Word Problems in Numerical Reasoning: How to Solve Them
Word problems are one of the most common question types in numerical reasoning tests, and they are also the type that candidates struggle with the most. Unlike table-based or graph-based questions where the data is presented in a structured visual format, word problems bury the numbers inside a narrative. You have to read carefully, extract the relevant figures, determine the correct mathematical operation, and solve the calculation, all under strict time pressure.
Employers at organisations like Google, Deloitte, Unilever, JP Morgan, and the Civil Service rely on word problems because they reflect how numerical challenges actually appear in the workplace. Reports, emails, and meeting notes present data in sentences, not in neatly labelled spreadsheets. The ability to pull accurate numbers from text and make sound calculations is a skill that translates directly to job performance.
This guide breaks down everything you need to know about word problems in numerical reasoning tests: what they look like, why employers use them, how to solve them efficiently, and which mistakes to avoid.
What Are Word Problems in Numerical Reasoning Tests?
Word problems in numerical reasoning tests describe a scenario using sentences rather than tables, charts, or graphs. The question provides contextual information, embeds numerical data within the text, and asks you to perform one or more calculations to arrive at the correct answer.
A typical word problem might describe a company's quarterly sales figures, an employee travel budget, or a production schedule. The challenge is not just mathematical. You must comprehend the scenario, identify which numbers are relevant, ignore any distracting information, and determine the correct sequence of calculations.
Word problems generally fall into several categories, and understanding these categories helps you recognise the required approach more quickly:
| Word Problem Type | What It Tests | Common Keywords | Example Scenario |
|---|---|---|---|
| Percentage change | Calculating increases, decreases, or margins | "increased by", "reduced to", "percentage of" | A product price rises by 15% after a supplier cost increase |
| Ratio and proportion | Dividing quantities or scaling values | "ratio", "for every", "in proportion to" | Splitting a budget across three departments in a 2:3:5 ratio |
| Rate and speed | Working with time, distance, or productivity | "per hour", "each day", "at a rate of" | A factory producing 450 units per shift across multiple shifts |
| Profit and loss | Revenue, cost, and margin calculations | "cost price", "selling price", "profit margin" | Calculating net profit after deducting operating costs from revenue |
| Currency and conversion | Exchange rates and unit conversions | "exchange rate", "converted to", "equivalent" | Converting project costs from euros to pounds at a given rate |
| Combined multi-step | Chaining two or more operations | Multiple keyword types in one question | Calculating total cost after a discount, then adding VAT |
The key difference between word problems and other numerical reasoning formats is that word problems require you to build the data set yourself from the text before you can begin calculating.
💡Word problems test reading comprehension and numerical ability simultaneously. The mathematical operations are usually straightforward, but extracting the right data from the text is where most candidates lose time and make errors.
Why Employers Use Word Problems in Assessments
Employers do not include word problems in their hiring assessments simply to make things difficult. Word problems serve a specific purpose: they simulate the kind of numerical thinking that professionals use every day.
Consider a financial analyst at JP Morgan reviewing a client report that describes revenue trends in paragraph form. Or a consultant at Deloitte interpreting a briefing document that mixes strategic insights with budget figures. Or a Civil Service policy officer reading a ministerial submission that includes statistical claims embedded in flowing text. In none of these situations does the data arrive in a clean table with clear labels. The professional must read, interpret, extract, and calculate, exactly what a word problem requires.
Employers also use word problems to differentiate between candidates who have genuine numerical fluency and those who can only work with pre-structured data. A candidate who scores well on table-based questions but struggles with word problems may find it harder to apply their numerical skills in a less structured work environment.
Major employers known to include word problems in their numerical reasoning assessments include Google, which uses them in technical and business role assessments, Deloitte and the other Big Four firms for consulting and audit positions, JP Morgan and other investment banks for analyst and associate roles, Unilever for their graduate and management programmes, and the Civil Service for fast-stream and operational delivery roles.
💡Word problems mirror how numerical data appears in professional settings. Employers use them to assess whether you can apply mathematical skills to real-world scenarios, not just to formatted data sets.
A Step-by-Step Method for Solving Word Problems
Having a consistent, repeatable method is the single most effective way to improve your word problem performance. Under time pressure, a reliable process prevents you from missing steps or making avoidable errors.
Step 1: Read the entire question before doing anything. Many candidates start calculating the moment they spot a number. This leads to errors because you may use a figure that is not relevant to what the question actually asks. Read the full text, including the answer options if they are visible, before you pick up the calculator.
Step 2: Identify what the question is asking for. The final sentence usually contains the actual question. Underline it mentally or physically. Are you looking for a total, a difference, a percentage, a ratio? Knowing the end point tells you what kind of calculation you need.
