UCAT Quantitative Reasoning: The Definitive Guide

What is the UCAT?

The UCAT is the ‘University Clinical Aptitude Test’, a 2-hour exam sat between the 1st July and 1st October just before you send off your medical school application. =

The UCAT is part of the entry requirements for nearly every medical and dental school in the UK and aims to set apart applicants based on mental aptitude rather than academic knowledge.

The idea behind the test is that it sets a level playing field for all candidates and doesn’t discriminate based on your academic background.

Different universities weight your UCAT score differently in their admissions criteria, this means that you score will be used different by each university that requires the UCAT.

The test consists of 5 sections which are all weighted slightly differently. These sections are:

This article focuses on the Quantitative Reasoning section.

Are you sitting the UCAT ANZ?  The test is exactly the same but you can read more about the UCAT ANZ Quantitative Reasoning section from an Australian student’s perspective here.

Introduction to Quantitative Reasoning

The word quantitative means ‘relating to numbers or amounts’ and hence this section tests your ability to apply simple mathematical skills to certain contexts.

Quantitative Reasoning is the third section of the UCAT and its aim is to assess your ability to use numbers to solve problems. It relies on your ability to apply your mathematic knowledge to answer the questions.

It assumes you have a good GCSE standard maths ability, but does not include any content above GCSE level. These questions assess your ability to interpret numerical data and pick out the important parts of it, which is a really important skill needed in medicine and dentistry.

Why is Quantitative Reasoning included?

As we’ve just said, the ability to interpret numerical data and put it into context is a key part of your job as a doctor or dentist.

From a really early stage as a junior doctor, prescribing will be a key part of your job. The ability to prescribe effectively (and more importantly, safely) relies on your ability to correctly calculate the right drug dose for each individual patient. It’s essential that you are able to calculate this correctly as it may have extremely dangerous consequences for the patient if not.

Other uses of Quantitative Reasoning in medicine include interpretation of research and academic papers.

Should you undertake a research project at any point during your career (which is extremely likely), you will need to be able to interpret and understand your own results data. This is often fairly complicated, so having a basic understanding and Quantitative Reasoning skills from early on will be extremely beneficial.

Throughout medical school and your career as a doctor, you’ll be able to further build on these skills until they become second nature.


What are the questions in Quantitative Reasoning like?

Number Of Questions36
Total Time1 minute reading of the instructions before the section starts, 24 minutes to complete the questions
Time Per Question40 seconds

The Quantitative Reasoning section generally consists of a number of data sets, each associated with 4 questions. There will also be a few standalone data sets with only one question. The data may be presented in the form of a graph, table or as part of a plain text question, but won’t come with any detailed explanation.

You will be expected to interpret and understand this data, and then apply your quantitative ability to answer the questions.

Answers are in the format of a single best answer, and there are 5 options to choose from per question. As we’ve mentioned before, it is assumed that all candidates have achieved a good pass at GCSE maths, but no further study is required.

You’ll be given an on-screen calculator and a whiteboard with a pen so that you can figure out the answers.

You can see how this looks in the next section where we’ll work through some question together.

TIP #1

Don’t forget that you only have 40 seconds per question.

If you find yourself doing any extra long-winded calculations, you’ve probably overcomplicated it!

TIP #2

Try to look for trends in the data.

Noticing these details will often allow you to rule out 2 or 3 answers really quickly and gives you more time for your calculations.

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Worked Example Quantitative Reasoning Practice Question & Answer

Quantitative Reasoning Practice Question

During the SARS outbreak in 2003, the World Health Organisation required countries to keep track of every case and death, to later enable them to calculate disease and epidemic statistics. The epidemic resulted in thousands of cases across 26 different countries and was also associated with hundreds of deaths around the world. In order to track transmission and calculate total disease figures, the governments of each country released their data to the World Health Organisation, who then made comparisons retrospectively.

Below is a table showing the cumulative the number of SARS cases over a 5-month period between three of the worst affected countries; Canada, Taiwan and Singapore.

February 2003355241
March 2003528990
April 200379134142
May 2003104173191
June 2003131221239
July 2003158263294

During the epidemic, countries were also required by the WHO to keep track of their death rates. Below are the deaths per month shown for the same 3 countries over the same time period.

February 2003374
March 200381916
April 2003142523
May 2003213734
June 2003245146
July 2003295659

Q1: In which month did Taiwan have the greatest rise in its number of cases?

  1. February
  2. March
  3. April
  4. May
  5. June

Q2: In which month did Singapore see its greatest percentage change in fatalities?

  1. February
  2. March
  3. April
  4. May
  5. June

Q3: What was Canada’s total fatality rate?

  1. 7%
  2. 2%
  3. 3%
  4. 6%
  5. 1%

Q4: What was the difference between the fatality rates of Taiwan and Singapore?

  1. 8%
  2. 0%
  3. 2%
  4. 4%
  5. 6%

Careful scrolling beyond this point if you are working through the question yourself!

Quantitative Reasoning Worked Solution

Q1 Answer: February.

The method for this solution is relatively simple. You just need to subtract the first month from the one after it to find the difference in case numbers. See the table below.

