Numerical Reasoning Practice Questions: Types, Examples and How to Prepare

Numerical reasoning tests are among the most common assessments in professional recruitment. Employers across every major industry, from the Big Four accounting firms to technology giants and investment banks, use these tests to evaluate how candidates handle data, interpret numbers and make decisions under time pressure. The difference between candidates who pass and those who do not often comes down to one factor: targeted practice with the right types of questions.

This guide breaks down every major category of numerical reasoning practice question you will encounter, provides worked examples to build your understanding, and gives you a structured approach to preparation that produces real score improvements. Whether you are preparing for a graduate scheme at Deloitte, a consulting role at McKinsey, or a management position at Unilever, the question types covered here reflect what you will face on test day.

Why Numerical Reasoning Practice Questions Matter

Numerical reasoning tests are designed to measure your ability to work with data quickly and accurately. Unlike school maths exams that test learned formulas, these assessments present real-world business scenarios and ask you to extract, calculate and interpret information from tables, charts and graphs. The skills being tested, including data interpretation, proportional reasoning and logical deduction, are the same skills you will use daily in professional roles.

Employers like Goldman Sachs, PwC and Unilever invest heavily in psychometric testing because decades of research in occupational psychology demonstrates that cognitive ability tests are among the strongest predictors of job performance. A candidate who scores well on a numerical reasoning test is statistically more likely to perform well in roles that require analytical thinking, financial analysis and evidence-based decision making.

The time pressure is what makes practice essential. Most numerical reasoning tests give you between 45 and 75 seconds per question. That is not enough time to figure out an unfamiliar question type from scratch. Candidates who have practised each question category beforehand recognise the pattern immediately, apply the right method, and move on. Candidates who have not practised waste valuable seconds trying to work out what the question is even asking.

Percentage Questions: The Foundation of Numerical Reasoning

Percentage questions appear on virtually every numerical reasoning test. They are the building block for more complex question types like profit margins, market share calculations and year-on-year growth analysis. Mastering percentages gives you a reliable foundation for the entire test.

There are several core percentage operations you need to handle fluently:

Calculating a percentage of a value. This is the most basic operation. If a company's revenue is £840,000 and operating costs represent 35% of revenue, you calculate 840,000 multiplied by 0.35 to get £294,000. The key is converting the percentage to a decimal quickly and accurately.

Percentage increase and decrease. These questions typically present two figures and ask you to calculate the change. The formula is: percentage change equals (new value minus old value) divided by old value, multiplied by 100. For example, if quarterly sales rose from £150,000 to £187,500, the increase is (187,500 minus 150,000) divided by 150,000, multiplied by 100, which gives 25%.

Reverse percentage calculations. These are trickier because they work backwards. If a product costs £360 after a 20% discount, you need to find the original price. Since £360 represents 80% of the original, you divide 360 by 0.80 to get £450. Many candidates make errors here by adding 20% to the discounted price, which gives the wrong answer.

Compound percentage changes. When a value increases by 10% one year and then decreases by 10% the next, the result is not zero change. You multiply the original by 1.10 and then by 0.90, which gives 0.99 of the original, a net decrease of 1%. This type of question catches out candidates who have not practised it specifically.

Percentage questions from providers like SHL and Cubiks/Talogy are almost always embedded within a data table or chart, so you need to combine your percentage skills with data extraction. Practise reading the data accurately before you start calculating.

Ratio and Proportion Questions

Ratio and proportion questions test your ability to compare quantities and scale values up or down. These questions are especially common in tests used by consulting firms and financial institutions, where proportional reasoning is a daily requirement.

Basic ratio problems. A typical question might state that a budget is split between marketing and operations in a 3:5 ratio. If the total budget is £640,000, you need to find each allocation. The total number of parts is 3 plus 5, which equals 8. Each part is worth £80,000. Marketing receives £240,000 and operations receives £400,000.

Scaling ratios. Some questions ask you to adjust a ratio when one quantity changes. If a recipe uses ingredients in a 2:3:5 ratio and you need to increase the total from 500g to 750g, you scale each part proportionally. The scaling factor is 750 divided by 500, which is 1.5. Each component is multiplied by 1.5.

