Basic Numeracy Test
Addition, subtraction, multiplication, division, fractions, decimals, percentages, rounding and averages, at the pace employers actually test. Every question comes with the working shown.
- 10 questions
- 10 minutes
- Worked solutions
- Printable PDF
Free · No sign-up · Scored the moment you finish
What is a basic numeracy test?
A basic numeracy test measures how confidently you handle everyday arithmetic without a calculator. Employers use it to check the core maths a role relies on before interview. You work through addition, subtraction, multiplication, division, percentages and simple fractions, then choose the correct answer from the options given. Accuracy under a little time pressure is what it rewards.
Free basic numeracy test
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Free Basic Numeracy Test
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Question 1 of 10
Of 480 survey responses received, 35% were positive. How many responses were positive?
- 168
- 312
- 35
- 16.8
Show the answer
Answer: A. 168
To find 35% of a number, multiply by 0.35: 480 × 0.35 = 168 positive responses. Working out the 65% that were not positive instead gives 480 × 0.65 = 312, which answers the opposite of the question. Reading the “35%” as a plain count of 35 ignores the 480 responses it is a share of. Using 3.5% by mistake (0.035 × 480) gives 16.8, which slips the decimal point one place and shrinks the answer tenfold.
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Question 2 of 10
A fuel tank is filled to three-eighths of its 2,400-litre capacity. How many litres of fuel are in the tank?
- 900 litres
- 300 litres
- 1,500 litres
- 6,400 litres
Show the answer
Answer: A. 900 litres
Three-eighths means three parts out of eight. One eighth is 2,400 ÷ 8 = 300 litres, so three eighths is 3 × 300 = 900 litres. Stopping at one eighth gives 300 and forgets to multiply by the three parts asked for. The other five eighths, the empty space, is 5 × 300 = 1,500 litres, which measures what is missing rather than what is present. Dividing by the fraction instead of multiplying, 2,400 × 8 ÷ 3, gives 6,400, but taking a fraction of an amount always makes it smaller, not larger.
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Question 3 of 10
A 72 kg batch of trail mix combines nuts, raisins and seeds in the ratio 3:4:2 by weight. How much does the heaviest ingredient weigh?
- 32 kg
- 24 kg
- 16 kg
- 8 kg
Show the answer
Answer: A. 32 kg
Add the ratio parts: 3 + 4 + 2 = 9 parts in total. One part is 72 ÷ 9 = 8 kg. The heaviest ingredient is raisins at 4 parts, so 4 × 8 = 32 kg. Nuts are 3 parts, 3 × 8 = 24 kg, and seeds are 2 parts, 2 × 8 = 16 kg; these three figures sum back to 72 kg as a check. Answering 24 or 16 reads off the wrong ingredient, and answering 8 stops at the value of a single part instead of the four parts the heaviest ingredient is made of.
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Question 4 of 10
Day Visitors Monday 320 Tuesday 450 Wednesday 380 Thursday 510 Friday 340 A museum recorded the following daily visitor numbers over five days. What was the mean number of visitors per day?
- 400
- 500
- 380
- 415
Show the answer
Answer: A. 400
The mean is the total divided by how many values there are. The total is 320 + 450 + 380 + 510 + 340 = 2,000 visitors across 5 days, so the mean is 2,000 ÷ 5 = 400 per day. Dividing by 4 instead of 5 gives 500, which loses one of the days. Picking 380 gives the middle value when the days are sorted, which is the median, not the mean. Averaging only the highest and lowest days, (510 + 320) ÷ 2, gives 415, but the mean has to take every day into account, not just the two extremes.
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Question 5 of 10
A bottling line fills 250-millilitre bottles. How many litres of liquid are needed to fill 60 bottles?
- 15 litres
- 15,000 litres
- 150 litres
- 1.5 litres
Show the answer
Answer: A. 15 litres
First find the total in millilitres: 250 × 60 = 15,000 ml. There are 1,000 millilitres in a litre, so divide by 1,000: 15,000 ÷ 1,000 = 15 litres. Leaving the answer as 15,000 forgets to convert millilitres into litres at all. Dividing by 100 gives 150 and treats a litre as 100 ml, and dividing by 10,000 gives 1.5, shifting the decimal one place too far. The conversion is always 1,000 millilitres to a litre.
