UCAT Quantitative Reasoning: Complete Guide, Timing and Question Types

UCAT Quantitative Reasoning (QR) is the numerical subtest of the UCAT (University Clinical Aptitude Test). You answer 36 questions in 26 minutes, about 43 seconds each, using data from tables, charts and graphs and a basic on-screen calculator. The maths is GCSE level. What makes QR hard is the clock, applied to unfamiliar data layouts.

QR is also the section where preparation pays off most reliably. The question types are finite, the formulas are learnable, and most lost marks come from technique (reading the wrong row, misjudging units, overusing the calculator), not from gaps in maths knowledge.

In medicine and dentistry, numerical reasoning under time pressure is a daily requirement: drug doses calculated from patient weight, audit data, trial results and infusion rates. QR is not a maths test. It is a proxy for how well you process numbers when the stakes are real and the time is short.

How long is UCAT Quantitative Reasoning and how many questions are there?

UCAT Quantitative Reasoning has 36 questions and 26 minutes of answering time, which is about 43 seconds per question. A separately timed 2-minute instruction screen comes before it, so QR takes 28 minutes from start to finish.

The 2 minutes of instructions are not taken out of your 26 minutes. The UCAT Consortium times each instruction screen separately, and its own table adds them up to a standard test of 117 minutes 30 seconds: 111 minutes of subtests plus 6 minutes 30 seconds of instructions. Candidates with approved access arrangements (UCATSEN) get longer QR timings:

Most questions are grouped in sets that share one data set (a table, chart, graph or short text), usually with four questions per set, and each question has five answer options. QR is the third subtest, after Verbal Reasoning and Decision Making. For every subtest side by side, see UCAT timings for every section, and if you may be eligible for extra time, read UCAT access arrangements and UCATSEN.

These are the timings for UCAT 2026. Abstract Reasoning was withdrawn from UCAT 2025, and QR has run at 36 questions in 26 minutes since then. UCAT had not published 2027 test dates or any 2027 format change as of 24 October 2026.

What does UCAT Quantitative Reasoning test?

QR tests whether you can use numbers to solve problems quickly: choosing which figures matter and which short calculation gets you to the answer. The UCAT Consortium describes its questions as less to do with numerical facility and more to do with problem solving.

The data arrives in several formats, and recognising each one quickly saves time:

• Written text with no diagram
• Tables, often with several similar rows or columns
• Charts, including pie charts, Venn diagrams and 3D charts
• Line and bar graphs
• 2D and 3D shapes, often a room, garden or container
• Other diagrams such as timetables, price lists and maps

The same subtest is used for the UCAT in Australia and New Zealand, so everything here applies there too. For the full test, start with what the UCAT is and how it works.

How is UCAT QR scored and what is a good QR score?

Each QR question is worth 1 mark, there is no negative marking, and your raw mark out of 36 converts to a scaled score from 300 to 900. In 2026 the average QR score was 675 (661 in 2025), the highest of the three cognitive subtests.

Your QR score adds to Verbal Reasoning and Decision Making to give a total from 900 to 2700; Situational Judgement is reported separately as Band 1 to 4. A QR score of 730 put you in the top 30% in 2026, and 820 in the top 10%. The official 2026 QR decile boundaries:

Because QR averages higher than VR and DM, a QR score that looks strong can still sit mid-table. Compare like with like using UCAT deciles and what a good UCAT score is, convert practice marks with the UCAT score calculator, and see how the total is built in UCAT scores and scoring. To see what your score means for applications, read how universities use the UCAT.

What topics come up in UCAT QR? Every question type

About a dozen topic types make up UCAT QR, all at GCSE level. Percentages, data interpretation, rates and ratios appear most often; each type below links to its dedicated guide.

Percentages and percentage change

The most frequent topic: percentage of a value, increase and decrease, reverse percentages (finding the original) and compound change. Find 15% as 10% plus half of it; 17.5% as 10% plus 5% plus 2.5%. The classic trap is confusing percentage change with percentage point change: 40% to 50% is 10 percentage points but a 25% increase. Shortcuts in UCAT QR percentage questions.

Ratios and proportion

Direct proportion (if A needs 3 of X, how many does 7 of A need?) and sharing a value in a ratio. Find the value of one part first. Scaling recipes, mixing solutions and splitting budgets all use the same move. More in UCAT QR ratio and proportion questions.

Speed, distance and time

Distance = speed x time. The trap is units: speed in km/h, distance in metres, the answer wanted in seconds. Write the conversion on your notebook before you calculate.

Averages: mean, median and mode

Usually a missing value given the mean, or a weighted mean across groups: multiply each value by its frequency, add them up, divide by the total frequency. For a median in a large data set, find the middle position, (n + 1) / 2, without listing every value. See UCAT QR averages.

Data interpretation: charts, graphs and tables

Every question is anchored to data, so reading the right value fast is the core skill. The commonest error is taking a number from the adjacent row or column. Technique in UCAT QR graphs and tables.

Unit conversions

Length, area, volume, mass, time, currency and speed. Area and volume catch most people: 1 m2 = 10,000 cm2 (not 100) and 1 m3 = 1,000,000 cm3 = 1,000 litres.