Ratio comparison across datasets. More advanced questions present two or more datasets and ask you to compare ratios. For instance, you might need to determine which of three regional offices has the highest staff-to-revenue ratio. This requires extracting the right numbers from a table and calculating each ratio before comparing.

The most common mistake candidates make with ratio questions is adding or subtracting instead of dividing. Ratios are multiplicative relationships, and treating them as additive differences leads to incorrect answers. If you find yourself struggling with ratio questions, go back to the fundamentals and practise converting between ratios, fractions and percentages until the relationships feel natural.

Data Interpretation: Tables, Charts and Graphs

Data interpretation questions form the backbone of most numerical reasoning tests. Rather than presenting a standalone calculation, these questions give you a table, bar chart, line graph or pie chart and ask you to extract specific values, perform calculations and draw conclusions. This is the question type that most closely mirrors real workplace tasks.

Table-based questions. You might see a table showing quarterly revenue figures for five product lines across four quarters. The question could ask you to calculate total annual revenue for a specific product, determine which quarter showed the highest growth, or find the percentage contribution of one product to total revenue. The challenge is navigating the table accurately under time pressure without misreading rows or columns.

Bar chart questions. Bar charts typically compare values across categories or time periods. Questions might ask you to identify the category with the largest increase between two years, calculate the difference between the highest and lowest values, or determine the average across all categories. Pay close attention to the scale on the y-axis, as some charts use increments that make estimation tricky.

Line graph questions. Line graphs show trends over time and are common in tests used by financial services employers like Barclays, JP Morgan and Deutsche Bank. Questions often focus on rates of change rather than absolute values. You might need to identify the period with the steepest growth, determine when a trend reversed, or compare growth rates between two lines on the same graph.

Pie chart questions. Pie charts show proportional distributions. Questions typically ask you to calculate the actual value represented by a segment when the total is given, or to compare segments across two pie charts. The key skill is converting between percentages and absolute values quickly.

Here is an overview of the main data formats you will encounter and the skills each one tests:

Data Format	What It Shows	Common Question Types	Key Skills Required
Tables	Precise values across multiple categories and time periods	Sum, average, percentage change, ranking	Accurate data extraction, cross-referencing rows and columns
Bar Charts	Comparison of values across categories	Difference, ratio, largest/smallest, percentage contribution	Reading scales, estimating values from bar heights
Line Graphs	Trends and changes over time	Growth rate, trend identification, forecasting	Calculating gradients, identifying inflection points
Pie Charts	Proportional distribution of a total	Segment value, comparison between charts, percentage to value	Converting percentages to absolutes, comparing proportions
Combination Charts	Multiple data types on one display	Cross-referencing, multi-step calculation	Integrating information from different visual formats

Practise with realistic data interpretation questions to build the speed and accuracy you need for your test.

Financial and Business Scenario Questions

Many numerical reasoning tests, particularly those used by employers in finance, consulting and management, include questions set within a business context. These go beyond basic arithmetic and require you to understand concepts like profit margins, market share, break-even points and currency conversions.

Profit and loss questions. You might be given a company's revenue, cost of goods sold and operating expenses, then asked to calculate the gross profit margin or net profit. The formulas are straightforward, but the challenge lies in extracting the right figures from a complex table and applying them in the correct order.

Market share calculations. These questions present sales data for multiple companies in a market and ask you to determine each company's share. For example, if Company A sold £45 million worth of products in a market worth £180 million, its market share is 25%. Follow-up questions might ask how much market share shifted between two time periods.

Currency conversion questions. You are given exchange rates and asked to convert amounts between currencies. The trick is knowing when to multiply and when to divide. If 1 GBP equals 1.25 EUR, then converting GBP to EUR requires multiplication, while converting EUR to GBP requires division.

Break-even analysis. Some tests ask when a business will break even given its fixed costs, variable costs per unit and selling price per unit. The formula is: break-even units equal fixed costs divided by (selling price minus variable cost per unit). These questions are especially common in tests used by PwC, EY and KPMG.

Employers in the financial sector specifically design these questions to mirror the type of analysis you would perform on the job. Goldman Sachs, for instance, uses numerical reasoning tests that heavily feature financial data interpretation because the ability to work with financial datasets is a core requirement for their analysts and associates.