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Question 6 of 10
A subscription currently costs £40 per month. The price is increased by 15%. What is the new monthly price?
- £46.00
- £6.00
- £55.00
- £34.00
Show the answer
Answer: A. £46.00
A 15% increase adds 15% of £40 on top of the original. 15% of 40 is 40 × 0.15 = £6, so the new price is 40 + 6 = £46.00. Answering £6.00 gives only the size of the increase and forgets to add it to the original price. Adding £15 rather than 15% gives 40 + 15 = £55.00, confusing a percentage with a flat amount of money. Subtracting the increase instead of adding it gives 40 − 6 = £34.00, but a price rise makes the figure larger, not smaller.
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Question 7 of 10
A warehouse receives 8 pallets, each holding 45 boxes. During the day 296 boxes are shipped out. How many boxes remain in the warehouse?
- 64
- 360
- 296
- 24
Show the answer
Answer: A. 64
First find how many boxes arrived: 8 pallets × 45 boxes = 360 boxes. Then subtract the 296 shipped out: 360 − 296 = 64 boxes remain. Answering 360 stops at the total received and forgets the boxes that left. Answering 296 gives the number shipped rather than the number left behind, which is the quantity the question asks for. Answering 24 comes from a multiplication slip: 8 × 40 = 320 while forgetting the 8 × 5 = 40, then 320 − 296 = 24; the full product is 8 × 45 = 360.
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Question 8 of 10
Category Amount (£) Rent 800 Food 400 Transport 300 Other 500 Total 2,000 What percentage of the monthly budget is spent on rent?
- 40%
- 25%
- 66.7%
- 4%
Show the answer
Answer: A. 40%
The rent share is the rent divided by the whole budget: 800 ÷ 2,000 = 0.40, which is 40%. Using the £500 “Other” row by mistake gives 500 ÷ 2,000 = 25%, the wrong row. Dividing rent by the £1,200 spent on everything except rent (2,000 − 800) gives 800 ÷ 1,200 = 66.7%, which uses the wrong base: the base must be the full budget, not the budget with rent removed. Reading 0.40 as 0.04 gives 4% and misplaces the decimal point by one place.
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Question 9 of 10
Driver Parcels delivered Driver A 84 Driver B 96 Driver C 72 Driver D 88 Four delivery drivers logged the parcels shown below in one day. What was the mean number of parcels per driver?
- 85
- 340
- 86
- 113
Show the answer
Answer: A. 85
Add the four figures: 84 + 96 + 72 + 88 = 340 parcels. Divide by the 4 drivers: 340 ÷ 4 = 85 parcels per driver. Answering 340 gives the total and forgets to divide. Answering 86 takes the median instead: sorted, the middle two are 84 and 88, and (84 + 88) ÷ 2 = 86, which is not the mean. Dividing by 3 rather than 4, 340 ÷ 3 = 113, counts one driver too few; there are four drivers to share the total between.
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Question 10 of 10
Five identical pumps can drain a reservoir in 6 hours. Working at the same rate, how long would 3 of the pumps take to drain the same reservoir?
- 10 hours
- 3.6 hours
- 18 hours
- 30 hours
Show the answer
Answer: A. 10 hours
The whole job takes 5 pumps × 6 hours = 30 pump-hours of work. With only 3 pumps, the time is 30 ÷ 3 = 10 hours. Fewer pumps means more time, so the answer must be larger than 6. Answering 3.6 hours treats it as direct proportion, 6 × 3 ÷ 5, making the time fall when pumps are removed, which is backwards. Answering 18 hours multiplies the 6 hours by the 3 pumps, and answering 30 hours stops at the 30 pump-hours of total work without dividing it among the 3 pumps.
