UCAT Quantitative Reasoning
Timing, the calculator and strategy
Quantitative Reasoning (QR) is the numbers subtest of the University Clinical Aptitude Test (UCAT): 36 questions in 26 minutes, mostly built on tables, charts and graphs, each with five answer options. It is scored 300 to 900; the 2026 average was 675. The core maths is percentages, ratios, rates and averages. Marks come from pace: about 43 seconds a question, mixing mental arithmetic with a basic on-screen calculator, and guessing then moving on when stuck.
- Questions and time
- 36 in 26 minutes
- Time per question
- About 43 seconds
- Score range
- 300 to 900
- 2026 QR average
- 675 (42,359 tests)
- Answer options
- 5 per question, 1 mark each
Photo: Jeremy Segrott (from Cardiff, Wales, UK) / Wikimedia Commons · CC BY 2.0 · cropped
Photo: Sarah Cossom · CC BY-SA 3.0 · Photo: Suicasmo · CC BY-SA 4.0 · Photo: Ydam / Wikimedia Commons · CC BY-SA 3.0
What is UCAT Quantitative Reasoning?
The UCAT is the admissions test a consortium of UK universities uses to help select applicants for medicine and dentistry, alongside qualifications and interviews. Quantitative Reasoning is one of its four subtests. The UCAT Consortium, which runs the test, says QR assesses your ability to use numerical skills to solve problems. The questions are less about hard sums and more about problem solving: finding the right numbers in a table or graph and knowing what to do with them.
Most questions come in sets of four built on one table, chart, graph or short text, so you read the data once and use it four times. A few questions stand alone.
Medicine and dentistry applicants sit exactly the same subtest, and the Consortium explains why it matters for both careers. Doctors and dentists review data and apply it to their own practice. Drug calculations based on a patient's weight and age have to be right. And clinical research comes as statistics they must interpret.
| Questions | 36. Most are in sets of four sharing one table, chart, graph or text; a few stand alone. |
|---|---|
| Time | 26 minutes, after a separately timed 2-minute instruction screen. |
| Answers and marks | Five options per question. One mark for each correct answer, with no negative marking. |
| Score | Scaled from 300 to 900, then added to your Verbal Reasoning and Decision Making scores for a total of 900 to 2700. |
| Calculator | A basic on-screen calculator with no scientific functions. |
| Notes | An A4 laminated notebook and pen at a test centre. Candidates approved for the online (OnVUE) test bring their own erasable whiteboard. |
| Extra time | With approved access arrangements: 32 minutes 30 seconds (25% extra), 34 minutes 40 seconds (33%) or 39 minutes (50%). |
| 2026 average | 675, from 42,359 tests taken up to 24 September 2026: the highest of the three subtests scored 300 to 900. |
What is a good UCAT Quantitative Reasoning score?
A QR score only means something next to other candidates' scores from the same year. This is where QR scores fell in the last two tests.
| Percentile | QR score 2026 | QR score 2025 |
|---|---|---|
| 10th | 530 | 520 |
| 20th | 580 | 570 |
| 30th | 600 | 590 |
| 40th | 640 | 630 |
| 50th (median) | 670 | 650 |
| 60th | 700 | 680 |
| 70th | 730 | 710 |
| 80th | 780 | 750 |
| 90th | 820 | 820 |
A score at the 80th percentile is higher than about 80% of that year's scores. The 2026 figures cover 42,359 tests taken up to 24 September 2026; the 2025 figures cover 41,354. Source: UCAT Consortium, Test Statistics.
QR scores run higher than Verbal Reasoning and Decision Making scores. In 2026 the QR average was 675, against 640 in Decision Making and 602 in Verbal Reasoning. So a QR score that sounds strong can be only middling: 670 was the 2026 median, and a score of 780 sat at the 80th percentile.
QR also spreads candidates out the most. In 2026, 290 points separated the 10th and 90th percentiles in QR (530 to 820), against 210 in Verbal Reasoning and 240 in Decision Making.
Averages also shift from year to year: the QR mean was 649 in 2024, 661 in 2025 and 675 in 2026. The Consortium warns that mean scores can shift between testing years, so judge your score against the statistics for the year you sit, not against older targets.