Geometry: areas and volumes

Rectangles, triangles, circles, trapeziums, cuboids and cylinders, often as a compound shape (a rectangle with a semicircle) or a container being filled. No formulas are provided in the exam. Practise with UCAT QR geometry questions.

Tax and financial maths

Tax bands apply each rate only to the income inside that band; applying one flat rate to the total is the standard trap. Compound interest uses A = P x (1 + r)^n; check whether the question says simple or compound. Worked examples in UCAT QR tax and financial maths.

Currency conversion and exchange rates

Find the rate, then the direction. If 1 GBP = 1.25 EUR, pounds to euros means multiply and euros to pounds means divide. Reversing the direction is the usual mistake.

Drug dose and rate calculations

A patient of X kg needs Y mg per kg per day in Z doses: what is each dose? The medical framing is new to most students, but the arithmetic is rate and proportion. Write each step down instead of holding several numbers in your head.

Probability

Single events, complementary probability (1 minus P), and combined events (and = multiply, or = add for mutually exclusive events). Less common in QR than in Decision Making, but slow when it appears: if the route is not obvious, flag it and come back.

Formulas given in the question

Some data sets supply a formula to apply or rearrange. Because it is given, this tests substitution and rearranging, not recall. Write the intermediate steps down.

Profit, loss and discount

Profit = selling price minus cost price; profit percentage = profit / cost price x 100. With discounts, check whether the question wants the amount taken off or the price paid.

Which formulas do you need for UCAT QR?

No formulas are given in the UCAT, so a small set has to be automatic. They fall into five groups:

• Percentages: percentage change, reverse percentages and percentage of a total.
• Rates: speed, distance and time, and unit rates such as cost per item.
• Money: profit and loss, simple and compound interest, tax bands and currency conversion.
• Shapes: area and perimeter of rectangles, triangles and circles, and volume of cuboids and cylinders.
• Data: mean, weighted mean, median, ratio and basic probability.

Every formula, with the unit conversions, is on our UCAT QR formula sheet. Learn it for two weeks until recall is instant, then drill conversions against the clock in the free unit conversions trainer.

How does the UCAT on-screen calculator work in QR?

You get a basic on-screen calculator in QR (and in Decision Making), not your own. It adds, subtracts, multiplies and divides and has a memory function, but no scientific functions: no square root, powers, brackets or percentage key. It opens in a separate window and stops responding if you click off it, so click back on it before typing.

There are three ways to enter numbers, and the keyboard number pad is the fastest:

• Number pad: every Pearson VUE test centre keyboard has one on the right. Make sure Num Lock is on, and do not use the row of numbers above the letters.
• Mouse: clicking the on-screen buttons works but is the slowest method.
• Touch screen: only relevant if your own practice device has one; test centres use a mouse and keyboard.

The calculator is slower than mental arithmetic for simple steps. Working out 15% of 320 mentally (32 + 16 = 48) beats opening the calculator by 5 to 8 seconds, and across a section that habit costs minutes.

Use the calculator for:

• Multi-step calculations where an intermediate value must be stored
• Division that does not resolve cleanly, such as 347 / 13
• Squaring or cubing (enter it as repeated multiplication)
• Close answer options that an estimate cannot separate

Do it mentally for:

• Round-number percentages (10%, 20%, 25%, 50%)
• Multiplying or dividing by 2, 4, 5, 10 or 100
• Adding or subtracting values you can hold in your head

Use the memory function in multi-step questions: with the calculator open, P adds the displayed value to memory, C recalls it, and pressing C twice clears it. You also get an A4 laminated notebook and pen for working. The full shortcut list is in the UCAT on-screen calculator guide. Build the speed with the on-screen calculator trainer and the mental maths trainer, because training both gives a faster combined speed than either alone.

How do you read QR data sets quickly?

Read the question before the data. You only need the one value or relationship the question asks for, not an understanding of the whole data set.

• Tables: name the row and column before reading any number ("row X, column Y"). The adjacent row is the commonest error in QR.
• Graphs and charts: read the axis labels and units first. Treating a y axis in thousands as units puts you out by a factor of 1,000.
• Text scenarios: note the key numbers on your notebook as you read. These often contain more figures than you need.
• Question sets: the questions on one data set often get harder. Answer the quick ones, and flag a slow fourth question instead of stalling on it.

Spend a few seconds understanding what the data set shows before the first question in a set. Individual words and units decide many answers, so read the question slowly once instead of quickly twice.

UCAT QR worked examples

Try each one before reading the working. Every example shows the distractor most students choose.

Example 1: percentage change with a trap

An NHS trust spent £4.2 million on agency staff in 2022 and £5.46 million in 2023. What was the percentage increase? A) 23% B) 25% C) 30% D) 33% E) 38%

Answer: C, 30%. Change = 5.46 minus 4.2 = 1.26; 1.26 / 4.2 x 100 = 30%. Option A comes from dividing by the new value (1.26 / 5.46 = 23%). Percentage change always divides by the original value.