 TaiwanRise In Cases
February 20035252
March 20038937
April 200313445
May 200317339
June 200322148
July 200326342

Q2 Answer: July.

This question asks for the percentage increase in fatalities per month in Singapore.

February % increase = (4 – 0 / 100) x 100% = 4%

March % increase = (16 – 4 / 100) x 100% = 12%

April % increase = (23 – 16 / 100) x 100% = 7%

May % increase = (34 – 23 / 100) x 100% = 11%

June % increase = (46 – 34 / 100) x 100% = 12%

July % increase = (59 – 46 / 100) x 100% = 13%

These solutions show that the greatest percentage increase was 13% and occurred in July.

Q3 Answer: 18.3%.

This solution requires you to calculate the total percentage of fatalities in Canada. The was to do this is to divide the total number of fatalities (29) by the total number of cases (158) and then multiplying by 100 to calculate the percentage.

( 29 / 158 ) x 100% = 18.3%

Q4 Answer: 1.2%.

To find the solution you need to find the fatality rate of each country separately and then calculate the difference.

Taiwan: ( 56 / 263 ) x 100% = 21.3%

Singapore: ( 59 / 294 ) x 100% = 20.1%

21.3 – 20.1 = 1.2%

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How is Quantitative Reasoning scored?

For every section of the UCAT, you’ll be given a score between 300 and 900 (300 being the worst, 900 being the best).

This makes 600 the median score for each section. Each question is worth 1 mark, meaning each passage of text carries 4 marks with it.

The Quantitative Reasoning section is, therefore, worth 36 points in total, which is then scaled up to give your total score. Quantitative Reasoning is often considered the easiest section, and most years it has the highest average score in the UCAT. The average score generally sits between 660 and 700. You can see all UCAT scores and results explained in another guide we wrote.

Below is a table showing the average scores for the Verbal Reasoning section over the last 4 years:

YearAverage score for Quantitative Reasoning section

Top Tips for Quantitative Reasoning

As we’ve established, the Quantitative Reasoning section is usually where people achieve their highest mark in the whole test. This means it’s important for you to do as well as you can to bring up your total score!

Here is a list of my top tips to help you do well in this section.


It’s important to remember that this test is assessing your problem-solving abilities.

Problem-solving abilities are rather more important than your academic knowledge in this section. Even if you don’t consider yourself to be great at maths, you’ll still be able to ace this section. Don’t let the idea of a maths test put you off and stress you out on the day!


Bear in mind the time limits for this section.

If you’re really struggling on something just make an educated guess, flag it and come back to it at the end. It’s more beneficial for you to get through all the questions in the section as this is likely to get you more points at the end of the day. Don’t use up all your time trying desperately to find one answer!


Do as many practice questions as you can and practice them all to time.

Maybe a little bias going on here… but really good resource for this is our UCAT Ninja or the UCAT Bundle.


Try to get your basic maths problem-solving calculations as slick as possible.

These include things like calculating percentages and using fractions.


Use the tools available to you!

The whiteboard and the calculator! It’ll save you so much time and if you go wrong somewhere, you’ll be able to track backwards. You should learn the calculator shortuts and the general test shortcuts:

  • Alt + p = previous question
  • Alt + n = next question
  • Alt + f = flag current question
  • Ctrl + C = to make the calculator appear
  • Num Lock = activate number keypad (if number lock is off)
  • Backspace for On/C = to go back and delete a number you have inputted in the calculator.


Usually, Quantitative Reasoning questions have a few answer options that are obvious outliers.

Try to exclude these as quickly as you can, as it will allow you to find the correct answers faster. It also means that if you need to make an educated guess, you are more likely to guess right as you have less answers to choose from


Following on from the tip above… have a quick look for any obvious trends in the data.

Often you’ll be able to rule out several answers straight away


Take a look at some research papers and the type of data they present.

This is a great way of improving your Quantitative Reasoning skills that not many students take advantage of is. They will be much, much more difficult than any of the questions you come across in the test, so if you can do them, you’ll ace it!


As this is the third section in the test, make sure you’re not constantly thinking back to what mistakes you may have made before that!

Take each section as it comes, and once you’re finished with one, block it from your mind and start again. The UCAT questions are under so much time pressure, you need your mind as clear as possible!

Closing Notes For UCAT Quantitative Reasoning

Thank you for reading this article!

We hope it’s given you all the information you need to get started on some practice questions for the Quantitative Reasoning section of the UCAT. You’re likely to find this the easiest section in the test, so it’s good to start with these questions to build your confidence before moving onto others.

We hope that the worked example gives you a good idea of the way your mathematical ability will be tested and that the answers make it clear what they’re looking for. It should also show you that you don’t need to be doing A level maths to ace this section of the test!

We’ve also got guides to every other section of the UCAT on our website, so go check them out to get even more ahead of the game!

Finally, we want to wish you good luck for the test and with the rest of your application to medical school!

If you are looking for support with your UCAT, 6med’s UCAT Bundle is a great way to make sure you get a good score. We think it’s pretty awesome, we think you’ll think so too.

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