Most universities look at your total, not your QR score alone. The Consortium notes that some do look at individual subtest scores and may even set a cut-off for one subtest, so read the UCAT rules on the website of every school on your list.
UCAT QR timing: how long you get for each question
26 minutes for 36 questions works out at about 43 seconds each. The Consortium's own QR tutorial gives approximately 40 seconds a question.
Those seconds cover three jobs: understanding what the question asks, finding the numbers you need, and working out the answer. The data sets are where time goes. In a set, four questions share one table or chart, so reading it with care once pays off four times.
The timer counts down in the top right of the screen and turns yellow when less than 5 minutes remain. The 2-minute instruction screen before QR is timed separately, so it does not come out of your 26 minutes. You can flag any question and return to it from the review screen if time is left at the end.
| After question | Time used at 40 seconds each | Timer shows about |
|---|---|---|
| 9 | 6 minutes | 20:00 |
| 18 | 12 minutes | 14:00 |
| 27 | 18 minutes | 8:00 |
| 36 | 24 minutes | 2:00, for flagged questions |
Arithmetic from the official 26 minutes and the tutorial's guide of about 40 seconds a question. Sets vary in difficulty, so treat the checkpoints as a guide rather than a rule.
First pass: answer what you can
Work through in order at about 40 seconds a question. Read the question first, then go to the data for only the numbers it needs. The Consortium's tutorial points out that some information may not be needed to reach an answer.
Stuck? Eliminate, guess, flag
If a question is heading past a minute, rule out the answers that are clearly wrong, pick the best of the rest and flag it. The tutorial suggests prioritising the simpler, quicker questions and returning to the others later.
Second pass: the flagged questions
After the last question, the review screen highlights flagged, incomplete and unseen questions. Go back first to the flagged ones you were close to finishing, not the hardest ones.
Last minute: no blanks
There is no negative marking, so make sure every question has an answer before time runs out. When the time-out message appears, click OK straight away, or the lost seconds come off the next subtest.
What maths is in UCAT QR? The topics to revise
QR does not need A-level maths. The four areas the Consortium tells QR candidates to practise all appear in the GCSE maths curriculum.
| Area | What the tutorial lists | How it can appear |
|---|---|---|
| Percentages | Basic percentages, percentage change, reverse percentages, and moving between percentages, decimals and fractions | A price after a discount, a rise from one year to the next, or the original value before an increase |
| Proportion and ratio | Direct and inverse proportion | Scaling a recipe or a dose, or working out how long a job takes with more people |
| Rates | Rates of flow, and speed using the speed, distance and time triangle | A drip rate in millilitres per minute, fuel used per 100 km, or average speed over a journey |
| Averages | Mean, mode, median and range | The mean of a column in a table, or how one new value changes it |
The GCSE mathematics subject content published by the Department for Education covers all four, including original-value percentage problems, inverse proportion and compound units such as speed.
Six mental shortcuts worth learning
Build any percentage from 10%, 5% and 1%
10% moves the decimal point one place, 5% is half of that, and 1% moves it two places. So 23% of 250 is 25 + 25 + 2.5 + 2.5 + 2.5 = 57.5, with no calculator.
Use multipliers for rises and falls
An 18% rise is × 1.18 and a 15% cut is × 0.85. One multiplication gives the new value. Two rises in a row multiply rather than add: 10% and then 10% is × 1.21, a 21% rise.
Undo a percentage by dividing
If a price is £60 after a 20% rise, the original is 60 ÷ 1.2 = £50. Taking 20% off £60 gives £48, which is wrong, because the 20% was worked out on the smaller, original price.
Percentage change: divide by the old value
Change ÷ original × 100. From £40,000 to £52,000 is 12,000 ÷ 40,000 = 30%. Dividing by the new figure gives about 23%, a different and wrong answer.
Know common fractions as percentages
1/8 = 12.5%, 1/6 ≈ 16.7%, 1/3 ≈ 33.3%, 2/3 ≈ 66.7% and 5/6 ≈ 83.3%. Spotting that 0.125 is 1/8, or that 0.2 is 1/5, turns a division into a quick mental step.
