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UCAT Quantitative Reasoning (QR UCAT) is the numerical reasoning section of the current four-subtest UCAT ANZ format. It gives you 36 questions in 26 minutes, so strong performance depends less on advanced maths and more on fast data selection, accurate calculation, estimation, calculator control, and knowing when to skip.
This UCAT ® Quantitative Reasoning guide covers QR timing, common UCAT QR question types, worked practice examples, calculator and noteboard strategy, score benchmarks, and exam-day tips. For broader study planning across all four subtests, start with how to prepare for the UCAT ® ; for score percentiles and cut-offs, see UCAT ® scores.
Quantitative Reasoning is the third cognitive subtest of the UCAT ® exam and is designed to assess your ability to use numerical information to solve problems. The required maths is closer to high-school arithmetic, percentages, ratios, units, charts and formula use than university-level mathematics. The difficulty comes from quickly deciding which data matters and which calculation route is shortest.
UCAT ® Quantitative Reasoning assesses numeracy, data interpretation and decision-making under pressure. That matters for medicine and dentistry because clinicians interpret clinical data, check risk figures, read research, calculate doses and communicate numerical information clearly. Universities are not looking for advanced pure mathematics here; they are looking for evidence that you can use numbers accurately when the clock is running.
The UCAT ® exam is characteristically a difficult exam, designed to differentiate the already competitive pool of medical and dental school applicants. In the case of UCAT ® Quantitative Reasoning, students may find the subtest difficult either due to the question style or the sheer number of questions within the limited time. The UCAT ® ANZ Consortium frames Quantitative Reasoning as problem solving with numbers rather than a test of numerical facility alone. Compared with Verbal Reasoning and Decision Making, official test statistics often show a higher mean score for UCAT ® Quantitative Reasoning, but that does not make it effortless: unit traps, dense tables, close answer options and calculator delays can quickly drain marks.
The current UCAT structure sets Quantitative Reasoning at 36 questions in 26 minutes of test time (2 minutes for instructions). UCAT ® Quantitative Reasoning questions are structured with a premise, followed by 1 to 4 questions. The premise may involve a graph, table, chart, diagram, conversion table or short worded scenario. Your job is to extract the necessary information from the premise and select one answer from five options.
Most QR UCAT questions are independently marked, and there is no negative marking on the UCAT ®. If a calculation is taking too long, guess, flag the question, and return later if time permits.
Each candidate is given 26 minutes of test time and 2 minutes for the instruction section. With 36 questions, that averages around 43 seconds per question.
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| Subtest Subtest |
Test Time Test Time |
Number of Questions Number of Questions |
Average Time per Question Average Time per Question |
|---|---|---|---|
| UCAT Quantitative Reasoning UCAT Quantitative Reasoning |
26 minutes 26 minutes |
36 questions 36 questions |
43 seconds 43 seconds |
It is very easy to underestimate the necessary preparation required for UCAT ® Quantitative Reasoning, given that the actual content of the subtest is not dissimilar to most high-school maths. However, the timing is often quite tight and you can easily be thrown off by having to use the calculator and noteboard. There are several techniques to maximise marks within the Quantitative Reasoning subtest in the given time; these are covered in the "UCAT ® Quantitative Reasoning Tips" section below.
A simple on-screen calculator is available for Quantitative Reasoning, and the official UCAT ANZ test tools guidance recommends practising with the calculator before test day. It is useful for awkward division, multi-step calculations and close answer options, but it is slower than mental maths for simple percentages, rounding and obvious estimates. Practise both approaches so you can decide quickly whether a question needs the calculator or can be solved faster by approximation.
Use your noteboard for interim values, unit conversions and flagged-question notes rather than trying to hold every number in memory. The safest QR habit is to write only what saves time: key numbers, converted units, and a short check of what the question is asking.
Throughout your preparation, you will come across many different UCAT ® Quantitative Reasoning topics. The same data set may combine several skills, such as reading a table, converting units and then calculating a percentage change. Treat the categories below as a practical checklist for QR UCAT practice rather than isolated topics.
Common UCAT ® Quantitative Reasoning question types include:
Each UCAT ® Quantitative Reasoning question type is explained in further detail below, along with some example questions.
These will ask you to calculate the average from a set of data, for example “calculate the average height of …”. Questions can become increasingly difficult with larger data sets and may include conversions. This can also include things such as the average speed of a vehicle or person for example. In this case it is important to remember that speed is simply distance over time.
Calculations may often include percentages. This can include things such as the percentage difference or what percentage of a set falls into a particular category.
Diagrams can vary vastly between questions and may include tables, tax tables, bar graphs, line graphs, pie charts or really any diagram. These questions can get more difficult when there are multiple tables or unique displays of data.