Common Mistakes and How to Avoid Them

Understanding where candidates typically go wrong is just as valuable as learning how to solve questions correctly. Occupational psychologists who design these tests have identified several consistent error patterns that affect scores. Avoiding these mistakes can be the difference between passing and failing.

Misreading the question. Under time pressure, candidates often answer a different question from the one being asked. A question might ask for the percentage decrease, but the candidate calculates the percentage of the remaining amount instead. Always read the question twice before you start calculating.

Unit confusion. Tables frequently mix units. One column might show values in thousands while another shows them in millions. A revenue figure of 45 in a table headed "Revenue (£m)" means £45 million, not £45. This is one of the most common sources of errors, and test designers include these traps deliberately.

Rounding too early. If a multi-step calculation requires you to use an intermediate result, rounding that intermediate result too aggressively can throw off your final answer. Keep as many decimal places as practical until the final step, then round to match the answer options.

Spending too long on one question. Most numerical reasoning tests allow you to skip questions and return to them later. If you are stuck after 60 seconds, mark the question, move on and come back if time allows. Getting eight straightforward questions right is worth more than getting one difficult question right and running out of time for three easy ones.

Not using estimation. When answer options are spread apart, estimation can save significant time. If the options are A) 12%, B) 25%, C) 38% and D) 51%, a rough calculation that gives you approximately 24% is enough to select B with confidence. You do not need to calculate to two decimal places when the options are that far apart.

For a deeper look at error patterns and how to correct them, read our guide on common numerical reasoning mistakes.

Building a Structured Practice Plan

Random practice is better than no practice, but a structured plan produces significantly better results. Here is a week-by-week approach that covers all the major question types and builds your speed systematically.

Week one: Foundation skills. Focus on percentage calculations, ratio problems and basic arithmetic under timed conditions. Complete 15 to 20 questions per day, reviewing every mistake thoroughly. The goal is accuracy, not speed. Use an online numerical reasoning practice test to identify which question types need the most attention.

Week two: Data interpretation. Shift your focus to table-based questions, chart reading and graph analysis. Practise extracting data accurately before attempting any calculations. Work through 20 to 25 questions per day and start introducing time limits, aiming for 90 seconds per question.

Week three: Business scenarios and speed. Tackle financial data questions, multi-step calculations and currency conversions. Reduce your target time to 60 seconds per question. Complete at least two full-length practice tests under realistic conditions, sitting at your desk with all distractions removed.

Week four: Test simulation. Complete three to four full-length practice tests under strict timed conditions. Review your results to identify any remaining weak areas and do targeted practice on those specific question types. By this point, you should be comfortable with every question format and able to maintain accuracy at speed.

This structured approach mirrors the preparation methodology recommended by assessment experts. If you are short on time, even one focused week of daily practice can produce measurable improvements. The key is practising with realistic materials that match the format and difficulty level of your actual test.

If you are also preparing for other assessment types alongside your numerical test, consider building a broader preparation routine that includes logical reasoning practice questions and aptitude test questions and answers.

Test Providers and What to Expect From Each

Different test providers design their numerical reasoning questions differently. Knowing which provider your employer uses allows you to practise with the right format and avoid surprises.

Test Provider	Question Style	Time Pressure	Calculator	Used By
SHL	Data tables and charts, business context, multi-step calculations	High (approximately 60 seconds per question)	On-screen calculator provided	Deloitte, Barclays, Unilever, Citigroup
Cubiks/Talogy	Logiks format, quick-fire questions, mix of pure arithmetic and data	Very high (approximately 45 seconds per question)	Varies by version	PwC, Siemens, Nestl
Aon/cut-e	Scales format, short adaptive subtests, comparative judgments	High (adaptive pacing)	On-screen calculator provided	Goldman Sachs, Deutsche Bank, ABN AMRO
Kenexa/IBM	Role-specific scenarios, longer question stems, applied context	Moderate (approximately 75 seconds per question)	Varies by test	HSBC, BT, Royal Mail
Cappfinity	Strengths-based numerical tasks, scenario-driven	Moderate	Varies	EY, Deloitte (some divisions)

SHL is the most widely used provider globally, and their numerical reasoning tests are the format you are most likely to encounter. Cubiks, now operating under the Talogy brand, is particularly popular among European employers. Aon's cut-e scales format is distinctive because it uses very short subtests with adaptive difficulty. Always check your test invitation email to confirm which provider is delivering your assessment.