Ratios: count the parts first
A 3:5 mix has 8 parts. For 800 ml, each part is 100 ml, so 300 ml is concentrate and 500 ml is water. Forgetting to add the parts together is an easy slip under time pressure.
The UCAT calculator: keys, shortcuts and when to use it
The facts here come from the Consortium's Test Tools page and its official Tour Tutorial, where you can try the same calculator before test day.
| What it is | A basic calculator for Decision Making and Quantitative Reasoning that cannot do scientific functions. In the Tour Tutorial it appears as an on-screen Texas Instruments TI-108. |
|---|---|
| Keys | Digits, decimal point, add, subtract, multiply, divide, equals, percent, square root, a sign-change key, memory keys M+, M− and MRC, and ON/C. |
| Opening it | Click Calculator in the toolbar above the question, or press Alt + C. |
| Typing numbers | Click the keys, or type numbers on the keyboard. If you type, Num Lock must be on. |
| Clearing | ON/C clears it. Backspace also clears every digit at once. There is no way to delete a single digit. |
| Closing | Click X, or move on to the next question, which closes it automatically. |
| If it stops responding | It runs in a separate window. Clicking the question or using a shortcut such as Alt + F deactivates it until you click back on it. |
| If it covers the data | Drag it by its title bar to another part of the screen. |
| Keys | What they do |
|---|---|
| Alt + N | Go to the next screen or question |
| Alt + P | Go back to the previous question |
| Alt + C | Open the calculator |
| Alt + F | Flag the question for review |
| Alt + V | Open the Navigator, which lists every question in the subtest and its status |
| Letter keys | Select that answer, for example B for answer B |
Any button with an underlined letter has an Alt shortcut. In the practice materials, Alt + F does not flag a question in Google Chrome, because Chrome uses that shortcut itself.
Do it in your head when
- The numbers are round: 15% of 200 is 30, from 10% plus 5%.
- You only need to compare sizes, or rule out options that are far apart.
- A fraction you know does the work, such as a quarter or an eighth.
- It is one short step you can check by rounding.
Open the calculator when
- The numbers are awkward, like 3,426 ÷ 3,377 in the Consortium's own tutorial.
- Several steps are chained together, so one slip would carry through.
- The options are close together and an estimate cannot separate them.
- You need a percentage of an untidy number to the nearest unit.
There are no separate MR and MC keys: memory runs on M+, M− and a single MRC key, so try them in the Tour Tutorial before you rely on them. Often it is just as quick, and easier to check, to write an intermediate result on your notebook. The Consortium's tutorial reminds you that your note-taking materials are there for calculations too.
How to answer UCAT QR questions: a method for every data set
The Consortium publishes three QR tips from candidates who scored in the top 3% in recent years. Brush up on basic maths and mental arithmetic. Mix mental, written and calculator methods. Round numbers to rule out clearly wrong answers first. This method builds on all three.
Read the question, not the whole chart
Start with the question, then find the one row, column or bar it needs. Studying every number first wastes time, and the tutorial warns that some information is not needed.
Check units and key words
Note the unit of every number you use: litres or millilitres, per month or per year, values in thousands on an axis. The tutorial says individual words and units can decide the answer.
Estimate before you calculate
Round the numbers and work out a rough answer. Options far from it can go straight away, and sometimes only one is left.
Work only as precisely as the options need
If the options are far apart, your estimate is enough. If they are close, use the calculator or a written method, and jot intermediate results on your notebook.
Answer the question asked
Before you click, re-read the last line. Check whether it wants a difference or a total, and a monthly or a yearly figure.
Reuse the data for the rest of the set
Most questions come in sets of four on the same data, so note any value you worked out that could come up again.
Three worked examples from the Consortium's QR tutorial
Two cars use 10.3 and 9.7 litres of fuel per 100 km in town. Over a 12-week term, each makes ten 25 km school trips a week. What is the difference in the fuel they use over the term? The options are 9, 10, 12, 16 and 18 litres.
Work with the difference straight away: 0.6 litres per 100 km. The distance is 10 × 12 × 25 = 3,000 km, which is 30 lots of 100 km, so 0.6 × 30 = 18 litres. The trap is the unit: fuel use is given per 100 km, so you must divide the distance by 100.