These are very similar to average type questions, and are often quite straight forward as long as you remember what these are. The median is the midpoint of the dataset when placed in ascending/descending order and the mode is the most common data point.
Conversions are often parts of more difficult questions to involve extra Quantitative Reasoning skills throughout. This can involve conversion between proportions, ratios, fractions, decimals or percentages as well as between units of measurement such as metres, miles, kilometres. For the most part, metric conversions are expected to be known such as 1000m in 1km however metric-imperial conversions will be provided.
Ratio and proportion questions ask you to compare quantities, scale recipes or mixtures, split totals into parts, or convert one representation into another. These are often faster when you simplify the ratio first, then estimate whether the answer options are far enough apart to avoid exact calculator work.
Speed, distance and time questions usually combine unit conversion with a familiar formula: speed = distance / time. Watch whether the question asks for minutes, hours, kilometres, metres, arrival times or differences between two routes.
These are often accompanied by a diagram to display this information in more detail. More often than not, a question will usually provide the necessary formula for a shape. However, in some cases it may be helpful to simply remember some key maths formulas such as the areas of triangles and rectangles/squares. In questions with circles or spheres, the UCAT ® exam will often provide a formula as well as a statement for what should be used as π (3.14, 3 etc…)
The below summary of question types may be useful:
| Averages | Calculate the average from a set of data. Questions can become increasingly difficult with larger data sets and may include conversions. |
| Percentages | Calculations may often include percentages. This can include things such as the percentage difference or what percentage of a set falls into a particular category. |
| Diagram, Charts and Tables | Expect a wide variety of diagrams and charts, including tax tables, bar graphs, line graphs, pie charts or really any diagram. Multiple formats can be combined for a single stem to increase the difficulty. |
| Median/Mode | Similar to average type questions - Remember that the median is the midpoint of the dataset when placed in ascending/descending order and the mode is the most common data point. |
| Conversion | This can involve conversion between proportions, ratios, fractions, decimals or percentages as well as between units of measurement such as metres, miles, kilometres. |
| Ratios and Proportions | Compare quantities, scale totals, split values into parts, or move between fractions, percentages and ratios. |
| Speed, Distance and Time | Combine distance, speed and time formulae with unit conversion and careful reading of routes, arrival times or differences. |
| Volume, Area, Perimeter | Expect a diagram to help display the information in more detail. More often than not a question will usually provide the necessary formula for a shape, as well as rough values for any mathematical constants, such as π. |
UCAT ® Quantitative Reasoning questions can involve a mix of various of these aforementioned topics. A set of sample questions has been provided below:
Curtis’ candy shop allows customers to buy a 500g variety pack whereby customers can choose the amount of different candies that they want in the pack. His 4 most common selections for variety packs are shown below:
| Variety Pack | % of M&Ms by weight | % of Maltesers by weight | % of Lollipops by weight |
| “Favourites” | 35 | 33 | 32 |
| “Chocolate Lover” | 40 | 40 | 20 |
| “Sweet Tooth” | 10 | 10 | 80 |
| “Confection Connection” | 20 | 50 | 30 |
The candy is measured by weight. M&M’s weigh 1.5g, Maltesers weigh 2.5g and Lollipops weigh 6g.
Question 1How many grams of Lollipops would be found within 2 “Favourites” variety packs?
How many M&M’s are within 2 “Chocolate Lover” variety packs?
Curtis mixes 40% of “Confection Connection” with 60% of “Favourites” to create a new variety pack called “Candy Crush.” How many Maltesers are in 2 “Candy Crush” Packs?
What would be the percentage of M&M’s by weight if Curtis was to mix the Top 4 Variety Packs in equal parts?
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Sarah recently bought a new house. The floorplan of her new house is shown below. It is known that Bedroom 1 is square-shaped.
Question 1
Sarah wants to lay carpet for all of the bedrooms. How much carpet does she need?
How many times is the Master Bedroom bigger than Bedroom 1?
Sarah buys a large dining table measuring 2m by 1.2m. After placing this dining table in the dining room, how much space is left in her living and dining room?
Sarah decides to install timber flooring for her porch with the help of Smart Timber Flooring Company. Smart Timber Flooring Company charges a material cost of $4.35 for every 1 m 2 of timber and a labour cost of $15.00 for every 5m 2 of timber floored. How much will it cost for Sarah to timber her porch?
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Nikki and Rachel go to the same school. The students are considered late if they arrive at school after 8:30 am. The diagram below shows Nikki and Rachel’s way to school:
Question 1
The ratio of the shortest distance from Nikki’s house to The Donut Shop and the shortest distance from Rachel’s house to The Donut Shop is 3:7. What is the distance between The Donut Shop and Rachel’s House?
