The Ultimate Quantitative Reasoning Guide

📑 29 questions 

 🛠️ 31 minutes

🏛️ Tests how effectively you can apply your logic in drawing conclusions, evaluating arguments, and analyzing data.

Work Experience

UCAT

Overview

Verbal Reasoning

Decision Making

Abstract Reasoning

Quantitative Reasoning

Situational Judgement

BMAT

Choosing Universities

Interviews

Oxbridge

Wellbeing

Reapplying

Introduction

 
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🔗Useful Links:

Rationale

 

They often need to make calculations quickly, and use them as a basis to make decisions and solve problems. As a medical student, there will be numerous modules which require you to have a firm grasp of basic mathematics and be able to apply it, such as in physiology and pharmacology.

Statistics is applied to every scientific discipline, including Medicine. Research is constantly being conducted in many areas of Medicine, and as a result, the practice of medicine is constantly evolving based on emerging research. 

It is not uncommon for medical research manuscripts to report improper statistics, unsupported conclusions, and incorrectly designed studies. With this skill, a doctor can identify which manuscripts contain solid data, and which conclusions are the results of poorly designed studies or inappropriate data analysis. This is an important skill to master in order to provide the best care to your patients.

Time pressure is something common between the UCAT exam and your job as a doctor.

 

Tips and Tricks

Quantitative Reasoning questions often include irrelevant mathematical details. Make sure to take time out in the beginning to extract relevant information to avoid mistakes. 

Make sure the unit in your answer matches the unit in the question.

The online calculator provided by the UCAT exam is very different to what you will be used to. Although mental maths should get you through much of the exam, there will be a few times where the calculator may be necessary, and being confident in using the calculator quickly will save precious seconds. We recommend practising using the calculator for more complicated calculations as part of your QR training, so it accurately simulates the exam conditions. We would also recommend familiarizing yourself with the memory function and other shortcuts (such as not typing the 0 before a decimal point) which may make you as fast as possible. 

  • Times tables up to 12 (and multiplying larger numbers by single-digit numbers)

  • Adding and subtracting up to 4-digit numbers

  • Unit conversions (milli to micro to nano, kilo to mega to giga etc.) 

  • Convert Fractions, decimals and percentages, and calculations involving these. (Top Tip: these calculations can be done either way round, e.g. 40% of 25 is the same as 25% of 40, and the latter is much easier to deal with mentally)

  • Working with different types of average (mean, median, mode and ranges)

  • Speed = Distance/Time calculations

  • Rearrangement of formulas and equations, and basic algebra

  • Areas and perimeter of triangles, rectangles, circles and parallelograms

  • Volume and surface area of spheres, cubes/cuboids and cylinder

  • Interpreting information from complex graphs and tables

  • Rounding where applicable (detail further down)

  • Practising these so that you are able to do simple calculations involving them quickly and without the need for writing or using a calculator will help you keep to time and allow you to score higher. 

The QR section relies very heavily on mental arithmetic, as you are forbidden to bring a handheld calculator into the exam, and the on-screen calculator is very slow and time-consuming, not to mention difficult to use.

After at least 1 year of A-Levels, you will be very reliant on your calculator for any maths work you're doing, meaning your mental maths will now be surprisingly bad, especially if you haven’t been taking a maths A-Level. Relying on the UCAT Calculator for anything that isn’t absolutely necessary, will drain your precious time. The answer to this, sadly, is spending hours and hours speeding yourself up. Spend as much time as possible practising maths without a calculator, because the more you do, the quicker and easier it will become. 

Sometimes a question will have numbers that are difficult to work with and require frustrating use of the calculator.

In these questions, it may be useful to take a glance at the answer options, and if they are far apart, doing a calculation using rounded values. This will hopefully give an approximation near to one of the options, saving the hassle of getting the exact figure on the calculator. Remember to keep note of whether you’ve rounded up and/or down as if you’ve rounded up on most values, the true answer should be smaller than the approximation you get, and vice versa.

