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Whilst some students may have a strong background in maths, the UCAT ® Quantitative Reasoning subtest aims to assess your problem solving abilities in a mathematical setting, in contrast to traditional high school maths skills. This is also in the context of intense time pressure, with the UCAT ® Quantitative Reasoning subtest requiring you to work both quickly and accurately. This guide aims to provide an overview of what to expect from the UCAT ® Quantitative Reasoning subtest, what kind of questions you will come across and how to best prepare.
Quantitative Reasoning is the third subtest of the UCAT ® exam and is designed to assess your ability to use numerical skills to solve problems. Sometimes considered an ‘easier section’ given that it is akin to high school maths exams, it is important to note that UCAT ® Quantitative Reasoning is more of a ‘reasoning’ test rather than a maths test.
UCAT ® Quantitative Reasoning assesses your ability to use numeracy skills to solve various problems. So you might be wondering, how does this relate to getting into medical school? Quantitative Reasoning is a necessary skill for doctors and dentists as they need to analyse data and make calculations on a daily basis. More practically, drug calculations require a certain level of numerical ability and in clinical research, the ability to interpret data and draw conclusions plays an essential role. Essentially, an aptitude in these quantitative problem solving abilities is useful for universities to be aware of when considering applicants.
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 difficulty of the questions or the sheer amount of questions within the limited time. The UCAT ® ANZ Consortium suggests that a “good pass at GCSE '' would approximate the numerical competency required for the exam. However, it is important to note again that UCAT ® Quantitative Reasoning tests problem solving skills rather than maths skills. Compared to the other sections, past years have shown that the mean score is often higher in UCAT ® Quantitative Reasoning, indicating that it may be the ‘easiest’ of the five subtests.
UCAT ® Quantitative Reasoning questions are structured with a premise, followed by 1 to 4 questions. This premise may involve a graph, table or chart but they vary significantly. Your job is to extract the necessary information from the premise to best answer the option. Each question will have five answer options.
You will also have access to whiteboards on the exam day as well as an online, on-screen calculator which can be used to work around difficult calculations.
In UCAT ® Quantitative Reasoning, you will be presented with 36 questions in total with 24 minutes to answer them all. This averages out to around 1.5 questions per minute or 40 seconds of UCAT ® Quantitative Reasoning time per question. This serves quite a difficult task when answering all of the questions within the given time frame.
| Subtest | Test Time | Number of Questions | Average Time per Question |
|---|---|---|---|
| UCAT Quantitative Reasoning | 24 minutes | 36 questions | 40 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 highschool maths. However, the timing is often quite tight and you can easily be thrown off by having to use calculators and whiteboards. There are several techniques to maximise marks within the Quantitative Reasoning subtest in the given time - these will be touched on in the “UCAT ® Quantitative Reasoning Tips” section below.
Throughout your preparation, you will come across many different UCAT ® Quantitative Reasoning topics. There are many different subtypes or topics however it is important to note that these can be tested in unison with one another, with multiple formats displayed as part of a single premise. This is just an overview of the question topics you may come across.
There are 6 main types of UCAT ® Quantitative Reasoning questions:
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.
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. |
| 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?
Sarah recently bought a new house. The floorplan of her new house is shown below. It is known that Bedroom 1 is square-shaped.
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?
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:
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?
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. Essentially, many students will go through hundreds of practice questions and reach a stagnation in their improvement. This is because you need to actually take time to look at mistakes and try to remember how and why this mistake occurred. Consistently doing this will maximise your chances at doing your best in Quantitative Reasoning. For further advice on how to prepare for the UCAT ® exam in general, read our guide to UCAT ® Preparation.
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.
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.
As with all the other subtests of the UCAT ® exam, the Quantitative Reasoning section is scored between 300 and 900. The average mark for Verbal Reasoning and Decision Making questions is typically lower than that of Quantitative Reasoning and Abstract Reasoning questions.
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 | 671 |
| Competitive Mark | 740 |
| 90th Percentile Estimate | 803 |
In 2022, the median UCAT ® Quantitative Reasoning score was 660 out of the available 900 points. For most candidates, a competitive UCAT ® score is around 90th percentile or 9th decile. The exam statistics for 2022 indicated that a score of 810 led to a 9th decile equivalent score. However, it is important to keep in mind that often the first four cognitive subtests are summed up for a final score out of 3600.
| Verbal Reasoning | Decision Making | Quantitative Reasoning | Abstract Reasoning | Total Cognitive Scaled Score | SJT | |
|---|---|---|---|---|---|---|
| Mean | 578 | 630 | 672 | 662 | 2543 | 568 |
| 1st decile | 480 | 510 | 550 | 530 | 2130 | 460 |
| 2nd decile | 520 | 550 | 590 | 570 | 2260 | 504 |
| 3rd decile | 540 | 580 | 610 | 600 | 2360 | 535 |
| 4th decile | 550 | 610 | 630 | 620 | 2450 | 559 |
| 5th decile | 580 | 630 | 660 | 650 | 2530 | 581 |
| 6th decile | 590 | 660 | 680 | 680 | 2610 | 599 |
| 7th decile | 610 | 680 | 710 | 710 | 2710 | 618 |
| 8th decile | 640 | 710 | 760 | 750 | 2830 | 639 |
| 9th decile | 680 | 750 | 810 | 830 | 2980 | 663 |
It is important to not get flustered in the exam and to remain composed, as it is possible to make up for poorer marks in one subtest by performing well in another.
|
UCAT
®
Quantitative Reasoning
|
2019 | 2020 | 2021 | 2022 |
|---|---|---|---|
| 663 | 671 | 679 | 672 |
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 some time without sacrificing incorrect answers. 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.
Ultimately, the UCAT ® exam will come down to preparation and remaining composed throughout such an intense exam. Knowing the key question types and keeping in mind timing and pace will give you the best chance to perform well. Practising with mental maths and using the calculator can maximise your speed and accuracy.
Everything you need to know on how to study for the UCAT ® Exam, including tips for each of the five sections.
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