How to interpret your score
| Score | What it suggests |
|---|---|
| 9 to 10 | Comfortably above the bar for most graduate schemes |
| 7 to 8 | Around the typical pass mark. Worth practising for speed |
| 5 to 6 | Below most employer thresholds. Focus on method before speed |
| 4 or fewer | Work through the worked solutions above before retrying |
Employers set their own thresholds and many sift on the top percentage of applicants rather than a fixed mark, so treat these as a guide.
Practise with the full pack
One test tells you the style. A pack gives you the pace: batches under time pressure, marked, with the working shown.
- 16
- Basic Numeracy tests
- 310
- questions, all solved
What maths is covered in a basic numeracy test?
Basic numeracy tests cover the core arithmetic taught by age sixteen, applied to short, practical questions. The topics are predictable, which is exactly why practice pays off.
Expect questions on:
- The four operations: addition, subtraction, multiplication and division, often with larger numbers than you would do casually in your head.
- Fractions and decimals: converting between them, and using them in calculations.
- Percentages: finding a percentage of an amount, and percentage increase or decrease.
- Rounding: to the nearest whole number, decimal place or significant figure.
- Averages: the mean, median and mode of a set of numbers.
- Ratios and proportion: splitting an amount, or scaling a recipe or rate.
- Number sequences: spotting the rule and continuing the pattern.
Some publishers also present short tables or charts and ask you to read a figure and calculate from it, which is where basic numeracy starts to look like numerical reasoning.
How do you work out the mean, median and mode?
The mean, median and mode are three different kinds of average, and mixing them up is one of the most common mistakes in the whole test. Each has a one-line definition worth committing to memory.
- Mean: add every value, then divide by how many there are. For -5, 12, 24, 46 and 60, the total is 137 and there are five values, so the mean is 137 divided by 5, which is 27.4.
- Median: the middle value once the numbers are in order. Put them in order first, then take the middle one. With an even count, take the mean of the middle two.
- Mode: the value that appears most often. A set can have more than one mode, or none at all.
When a question names one of the three, underline it. The answer options are usually built so that the mean, median and mode all appear, and picking the wrong average is the trap.
Can you use a calculator in a basic numeracy test?
Often not, and that is the single biggest thing to check before you sit one. Many basic numeracy tests are designed to assess mental arithmetic, so a calculator is not allowed and the numbers are kept manageable by hand.
Where a calculator is permitted, an on-screen or basic model is usual. If you are sitting the test at an assessment centre you may be given one, but it is worth taking your own where the rules allow, because you will be faster on buttons you know.
Either way, estimating first saves time. If you can see an answer is roughly a quarter, or clearly more than half, you can often eliminate two or three options before doing the exact sum. Check the instructions in your invitation, because the calculator rule changes the right approach.
How are basic numeracy tests scored?
Most employers score you against other candidates, not against a fixed pass mark: your raw score becomes a percentile. Attempting questions matters, because most tests are built so few candidates finish, and guessing usually pays: negative marking is rare, but check the instructions.
How do you manage your time under the clock?
Work out your budget before you start and stick to it, because getting stuck on one question is what sinks most candidates. Divide the time by the number of questions and you have a rough seconds-per-question figure to pace against.
Three habits help:
- Do not stall. If a question is not coming, mark it, move on, and return if time allows. The easy marks later are worth more than one hard mark now.
- Use rough paper. Where it is allowed, writing your working down cuts slips and lets you pick up a half-finished calculation without starting over.
- Read the units and the question again. Many wrong answers come from misreading what was asked, not from bad arithmetic, so a quick re-read before you commit is cheap insurance.
Practice Aptitude Tests · Original data
How our test takers score
Results from every test in our Basic Numeracy pack, past and present.
Key finding72% of Basic Numeracy test takers score 80% or more.
How scores spread
72% scored 80% or more, and 5% scored under 40%.
Share of sittings in each score band.
Does practice help?
Regular practisers scored about the same on their fifth test as their first.
1,212 people who took five or more tests.
Does speed help?
Speed makes little difference here.
Typical pace: 36 seconds a question.
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Video tutorials
The methods behind the questions above, from our team
