Aug 8, 2026 | Kritika Kumar, PhD (Imperial College London)
UCAT Quantitative Reasoning is the numerical section of the UCAT: 36 questions in 26 minutes, answered from tables, charts and short passages of data, and scored on the 300-900 scale like the other cognitive subtests. It is not an open-ended maths syllabus: the questions fall into four families — rates and per-unit work, percentages, averages, and ratios — and they appear in stable proportions, so you can decide what to drill first instead of guessing.
We counted. Across 144 questions from UCAT’s own official practice material, read alongside the published rationale for each one, over half turned out to be rates and per-unit questions. Most QR advice you will read online, including our own before we ran the count, opens with percentage tricks. That is the wrong end of the paper.
The format is 36 questions in 26 minutes, which works out at roughly 43 seconds per question including the time you spend reading the data set (ucat.ac.uk). In practice the reading is front-loaded: once you have understood a data set, the questions drawing on it come faster than the first one did.
You get an on-screen calculator, opened with Alt+C, plus a whiteboard and pen. That is the whole toolkit.
The maths level is GCSE. There is no algebra beyond rearranging a formula you have been given, and the statistics in our corpus went no further than mean, mode, median and range. If you are sitting A-level maths, nothing here is new content — the difficulty is entirely in the reading, the setup and the clock.
Two things about scoring are worth knowing before you plan your prep. QR is the highest-scoring cognitive section nationally: the final 2026 subtest means were 602 for Verbal Reasoning, 640 for Decision Making and 675 for Quantitative Reasoning (ucat.ac.uk). That cuts both ways. It is the easiest section to pick up marks in, and a weak QR stands out more than a weak VR does.
The 2026 mean total across the three cognitive subtests was 1918 from 42,359 tests, on a 900-2700 scale, and the 9th decile — the top 10% — sat at 2250 (ucat.ac.uk). If you want to see where a given total or subtest score falls, our deciles tool converts it against the published boundaries. These are UCAT’s final 2026 figures.
Here is the breakdown from our 144-item count. Each question was classified by what it fundamentally asks you to do; a sample was then re-coded blind by three people working only from the definitions, to check the classification held up. The shares add to more than 100% on purpose: one item often chains two families, such as a rate you have to work out before you can express the change as a percentage.
Family | Share of the 144 practice questions |
Rates and per-unit — speed, flow, dosage, price per unit, direct and inverse proportion | 56% |
Percentages — of a number, change between two, reverse | 35% |
Averages — mean, mode, median, range | 21% |
Ratios — splitting and scaling | 8% |
UCAT’s own QR Question Tutorial lists the same underlying skills, so this is not a private theory about the exam. What the count adds is the weighting — and the weighting is what tells you where to spend a limited week.
A rate question gives you a quantity and a unit, and asks you to convert between them: cost per litre, patients per hour, millilitres per kilogram, kilometres per hour. Direct and inverse proportion sit in the same family.
The method is always the same. Write down what one unit is worth, then multiply.
A clinic uses 4.5 litres of a disinfectant solution over 6 days. At the same rate, how much does it use over 10 days? One day is 4.5 ÷ 6 = 0.75 litres. Ten days is 7.5 litres. The trap is not the arithmetic; it is that the table gives you weekly figures and the question asks about days, or gives you a total for four wards and asks about one.
Before you touch the numbers, say the unit out loud: “per what?” That single habit fixes most rate errors.
Three shapes appear: a percentage of a number, the percentage change between two numbers, and the reverse percentage where you are given the post-change figure and asked for the original.
Reverse percentages are the ones people lose marks on. If a price is £68 after a 15% discount, the original is not £68 × 1.15. It is 68 ÷ 0.85 = £80. Whenever a question tells you the value after a change, divide by the multiplier rather than multiplying by it.
For percentage change, keep the formula in one form so you never have to think about it under time pressure: (new − old) ÷ old × 100.
Averages were a fifth of the questions we counted, and the students we work with almost never practise them, because mean, mode, median and range feel too easy to be worth a session. The questions are rarely “find the mean”. They run backwards.
A student’s mean score across 5 mocks is 62. Their first four scores are 58, 64, 61 and 60. What did they get in the fifth? The total must be 62 × 5 = 310. The first four sum to 243. The fifth is 67.
That reversal — total first, then subtract — covers most average questions in the paper. Median questions mainly test whether you remembered to sort the list, and range questions mainly test whether you read the axis correctly.
Ratios are the smallest family at 8%, and they are worth the least of your time. Splitting an amount in a given ratio and scaling a recipe or dosage upward covers nearly all of them.
Split £4,200 in the ratio 3:5. There are 8 parts, so one part is £525, giving £1,575 and £2,625. Add the parts first, always.
You will see “cheat sheets” of arithmetic shortcuts: multiply by 25 by multiplying by 100 and dividing by 4, halve twice instead of dividing by 4, and so on. Those are fine, and they do speed you up.
But they appear nowhere in UCAT’s own list of tested skills, and they were not what any question in our corpus was about. They are how you execute a step, not a topic to study. Drilling shortcuts while your rate setup is shaky is polishing the tool instead of learning the job.