Example 2: weighted mean

Three assessments are worth 20%, 30% and 50% of a final mark. A student scores 64, 71 and 58. What is the weighted final mark? A) 63.1 B) 63.0 C) 63.5 D) 64.1 E) 64.9

Answer: A, 63.1. (64 x 0.2) + (71 x 0.3) + (58 x 0.5) = 12.8 + 21.3 + 29.0 = 63.1. The simple mean, 64.3, is the classic error. The lowest score carries the biggest weight, so the weighted mean sits below it.

Example 3: average speed

A consultant drives 24 km between two hospital sites: the first half at 40 km/h, the second half at 60 km/h. What is her average speed? A) 46 B) 48 C) 50 D) 52 E) 54 km/h

Answer: B, 48 km/h. 12 / 40 = 0.3 hours, 12 / 60 = 0.2 hours, total 0.5 hours; 24 / 0.5 = 48 km/h. Most students choose C, the simple mean of 40 and 60. Equal distances at different speeds always average below the simple mean.

Example 4: tax bands

Tax bands: 0% up to £12,570; 20% from £12,571 to £50,270; 40% from £50,271 to £125,140. A newly qualified doctor earns £55,000. How much income tax do they pay? A) £8,686 B) £11,486 C) £9,432 D) £14,286 E) £22,000

Answer: C, £9,432. Basic rate: £37,700 x 20% = £7,540. Higher rate: £4,730 x 40% = £1,892. Total £9,432. Option E is 40% of the whole salary, the flat-rate error.

Example 5: volume and unit conversion

A cylindrical tank has radius 0.8 m and height 2.5 m and is 60% full. How many litres does it hold, to the nearest 10 litres? (pi = 3.14) A) 2,390 B) 2,410 C) 3,010 D) 3,990 E) 4,020

Answer: C, 3,010 litres. 3.14 x 0.64 x 2.5 = 5.024 m3; 60% = 3.0144 m3; x 1,000 = 3,014 litres, so 3,010. Using 1 m3 = 100 litres gives 301, which matches no option: the signal to recheck your conversion.

Example 6: a semicircle working backwards

A kitchen measures 5 m x 4 m. A semicircular conservatory increases its floor area by 50%. To the nearest half metre, what is the conservatory's diameter? A) 2.5 m B) 3 m C) 5 m D) 6 m E) 10 m

Answer: C, 5 m. The kitchen is 20 m2, so the conservatory is 10 m2. Half of pi x r2 = 10, so r2 = 20 / 3.14 = 6.37. There is no square root key, so estimate: 2.5 x 2.5 = 6.25, so r is about 2.5 m and the diameter is 5 m. Option A is the radius, the trap for anyone who stops a step early.

How should you pace QR in 26 minutes?

Pace QR with checkpoints, not a strict 43 seconds per question. Some questions take 15 seconds and some take 90; the skill is finishing the quick ones in under 30 seconds to bank time for the multi-step ones.

• Behind at a checkpoint? The next question with no obvious route gets a best guess and a flag. Do not go back until the end.
• There is no negative marking, so never leave a question blank. A flagged guess can only help.
• The usual time traps are multi-step geometry with unit conversions and probability built on a table. If your first read gives no route, flag and move on.

For section-wide timing technique, read UCAT QR speed and estimation and how to beat UCAT time pressure.

How do you prepare for UCAT Quantitative Reasoning?

Work from formulas to topics to timed sets, and review every mistake:

1. Learn the UCAT QR formula sheet until recall is instant.
2. Drill mental arithmetic and the calculator separately with the free trainers (links below).
3. Work topic by topic, starting with your two or three weakest question types from the list above.
4. Move to timed sets in QR practice questions, then full mocks, so 43 seconds a question feels normal.
5. Log every error by cause (units, wrong row, method, time) and rework it. Reflective revision is how scores move.

For specific tactics from a top scorer, read our UCAT QR tips. To fit QR into your wider plan, use the UCAT revision timetable and the UCAT preparation guide. If you want an expert to diagnose your QR errors, 1-to-1 UCAT tutoring is online, and our UCAT courses run live online.

Every UCAT QR guide and free trainer

Each guide covers one QR topic in depth with worked examples. Start with your weakest.

• UCAT QR formulae and cheat sheet
• UCAT QR percentage questions: mental maths shortcuts
• UCAT QR ratio and proportion questions
• UCAT QR averages: mean, median, mode and weighted mean
• UCAT QR graphs and tables: data interpretation
• UCAT QR speed and estimation
• UCAT QR tax and financial maths
• UCAT QR geometry questions
• UCAT on-screen calculator: shortcuts and how to use it

Free trainers:

• UCAT QR practice questions: timed questions on a test-style interface
• Mental maths trainer: fast arithmetic for every QR question
• On-screen calculator trainer: keyboard and memory speed
• Unit conversions trainer: stop unit slips
• Free UCAT skills trainer: every trainer and subtest in one place

For the other subtests, scores and test day, browse all UCAT guides.

Checked against ucat.ac.uk on 24 October 2026. Score figures are the UCAT Consortium's final 2026 test statistics.