Start practising with provider-specific test materials to prepare for the exact format you will face.

Expert Tips for Test Day Performance

Preparation gets you ready. Test day execution determines your score. Here are the strategies that experienced candidates and assessment professionals recommend for peak performance on numerical reasoning tests.

Set up your environment before you start. Choose a quiet room with good lighting. Clear your desk of everything except your computer, a glass of water and any permitted materials. Close all other browser tabs and applications. If the test is proctored, make sure your webcam and microphone are working and your background is clean and professional.

Read the instructions carefully. Every test begins with instructions and usually includes one or two practice questions. Use this time fully. The practice questions show you the exact format, the interface controls and how to navigate between questions. Do not rush through them.

Manage your time actively. Keep track of how many questions remain and how much time is left. If you are halfway through the questions with less than half the time remaining, you need to increase your pace. Skip difficult questions and return to them if time allows.

Use the answer options to your advantage. Before calculating, glance at the answer options. If they are widely spaced, a quick estimate may be sufficient. If they are close together, you need to calculate precisely. This simple check can save you significant time across the full test.

Stay calm when you hit a difficult question. Every candidate encounters questions they find challenging. The difference between high scorers and low scorers is not that high scorers find every question easy. It is that they do not let a difficult question derail the rest of their performance. Mark it, move on and return later with fresh eyes.

Frequently Asked Questions

How many numerical reasoning practice questions should I complete before my test?

Aim for at least 50 to 100 timed practice questions spread across all question types. Research from occupational psychology shows that candidates who complete structured practice sessions score significantly higher than those who review theory alone. Quality matters more than quantity, so always review your mistakes and understand the underlying logic before moving on to the next set.

Should I use a calculator when practising numerical reasoning questions?

Match your practice setup to the real test conditions. If the employer or test provider allows an on-screen calculator, practise with one. If calculators are not permitted, focus on building mental arithmetic speed with techniques like rounding, estimation and breaking complex operations into simpler steps. SHL and Aon tests typically provide an on-screen calculator, while some Cubiks/Talogy assessments do not.

What is the difference between numerical reasoning and a maths test?

A maths test assesses your knowledge of mathematical concepts and formulas. A numerical reasoning test measures your ability to interpret data, draw conclusions from tables and charts, and apply basic arithmetic in a business context. You do not need advanced maths skills, but you do need strong data interpretation and logical thinking under time pressure.

Which employers use numerical reasoning tests in their hiring process?

Most large employers include numerical reasoning tests as part of their recruitment process. This includes the Big Four accounting firms like Deloitte, PwC, EY and KPMG, investment banks such as Goldman Sachs and JP Morgan, consulting firms like McKinsey, BCG and Bain, consumer goods companies like Unilever, and technology firms. Graduate schemes and management trainee programmes almost always require a numerical reasoning assessment.

How long does a typical numerical reasoning test take?

Most numerical reasoning tests last between 15 and 25 minutes and contain 18 to 25 questions. This gives you roughly 45 to 75 seconds per question, which is why speed and familiarity with question types are so important. Some adaptive tests from providers like SHL may adjust the number of questions based on your performance.

Can I retake a numerical reasoning test if I fail?

This depends on the employer's policy. Some companies allow candidates to retake the test after a waiting period of 6 to 12 months, while others permit a retake within the same recruitment cycle if technical issues occurred. The best strategy is to prepare thoroughly before your first attempt so you perform at your best from the start.

Start Practising Numerical Reasoning Questions Today

The candidates who achieve the highest scores on numerical reasoning tests are not necessarily the strongest mathematicians. They are the candidates who have practised each question type until the format feels familiar, who have built their speed through structured repetition, and who walk into the test confident in their ability to handle whatever data is placed in front of them.

Every question you practise now is one less surprise on test day. The investment you make in preparation directly translates into a higher score, a stronger application and a better chance of progressing to the next stage of the hiring process.

Get started with the complete numerical reasoning practice package to access hundreds of realistic practice questions covering every question type, every major test provider and every difficulty level. Build your skills, track your improvement and approach your test with the confidence that comes from thorough preparation.