Forty-three seconds is an average, not a budget for every question. Some items take fifteen seconds; a multi-step rate question with a unit conversion takes ninety.
The decision that matters is the one you make at about the twenty-second mark. By then you should know whether you have a route to the answer. If you do, commit and finish it. If you do not — you are still re-reading the table, or you cannot tell which column you need — mark it, put an answer down, and move.
An answered question you were going to lose anyway is better than a blank one, and the real cost of a hard question is the three easy questions at the end of the section that you never reach.
In practice, the students we see run out of time are rarely slow at arithmetic. They are slow at abandoning.
The on-screen calculator opens with Alt+C. Every use costs you the move to it, the entry, and the read back.
For anything you can do in your head, that overhead is larger than the calculation. Percentages of round numbers, halving, doubling, multiplying by ten, and comparing two obviously different quantities are all faster on the whiteboard or in your head.
Use the calculator when the numbers are genuinely awkward — long division, multi-digit multiplication, chained conversions — and when a slip would be invisible. Do not use it to compute 10% of 240.
The habit to build is deciding before you reach for it. Practise with the calculator open on screen the way it will be in the exam, so the choice becomes automatic rather than a reflex.
If you have four weeks and QR is your weak section, weight your practice the way the paper is weighted rather than splitting it evenly across topics.
Week 1 — rates and per-unit. Nothing else. Work untimed at first and write the unit down before every calculation. You are building the setup habit, not the speed.
Week 2 — percentages, with rates kept warm. Roughly two thirds percentages, one third mixed rate questions so week 1 does not decay. Spend a full session on reverse percentages alone.
Week 3 — averages and ratios, then timed mixed sets. Averages first, backwards questions especially. Ratios need about one session. Then start doing 36-question sets under the full 26 minutes.
Week 4 — full timed sections and error review. The review matters more than the volume here. For every question you got wrong, write one line: was it the setup, the arithmetic, or the clock? After a week you will see which of the three is actually costing you, and it is usually not the arithmetic.
If you would rather work this into a full schedule alongside the other subtests, our UCAT preparation course covers the same weighting across a structured timetable.
One honest caveat: how much this moves your score depends on where you are starting and how much time you have left, and we will not put a number on it. What the weighting does reliably is stop you spending three of your four weeks on the family that was 8% of the questions we counted.
The four-week plan tells you what to practise. This is how to run a single session.
10 minutes, estimation only. Pick questions whose answer options are far apart, and round everything. What you are training is the decision that an exact figure is not needed, and that decision saves more time in the real section than faster arithmetic does.
15 minutes, mixed arithmetic. Percentages, rates, averages and ratios shuffled together, as many as you get through. Mixing them is the point: the paper does not group questions by topic, so practice that does trains the wrong reflex.
20 minutes, 20 percentage questions. A fixed count against a fixed clock, so you can see your pace rather than feel it. Reverse percentages belong in this one.
25 minutes, data interpretation. Tables, bar charts and pie charts. Most of the time lost here goes on reading the data set rather than on the calculation, so if you can, time the read separately.
26 minutes, the full section. Thirty-six questions, with two checkpoints instead of watching the clock question by question: question 12 with 18 minutes left, question 24 with 9 minutes left. Behind at either one and you know early enough to start abandoning, rather than finding out at question 30 when it is too late.
After every drill, write down three things: the questions you got wrong, the questions that took more than a minute, and the topic that keeps appearing on both lists. The third line is the one that changes what you practise next week.
The 2026 QR subtest mean was 675, and the 9th decile — top 10% — was 820 for QR (ucat.ac.uk). QR scores higher than the other cognitive subtests nationally, so a score that would be strong in Verbal Reasoning is only average here. What counts as "good" also depends entirely on the universities you apply to, because they weight the UCAT very differently from one another.
36 questions in 26 minutes, which averages about 43 seconds per question. The average hides a wide spread — some items are fifteen-second reads and some are multi-step conversions.
GCSE level. Rates and proportion, percentages including reverse percentages, mean, mode, median and range, and ratios. There is no algebra beyond rearranging a formula you are given.
Only when the numbers are genuinely awkward. The on-screen calculator opens with Alt+C, and the time cost of moving to it, entering the numbers and reading the result is often greater than doing the calculation in your head or on the whiteboard. Long division and multi-digit multiplication are worth it; 10% of 240 is not.
Across 144 questions from UCAT's official practice material, rates and per-unit questions were 56%, percentages 35%, averages 21% and ratios 8%. The shares overlap because one question often chains two families. Most people drill percentages first; the data says rates should come first.
Work on abandoning rather than on arithmetic speed. Decide at around twenty seconds whether you have a route to the answer, and if you do not, put an answer down and move on. An answered question you were going to lose anyway is better than a blank one, and the real cost of a hard question is the easy questions at the end you never reach.
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If you want a second opinion on where your QR sits and what to drill with the time you have left, book a 30-minute consultation with the DreamMedic team through the booking calendar, message us on WhatsApp, or email info@dreammedic.co.uk.
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