A table gives the world's urban and rural populations in four different years. In the year with the smallest percentage rise in urban population, what was the percentage rise in rural population? The options run from 1.45% to 39.15%.
Scan before you calculate. In two of the years the urban population roughly doubles, so the smallest rise must be in the remaining year, with no working needed. Then one division settles it: 3,426 ÷ 3,377 = 1.0145, a rise of 1.45%.
A growth chart shows boys' heights from birth to 36 months, with a line for the median. What is the average rate of increase of the median between birth and one year? The options are 0.55, 1.7, 2.2, 5.5 and 22 cm per month.
Read just two points: the median starts at 50 cm and reaches 76 cm at 12 months. That is 26 cm in 12 months, and 26 ÷ 12 = 2.17, or about 2.2 cm per month. Check the decimal point before you click: 22 cm is also an option.
UCAT QR practice questions with worked answers
Six questions on the core skills: a percentage, a ratio, average speed, unit conversion, percentage change and growth. Choose an answer, check it, then read the working. The real test gives five options and shared data; these give four to keep them quick.
A drug dose of 350 mg is increased by 18%. What is the new dose?
A solution is mixed in the ratio 3:5 (concentrate:water). To make 800 ml of solution, how much concentrate is needed?
A train travels 240 km at 80 km/h, then 180 km at 60 km/h. What is the average speed for the whole journey?
A patient drinks 1.5 L of water spread evenly over 6 hours. What is the average rate in mL per minute?
Sales were £40,000 last quarter and £52,000 this quarter. What is the percentage increase?
A bacterial colony doubles every 2 hours. Starting with 50 cells, how many after 8 hours?
Timed UCAT QR practice: data sets at test pace
Each set has two data sets with four questions on each and one standalone question, all with five options, as in the test. The clock gives you 6 minutes 30 seconds, the live pace of about 43 seconds a question, and the calculator works by click or keyboard.
Quantitative Reasoning practice sets
Pick a set and work through it as you would in the test: read each data set once, flag anything slow, use the calculator by click or keyboard, and check the review screen before you finish.
- 2 data sets with 4 questions each, plus 1 standalone question
- 6 min 30 s: about 43 seconds a question, as in the test
- Five options per question, on-screen calculator
Original questions written for practice in the real format. They are not taken from the UCAT.
If you finished in time but dropped marks, slow down on units and on the last line of each question. If you ran out of time, look at where it went: the first question on a data set takes longest, so note any value you work out that a later question can reuse.
Common UCAT QR mistakes and how to avoid them
How to prepare for UCAT QR with the free official materials
The Consortium's materials are free, and it says its question banks and practice tests are representative of the live test. It recommends working through them in this order.
Tour Tutorial
Learn the test software: the calculator, the keyboard shortcuts, the Navigator and flagging. The Consortium says knowing these tools can save valuable time on the day.
Quantitative Reasoning Question Tutorial
Fifteen slides covering the format, the four skill areas, timing tips and three worked examples with the data shown.
Four QR question banks
Questions with an Explain Answer button that shows the reasoning. Your progress is not saved, so keep a note of which questions you have done. Use a computer, not a phone, to match the live test.
Four full practice tests
Tests A to D, each with standard timing, with 25% extra time, or untimed. They give no score, but the review screen marks each answer right or wrong and explains it. The Consortium advises using them nearer your test date.
Track your marks and target your errors
Count your QR marks in every timed set and keep them in a simple spreadsheet, as one of the Consortium's top-scoring 2025 candidates suggests. Then drill the question types you get wrong, not the ones you already find easy.
Plan for 4 to 8 weeks of preparation, the range the Consortium's top-scoring candidates suggest, and fit a few minutes of mental arithmetic into most days. There are only four official full tests, so use the question banks to learn and keep the full tests for checking your pace.
Are you ready for QR? Tick off what you can already do
UCAT Quantitative Reasoning: your questions answered
Where this guide's facts come from
Checked against these sources on 19 October 2026. Rules change between cycles, so confirm anything that decides your application on the official page for your entry year.
Want a second pair of eyes on your QR?
A UCAT tutor can go through your timed QR practice with you, from how you read the data to how you use the calculator, and help you fix the habits that cost you time. For a week-by-week schedule, try the revision planner.