Rachel walks to school at a speed of 4.5km/hr. Rachel leaves home at 8:15 am and takes the direct route to school. How many minutes early or late will Rachel be, to the nearest minute?
Nikki drives to Rachel’s house at 50km/hr and picks up Rachel then drives the rest of the way to school at 35km/hr. What is the shortest time taken for Nikki to get to school?
Assuming that the Donut Shop is 300m away from Nikki’s house. Nikki rides her bike at 10.25km/hr to school while stopping at The Donut Shop for 5 minutes to buy her lunch. Rachel walks the direct route school at 4.75km/hr. If Nikki leaves home at 8:00 am and Rachel wants to arrive at school at the same time as Nikki, at what time should Rachel leave her house?
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Ultimately, as with any other exam, practice is key to improving your UCAT ® Quantitative Reasoning skills. It is important to keep in mind that for UCAT ® Quantitative Reasoning practice doesn’t make perfect, rather perfect practice makes perfect. Many students complete hundreds of practice questions and then stagnate because they repeat the same errors. Review each missed QR question by category: wrong data selected, wrong unit, calculator entry error, poor estimate, slow method, or conceptual gap. Consistently doing this will maximise your chances at doing your best in Quantitative Reasoning. For broader advice on how to prepare for the UCAT ® exam, read our guide to UCAT ® Preparation.
A useful UCAT QR preparation sequence is: untimed question-type drills first, then timed mini-sets, then full subtest practice, then full UCAT ® mocks. Keep your practice interface close to the official format where possible so the calculator, noteboard and flagging workflow feel familiar on exam day.
Polishing your graph and table interpretation skills is key. Some UCAT ® Quantitative Reasoning questions require you to interpret information from graphs or tables and it is important to get into the habit of making sense of this data quickly and efficiently. Whilst these skills can be improved generally through wider reading, it is more time efficient to practise Quantitative Reasoning questions, tailored to match the difficulty of the UCAT ®.
Given the time pressure of UCAT ® Quantitative Reasoning, there are several strategies that can help you to maximise your marks within the given time. Whilst each unique question type requires its own individual approach with separate strategies, there are a couple of strategies that can be applied universally to UCAT ® Quantitative Reasoning questions.
Whilst this may sound quite self-explanatory, it remains quite an important tip for the Quantitative Reasoning subtest. For certain questions, reading the question and then sifting through the premise for relevant information will often suffice. However, often diagrams have important explanations and titles which may be necessary to solve some of the problems. This includes things like unit changes which are often misread and lead to incorrect answers.
Furthermore, misreading the passage or question can often cost students many marks throughout the exam. Whilst it is inevitable given the time pressure and difficulty of the subtest, it can still be minimised. Further practice is ultimately what will help to reduce these errors.
As mentioned before, reading the headings and titles of any diagram is essential, as they often contain necessary information. An example of these would be a graph presenting the average weight of males overtime whilst a question asks for the average weight of females overtime. Reading these carefully can avoid silly mistakes and boost your UCAT ® score.
With any test, it is important to prioritise your time and answer the questions that you can within the given time. This also applies to the UCAT ®. Through increasing practice, you will be able to identify when you are struggling with a question and how much time you should dedicate to a question. Whilst there is no hard and fast rule for this, it can be helpful to skip questions if it is taking you too long to understand a question. Because there are options to flag and go back to flagged questions, it makes sense to finish as many questions as possible before returning to the more difficult ones.
The on-screen calculator can often be tedious to use without any practice. As such, it is best to break up the calculation into simpler equations and then type them into the calculator in one calculation. For example, a UCAT ® Quantitative Reasoning question may involve a conversion between km and miles - in this case, you would perform the calculation within the necessary equation to answer the question. This saves time as it limits the amount of typing and writing necessary in the exam.
The UCAT ® on-screen calculator is helpful, but it can become a time sink if you reach for it automatically. Use it for awkward division, close answer options and long chained calculations. For simple percentages, ratio scaling and rough comparisons, mental maths or estimation is usually faster.
Before entering numbers, scan the answer options and estimate the likely range. If one option is clearly in the right ballpark, you may not need exact working. If the options are close together, switch to precise calculation and double-check units.
If you're wondering how to improve Quantitative Reasoning UCAT ®, below you will find four useful tips from our expert tutor:
As mentioned before, timing plays a huge part in the difficulty of the UCAT ® exam. These previous strategies such as multi-step calculations, reading critically and skipping difficult questions will give you the best chance at performing well in UCAT ® Quantitative Reasoning.