Step 3: Extract the relevant numbers. Go back through the text and pull out every number that relates to the question. Ignore figures that are contextual background but not needed for the calculation. Write them down if you are allowed scrap paper.
Step 4: Determine the operation or sequence of operations. Based on the question type and the data you have extracted, decide whether you need addition, subtraction, multiplication, division, or a combination. For multi-step problems, plan the sequence before you start calculating.
Step 5: Set up the calculation and solve. Write out the equation before punching numbers into the calculator. This reduces input errors and makes it easier to check your work.
Step 6: Verify your answer against the question. Does your answer make logical sense? Is it in the right units? If the question asks for a percentage and your answer is 4,500, something has gone wrong. A quick sense-check catches many errors.
Practise this method with realistic numerical reasoning questions to build speed and confidence before your real assessment.
Worked Examples: Common Word Problem Types
Working through examples is the fastest way to internalise the step-by-step method. Below are three word problem types you are likely to encounter in real assessments.
Example 1: Percentage Change
A retail company reported revenue of £2.4 million in Q1. In Q2, revenue increased by 12.5%. What was the Q2 revenue?
- Identify the question: Find Q2 revenue after a 12.5% increase.
- Extract data: Q1 revenue = £2,400,000. Increase = 12.5%.
- Calculate: 12.5% of 2,400,000 = 300,000.
- Q2 revenue: 2,400,000 + 300,000 = £2,700,000.
Example 2: Ratio and Proportion
A training budget of £45,000 is split between three departments in a ratio of 2:3:4. How much does the department with the largest share receive?
- Total parts in the ratio: 2 + 3 + 4 = 9.
- Value of one part: 45,000 / 9 = 5,000.
- Largest share (4 parts): 4 x 5,000 = £20,000.
Example 3: Multi-Step Problem
A company buys 800 units at £6.50 each. Shipping costs are 8% of the purchase price. The company sells all units at £11.25 each. What is the total profit?
- Purchase cost: 800 x 6.50 = £5,200.
- Shipping: 8% of 5,200 = £416.
- Total cost: 5,200 + 416 = £5,616.
- Revenue: 800 x 11.25 = £9,000.
- Profit: 9,000 - 5,616 = £3,384.
💡Multi-step word problems are not harder mathematically. They simply require you to chain several straightforward calculations together in the correct order. Planning the sequence before you start prevents errors.
Common Mistakes and How to Avoid Them
Understanding where candidates typically go wrong is just as important as knowing the correct method. These are the most frequent errors that cost marks in numerical reasoning word problems.
Misreading "increased by" versus "increased to." These phrases mean very different things. If a value of 200 is increased by 50%, the new value is 300. If a value is increased to 50%, you are looking at a final value that represents 50% of some base. This confusion is one of the most common sources of wrong answers.
Using the wrong base for percentage calculations. When a question says that prices rose by 20% and then fell by 20%, many candidates assume the final price equals the original. It does not. The 20% decrease applies to the higher post-increase value, so the final price is lower than the original.
Ignoring irrelevant information. Test designers deliberately include extra numbers in word problems to see whether you can distinguish relevant data from noise. Not every number in the text is needed for the calculation. Always anchor your work to what the question specifically asks.
Forgetting to convert units. If a question gives some figures in thousands and others in millions, or mixes hours with minutes, you must convert to consistent units before calculating. This is especially common in multi-step numerical problems where data comes from different parts of the scenario.
Rushing the reading phase. The instinct to start calculating immediately is strong, especially under time pressure. But spending an extra ten seconds reading carefully saves you from a wrong answer that costs you the full 60 to 90 seconds. Slow reading leads to fast solving. Fast reading leads to slow recovery from errors.
Developing awareness of these pitfalls through regular practice is the best defence. Work through common numerical reasoning mistakes to see detailed breakdowns of each error type.
Word Problems Compared to Other Numerical Reasoning Formats
Numerical reasoning tests typically include three main question formats: word problems, table-based questions, and graph or chart-based questions. Each format tests a slightly different combination of skills, and understanding the differences helps you allocate your preparation time effectively.
| Feature | Word Problems | Table-Based Questions | Graph/Chart Questions |
|---|---|---|---|
| Data presentation | Embedded in narrative text | Organised in rows and columns | Displayed as bar, line, or pie charts |
| Primary skill tested | Reading comprehension + calculation | Data location + calculation | Visual interpretation + calculation |
| Time to extract data | Highest - requires careful reading | Medium - requires scanning rows/columns | Medium - requires reading axes and legends |
| Common operations | Percentages, ratios, multi-step | Comparisons, totals, averages | Trends, proportions, estimates |
| Difficulty source | Identifying relevant vs irrelevant data | Navigating large data sets | Reading values accurately from visual scales |
| Employer preference | Common across all sectors | Dominant in finance and consulting | Frequent in marketing and operations roles |
The key insight is that word problems are not inherently more difficult in terms of the mathematics involved. The challenge lies in the data extraction phase. Once you have identified the relevant numbers and the required operation, the actual calculation is typically no harder than what you would face in a table-based question.
