Numerical Reasoning Test Practice: Sample Questions and Worked Answers
A numerical reasoning test asks you to read a data table or chart and answer using ratios, percentages, rates or currency conversion. The maths itself is simple, roughly school level. What actually causes low scores is time pressure and misreading the table, not the calculations, so practice should focus on speed and careful data-reading rather than harder sums.
A numerical reasoning test presents data, usually a table or a chart, and asks a series of questions that require you to extract the right figures and calculate something from them: a percentage change, a ratio, a rate, or a currency conversion. The calculations are rarely difficult in isolation. What makes the test hard is doing them accurately, from the correct cells in the table, inside a tight time limit.
Most numerical reasoning tests run as a short, tightly timed block, with little time allowed per question once you account for reading the data first. Some employers use a shorter screener version early in the process and a longer, harder version later for shortlisted candidates.
Because the maths is usually straightforward, the real skill being tested is reading discipline: identifying which row, column or unit a question actually refers to, not confusing similar-looking figures, and rounding only at the final step so small errors don't compound across a calculation.
The format at a glance
- Format
- A data table, bar chart or line chart, followed by multiple-choice questions that require a calculation from the data shown
- Typical length
- Most numerical reasoning tests run as a short, tightly timed set with a limited number of questions rather than a long exam
- Calculator
- Many numerical reasoning tests allow a basic on-screen or handheld calculator, but this varies by provider, so check the instructions before you start
- Content
- Percentage change, ratios and proportions, rate and speed problems, and currency or unit conversion, usually drawn from a business-style data table
- Who uses it
- Finance, analyst, operations and graduate roles particularly, alongside general aptitude batteries for other positions
What it measures
Data interpretation
This is the ability to find the specific figure a question is asking about inside a table or chart without confusing rows, columns, time periods or units. It sounds trivial in isolation, but under time pressure with several similar numbers nearby, misreading the table is the single most common reason for a wrong answer on an otherwise easy calculation.
Percentages and ratios
Percentage change, percentage of a total, and simplifying a ratio to its lowest terms come up constantly across numerical reasoning tests. These measure whether you can apply the same handful of formulas quickly and consistently, question after question, rather than working each one out from first principles every time.
Rates and conversions
Speed, distance and time problems, and currency or unit conversions, test whether you can rearrange a simple formula correctly under pressure: for example converting miles per hour into a travel time, or converting a foreign price into your own currency using a given exchange rate.
Working at speed without errors
Because the time allowed per question is short, the test also measures whether you can work quickly without your accuracy dropping. Many candidates who can do every calculation correctly untimed still score poorly once a countdown is introduced, which is exactly why timed practice matters more than reviewing maths theory.
Practice questions with worked answers
Written by us to mirror the published format. Work each one out before you read the explanation — the method is the part that transfers, the answer is not.
- Q1Data interpretation
Quarterly revenue by region (£000s): Region | Q1 | Q2 North | 120 | 150 South | 90 | 108 East | 60 | 75 What is the percentage increase in South region revenue from Q1 to Q2?
- 18%
- 12%
- 15%
- 20%
Correct answer
20%. Increase = 108 - 90 = 18. Percentage change = 18 / 90 = 0.20, which is 20%. The most common mistake here is dividing the increase by the Q2 figure (18/108) instead of the original Q1 figure, which gives the wrong answer.
- Q2Ratio
A factory's output last month: Size | Units produced Small | 4,200 Medium | 3,150 Large | 2,100 What is the ratio of small to medium to large output, in its simplest form?
- 4:3:2
- 2:3:4
- 3:2:4
- 4:2:3
Correct answer
4:3:2. All three figures share a common factor of 1,050: 4,200 / 1,050 = 4, 3,150 / 1,050 = 3, 2,100 / 1,050 = 2. So the simplified ratio, in the same order the sizes were given, is 4:3:2.
- Q3Currency conversion
An item costs $54.00 in the United States. The exchange rate is £1 = $1.35. To the nearest penny, what is the item's price in pounds?
- £72.90
- £40.00
- £36.00
- £45.90
Correct answer
£40.00. To convert dollars to pounds using this rate, divide by 1.35: 54.00 / 1.35 = 40.00. A common error is multiplying by 1.35 instead of dividing, which produces £72.90 and answers the reverse question of what the item would cost in dollars if it were priced at £54.