Being able to perform simple calculations in your head will allow you to shave a couple of minutes of your exam time and allow you to answer more questions. This can be used alongside rounding and estimation skills. When answer options are quite far apart, it can be helpful to estimate throughout your calculations to save time and still get a correct answer. Notably, this won't work when answers are quite close together and the precise calculations are required.
These can vary vastly between questions, from pie charts to tax tables and graphs. The pretext and headings are crucial to read and may help you to quickly gather the necessary information before approaching the questions.
The UCAT ® on-screen calculator can be a little bit tedious to use and quite different from the scientific calculators we are quite used to. Make sure to use the UCAT ® calculator throughout practice to ensure that you know the relevant shortcuts and functions that will help you to save time on exam day.
Many QR UCAT stems contain more data than you need. Read the question and answer options first, then inspect the table, chart or diagram with a purpose. This helps you avoid wasting time processing irrelevant rows, headings or units.
As with the other cognitive subtests on the current UCAT ® exam, Quantitative Reasoning is scored between 300 and 900. Average marks for UCAT ® Verbal Reasoning and Decision Making are typically lower than Quantitative Reasoning. Abstract Reasoning is no longer part of UCAT ANZ — the live exam has four subtests only.
For the UCAT ® Quantitative Reasoning subtest, a rough guide for where you would want to score to be competitive would be:
|
UCAT ® Quantitative Reasoning
|
|
|---|---|
| Average Mark | 679 |
| Competitive Mark | 780 |
| 90th Percentile Estimate | 880 |
In 2025, the median UCAT ® Quantitative Reasoning score was 660 out of 900, and the 90th percentile corresponded to 880. The three cognitive subtests are summed for a total scaled score of 900–2700 (Verbal Reasoning + Decision Making + Quantitative Reasoning). Quantitative Reasoning decile scores from 2025 are below for trend context — totals before 2025 included Abstract Reasoning and are not directly comparable to the current scale.
| Quantitative Reasoning | |
|---|---|
| Mean (2025) | 679 |
| 1st decile | 530 |
| 5th decile | 660 |
| 9th decile | 880 |
As with any other exam, it is important to remain composed and not get flustered throughout the exam as it is possible to make up for a weaker Quantitative Reasoning mark by performing well in Verbal Reasoning or Decision Making.
|
UCAT ® Quantitative Reasoning
|
2019 | 2020 | 2021 | 2022 | 2023 | 2024 | 2025 |
|---|---|---|---|---|---|---|
| 663 | 671 | 679 | 672 | 663 | 667 | 679 |
Here are a couple of tips for exam day when approaching UCAT ® Quantitative Reasoning questions:
Students often lose marks on silly mistakes and misreading the question. Always keep this at the front of your mind when approaching UCAT ® Quantitative Reasoning questions. The calculator has a limited memory function and it can be helpful to write down your answers throughout calculations as you go along in the case that you accidentally misclick on the calculator.
Avoiding the calculator when you can will help to save time without sacrificing accuracy. The time saved here can be invested in cracking the more difficult problems.
Don't be afraid to guess, flag questions and move on. It can be very easy to become obsessed with solving a difficult question and sacrifice your chance at solving easier questions. On exam day, you should guess questions which you find yourself struggling with before flagging and moving onto the next question. This will give you the best chance at answering as many questions before time runs out. Knowing that you have filled in all the answers before coming back to the more difficult questions can take off the mental toll and pressure that flusters many students.
There is no negative marking on the UCAT ®, so leaving QR questions blank only costs opportunity. If time is nearly gone, make a best guess on anything unanswered before returning to flagged questions.
Ultimately, UCAT ® Quantitative Reasoning comes down to disciplined preparation and staying composed under time pressure. Know the main QR question types, practise official-style timing, build calculator fluency, estimate before calculating, and use a skip strategy that lets you collect the marks you can reach quickly.
For the full current exam format, including how QR fits with Verbal Reasoning, Decision Making and Situational Judgement, read the UCAT ® structure guide.
Meaning, who needs UCAT ANZ, registration overview, and how the exam fits undergraduate applications.
Four subtests, question counts, subtest times, and scoring overview (900–2700 cognitive total).
Booking windows, concessions, and the 2026 testing period.
Scaled totals (900–2700), percentiles, and what universities treat as competitive.
UCAT preparation strategy, study plan, timelines, and tips across all four current subtests.
Free practice and reading links to start without a paid course.
Question types, timing, and preparation tips for the first subtest.
Question types, timing, and preparation tips for the second subtest.
Scenario-based judgement questions and how SJT is scored separately (300–900).