This is why a structured reading method matters so much. Candidates who approach word problems systematically close the performance gap quickly, while those who rely on intuition continue to lose time to re-reading and confusion.
💡Word problems test the same mathematical operations as table and graph questions. The difference is in how the data is presented. A consistent reading method eliminates the extra difficulty that narrative formatting creates.
How to Practise Word Problems Effectively
Effective practice follows a progression from untimed comprehension work to full-speed timed simulations. Jumping straight into timed practice without first building your method leads to reinforcing bad habits rather than correcting them.
Phase 1: Untimed method practice. Work through word problems slowly, focusing on applying the six-step method described earlier. Do not worry about speed at this stage. Your goal is to make the process automatic so that you do not need to think about what to do next.
Phase 2: Timed individual questions. Once your method feels natural, start timing individual questions. Give yourself 90 seconds per question and track how many you answer correctly. Identify which question types take you the longest and focus your practice on those areas.
Phase 3: Full timed test simulations. Replicate real test conditions as closely as possible. Sit at a desk, remove distractions, set an overall time limit, and work through a full set of questions without pausing. This builds stamina and teaches you how to manage your time across an entire assessment. Reading ratio questions explained and other topic-specific guides helps you sharpen weaker areas before your timed runs.
Phase 4: Review and error analysis. After each practice session, review every question you got wrong or spent too long on. Categorise your errors: was it a reading comprehension mistake, a calculation error, a unit conversion issue, or a time management problem? This analysis tells you exactly what to work on next.
Start building your word problem skills with free practice tests to experience realistic question formats from major test providers.
Frequently Asked Questions
How do I know which operation to use in a word problem?
Look for keywords in the question stem. Words like "total" and "sum" point to addition. "Of" and "times" suggest multiplication. "Per", "each", and "for every" indicate division or rate calculations. "Difference" and "less than" mean subtraction. With practice, spotting these signal words becomes automatic, and you will spend less time deciding which operation to apply. Building a mental library of keyword-to-operation mappings is one of the most effective shortcuts for improving your speed.
Are word problems harder than table-based numerical reasoning questions?
Word problems add an extra layer of difficulty because you must extract data from narrative text before you can calculate. Table-based questions present numbers directly in a structured format, so you spend less time on comprehension and more time on computation. However, once you develop a consistent method for reading and translating word problems, the mathematical calculations themselves are usually no more complex. The difficulty is in the extraction, not the arithmetic.
Can I use a calculator for word problems in aptitude tests?
It depends on the test provider and the employer. Many numerical reasoning tests from providers like SHL and Cubiks allow a basic on-screen calculator. Some employers, particularly in finance and consulting, require mental arithmetic for at least part of the assessment. Google and JP Morgan, for instance, may include sections where calculators are not permitted. Always check your invitation email or the test instructions before you begin so you know what to expect.
How much time should I spend on each word problem?
Most numerical reasoning tests allow between 60 and 90 seconds per question. For word problems specifically, aim to spend no more than 20 seconds reading and extracting data, and the remaining time setting up and solving the calculation. If a question is taking significantly longer than 90 seconds, make your best estimate, select an answer, and move on. Leaving questions unanswered is almost always worse than making an educated guess.
What is the best way to practise word problems for numerical reasoning?
Start by working through practice questions without a timer to build your method and confidence. Once the process feels natural, introduce timed conditions that mirror the real test. Focus on recognising question types and keyword patterns so you can quickly identify the required operation. Practising with realistic test materials that match your specific test provider is the most effective approach, because question styles and difficulty levels vary between providers like SHL, Cubiks, and Kenexa.
Do all employers use word problems in their numerical reasoning tests?
Not all, but the vast majority do. Employers like Google, Deloitte, JP Morgan, Unilever, and the Civil Service include word problems alongside table and graph-based questions in their numerical reasoning assessments. Word problems test your ability to interpret real-world scenarios, which is a skill employers value across virtually every industry. Even employers who favour table-heavy formats often include at least a few word-based questions to assess reading comprehension alongside numerical ability.
Start Preparing for Your Numerical Reasoning Test
Word problems do not need to be the question type that holds you back. With a structured method, targeted practice, and awareness of the most common pitfalls, you can approach word problems with the same confidence you bring to table and graph-based questions. The candidates who perform best are the ones who invest time in building a repeatable process and then sharpen it through realistic practice.
Get started with the complete numerical reasoning test package to access practice materials covering word problems, data interpretation, and every other question type you will face in your assessment. Build your skills, learn the formats, and walk into your test ready to perform at your best.