- Q4Rate and speed
A delivery van travels 180 miles in 3 hours 45 minutes. What is its average speed in miles per hour?
- 45 mph
- 50 mph
- 48 mph
- 40 mph
Correct answer
48 mph. Convert the time to hours first: 3 hours 45 minutes = 3.75 hours. Speed = distance / time = 180 / 3.75 = 48 mph. Leaving the time as '3 hours 45' instead of converting the minutes to a decimal is the usual source of error on this type of question.
- Q5Percentage of total
Monthly household expenses: Rent | £750 Utilities | £150 Food | £300 Transport | £200 Other | £100 Total | £1,500 What percentage of total monthly expenses is spent on Utilities?
- 15%
- 9%
- 12%
- 10%
Correct answer
10%. Percentage of total = (part / whole) x 100 = (150 / 1,500) x 100 = 10%. Checking that the individual categories sum to the stated total (750 + 150 + 300 + 200 + 100 = 1,500) is a fast way to confirm you're using the right total before dividing.
How scores are read
Below average
More errors or slower pace than most candidates on the same test, often from time pressure rather than the maths itself. Usually improves fastest with timed drills rather than more theory revision.
Average
In line with most candidates who sat the same test. Where many employers set their internal cut-off, though the exact bar is rarely published.
Above average
Faster and more accurate reading of the data than most candidates, with fewer errors compounding across multi-step calculations.
A note on cut-offs
Published pass marks vary by employer, provider and role, and most are never made public. There is no single percentage score that counts as 'passing' a numerical reasoning test in general.
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How to prepare
Read the table headers and units before you read the question
Note what each column represents, what units it's in, and whether figures are in thousands, percentages, or currency, before you look at what's being asked. Ten seconds spent here prevents the most common source of wrong answers: applying the right formula to the wrong number.
Round only at the final step
If a question involves more than one calculation, keep full precision through the intermediate steps and round only your final answer. Rounding early and compounding that rounding across two or three steps is enough to land you on a plausible-looking wrong option.
Memorise the percentage change formula cold
Percentage change is (new minus old) divided by old, multiplied by one hundred. Get this automatic so you're not re-deriving it under pressure, and double-check you divided by the original figure, not the new one, since that's the single most common slip.
Practise simplifying ratios quickly
Spend time finding the highest common factor of two or three numbers fast, since most ratio questions reward speed here over anything conceptually hard. If the numbers don't simplify cleanly, double-check you copied them from the right row of the table.
Use scratch space, don't do it in your head
Write down each intermediate figure as you calculate it rather than trying to hold several numbers in your head at once. This cuts careless arithmetic slips and makes it faster to spot where an error crept in if your answer doesn't match any option.
Eliminate implausible options before calculating precisely
A quick estimate often rules out two of the four options immediately, narrowing what you need to calculate exactly. If a question asks for a percentage increase and one option is over 100%, for instance, a rough glance at the figures usually rules it out on sight.
Time-box each question and move on
Decide in advance roughly how long you'll give any single question, and if you're still stuck at that point, take your best estimate and move on. One unfinished hard question rarely costs as much as two or three easy questions left unanswered because you ran out of time.
No, the arithmetic itself is usually straightforward, roughly school level: percentages, ratios and rates. The real difficulty is reading the data table correctly and working fast enough within the time allowed, not the underlying calculations.
Many providers allow a basic on-screen or handheld calculator, but this isn't universal, so check the specific instructions you're sent before test day rather than assuming either way.
This varies by employer and test provider, so there's no single number that applies everywhere. Sets are usually short and tightly timed rather than a long exam, with a limited number of questions and little time allowed for each.
Some providers show a percentile immediately after you finish; others release results later through the recruiter, sometimes alongside other stages of the process. Free practice tests, including this one, usually show your score right away.
There is no universal good score. Providers typically compare your result against a norm group of similar candidates and report a percentile, and each employer sets its own cut-off within that range for a given role.
Not quite. A maths test checks whether you can do a calculation you're handed directly, while a numerical reasoning test also checks whether you can find the right figures inside a table or chart first, under time pressure, before you calculate anything.
Do short, timed practice sets rather than untimed review, focus on reading the data correctly before calculating, and drill the percentage-change and ratio formulas until they're automatic. Speed and data-reading habits improve faster than raw maths ability in a short window.
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