%, a fall
South: 40 ÷ 320 = 12.5%
Scotland: 15 ÷ 150 = 10%

Answer: North. Notice that the South had the biggest increase in pounds (£40,000, as the figures are in thousands) but not in percentage terms. Tests often include that trap.

Example 2: Ratios

Question: Using the same table, what is the ratio of South sales to Midlands sales in 2024, in its simplest form?

Working: 320 : 180. Divide both by 20 to get 16 : 9. Nothing else divides into both 16 and 9.

Answer: 16 : 9.

Example 3: Splitting an amount in a ratio

Question: A training budget of £24,000 is split between courses, travel and materials in the ratio 5 : 2 : 1. How much goes on courses?

Working: Total parts = 5 + 2 + 1 = 8. One part = £24,000 ÷ 8 = £3,000. Courses = 5 × £3,000 = £15,000. (Check: travel £6,000 + materials £3,000 + courses £15,000 = £24,000.)

Answer: £15,000.

Example 4: Currency conversion

Question: A supplier invoices €4,600. The exchange rate is £1 = €1.15. What is the cost in pounds?

Working: You are going from euros to pounds, so divide by the rate: 4,600 ÷ 1.15 = 4,000. (Check: 4,000 × 1.15 = 4,600.)

Answer: £4,000.

Follow-up: If the rate moves to £1 = €1.25, how much less does the same invoice cost in pounds?

Working: 4,600 ÷ 1.25 = 3,680. Difference = 4,000 − 3,680 = 320.

Answer: £320 less.

A quick sense check helps here: if one pound buys more euros, the euro invoice costs fewer pounds.

Example 5: Reverse percentage

Question: After a 20% price increase, a product costs £540. What was the original price?

Working: The new price is 120% of the original, so divide by 1.2: 540 ÷ 1.2 = 450. (Check: 450 × 1.2 = 540.)

Answer: £450.

The common wrong answer is £432, which comes from taking 20% off £540. That is 20% of the new price, not the original.

Example 6: Two changes in a row

Question: A price rises by 10%, then falls by 10%. What is the overall change?

Working: Multiply the factors: 1.10 × 0.90 = 0.99. So the final price is 99% of the original.

Answer: a 1% decrease, not zero.

How to practise and prepare

Brush up on the core skills first. Percentages, percentage change, ratios and conversions cover most questions. If any of them feel shaky, practise them on their own before timing yourself.

Then practise under time pressure. Use free practice tests, including any the employer links to in your invitation. Many employers give a practice version before the real test; always do it, as it shows you the format and screen layout.

Read the question before the data. Know what you are looking for, then find only those figures. Most charts contain far more information than any one question needs.

Watch the units. "£000s", "millions" and "per cent of total" catch people out more than the arithmetic does.

Estimate before you calculate. If you expect about 15% and your calculator says 150%, you have slipped a decimal place. With multiple-choice answers, a rough estimate can often rule out two options straight away.

Set yourself up properly on the day. Use a laptop or desktop rather than a phone, find a quiet room with a reliable connection, and have a calculator (if allowed), pen and paper to hand.

Reflect after each practice test. Note which question types you got wrong and why. Misreading the data and running out of time are fixed in different ways.

Reasonable adjustments

In England, Scotland and Wales, the Equality Act 2010 says employers must make reasonable adjustments for disabled candidates, and that includes online tests. Northern Ireland has its own equivalent disability discrimination law. If you have dyscalculia, dyslexia, a visual impairment, ADHD or another condition that affects how you take timed tests, you can ask for adjustments. Common examples include extra time, a different format that works with assistive technology, or rest breaks.

Contact the recruitment team as soon as you get the invitation, before you start the test. You do not need to give more detail than is needed to arrange the adjustment.

After the test

If you pass, the next stage is usually an interview or an assessment centre. Our guide to common interview questions and answers is a good place to start, and our STAR method guide covers the "tell me about a time" questions that follow.

If you do not pass, ask whether feedback is available, and keep practising. Results vary from day to day, and different employers set different cut-offs, so one result does not decide your future.

Find the kind of reasoning that suits you Career Strengths is our aptitude-style assessment of the kinds of reasoning you handle best, from numbers and patterns to words and people.

Take Career Strengths

Frequently asked questions

What is a numerical reasoning test?

It is a timed test that asks you to interpret data in tables and charts and work with it, using percentages, ratios, conversions and changes over time. Employers use it to see how accurately you handle numbers under time pressure. The maths itself is usually no harder than GCSE level.

Can I use a calculator in a numerical reasoning test?

Often yes, but not always. Rules vary between employers and tests, so check your invitation email and the instructions on screen before you begin. Keep pen and paper to hand either way.

How is a numerical reasoning test scored?

Your raw score is usually compared with a comparison group, such as other graduates or applicants, to give a percentile. Each employer then sets its own pass mark, which can differ by role.

What if I have dyscalculia?

Ask the employer for reasonable adjustments, such as extra time, as soon as you are invited to the test. Employers have a duty under the Equality Act 2010 (and equivalent law in Northern Ireland) to make reasonable adjustments for disabled candidates, and asking early gives them time to set it up.

How long should I practise for?

There is no set amount, but steady practice over a week or two usually helps more than cramming the night before. Start by fixing weak skills, then move on to timed practice tests in the same format as the real one.