You should be familiar with all the formulae that you will be using in the UCAT to make your experience easier. This includes all the shape formulae for perimeter, area, and volume​

Practice is key to performing well in the UCAT. Practice both your speed and using the calculator.

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Extra Resources

 

Decision Making Tips

 

 ✅ Practice under the right test conditions 

The whiteboard and online calculator feature is going to be very useful in this subtest, so make sure to keep using these throughout your practice. 

❌ Do NOT use outside knowledge

Make sure you’re only using the information you’re presented with when coming to an answer – don’t make assumptions based on your outside knowledge. This is especially important in the syllogisms and interpreting information questions. 

Be objective and do not let your personal beliefs influence your answers in the recognising assumptions questions. 

🔬 Be objective 

Take care to only use information that is relevant for answering the question in the Venn diagram questions. Doing unnecessary working out will waste valuable time. 

⏰ Do NOT waste time 

Revisit common GCSE maths topics such as probability (especially using the AND and OR rule), percentages and Venn diagrams. 

➗ Revisit common GCSE maths topics

 Do not limit yourself to practicing with only  UCAT resources. GCSE maths and A Level Biology past papers can be used to practice interpreting information from graphs and BMAT section 1 past papers will help you to develop the skills necessary for the evaluative questions. 

✏️ Think outside the box when practicing 

Quantitative Reasoning Tips

 

💯 Develop your Mental Maths

The QR section relies very heavily on mental arithmetic, as you are forbidden to bring a handheld calculator into the exam, and the on screen calculator is very slow and time consuming, not to mention difficult to use. After at least 1 year of A-Levels, you will be very reliant on your calculator for any maths work you're doing, meaning your mental maths will now be surprisingly bad, especially if you haven’t been taking a maths A-Level. Relying on the UCAT Calculator (which can be found here) for anything that isn’t absolutely necessary, will drain your precious time. The answer to this, sadly, is spending hours and hours speeding yourself up. Spend as much time as possible practising maths without a calculator, because the more you do, the quicker and easier it will become. 

🙋 What do you need to learn?

In fact, you are unlikely to need to learn anything, as the maths required is basic GCSE knowledge, and can mostly be done mentally with ease (if you practise!). However there is a series of common skills that will serve you well for the majority of the questions in the QR section.

 

These include:

  • Times tables up to 12 (and multiplying larger numbers by single digit numbers)

  • Adding and subtracting up to 4-digit numbers

  • Unit conversions (milli to micro to nano, kilo to mega to giga etc.) 

  • Convert Fractions, decimals and percentages, and calculations involving these. (Top Tip: these calculations can be done either way around, e.g. 40% of 25 is the same as 25% of 40, and the latter is much easier to deal with mentally)

  • Working with different types of average (mean, median, mode and ranges)

  • Speed = Distance/Time calculations

  • Rearrangement of formulas and equations, and basic algebra

  • Areas and perimeter of Triangles, rectangles, circles and parallelograms

  • Volume and surface area of spheres, cubes/cuboids and cylinder

  • Interpreting information from complex graphs and tables

  • Rounding where applicable (detail further down)

  • Practising these so that you are able to do simple calculations involving them quickly and without the need for writing or using a calculator will help you keep to time and allow you to score higher. 

🧮 Using the Calculator

The online calculator provided by the UCAT exam (found here) is very different to what you will be used to. Although mental maths should get you through much of the exam, there will be a few times where the calculator may be necessary, and being confident in using the calculator quickly will save precious seconds. I recommend practising using the calculator for more complicated calculations as part of your QR training, so it accurately simulates the exam conditions. I would recommend familiarising yourself with the memory function and other shortcuts (such as not typing the 0 before a decimal point) which may make you as fast as possible. 

🔵 Rounding

Sometimes a question will have numbers which are difficult to work with, and require frustrating use of the calculator. In these questions, it may be useful to take a glance at the answer options, and if they are far apart*, doing a calculation using rounded values. This will hopefully give an approximation near to one of the options, saving the hassle of getting the exact figure on the calculator. Remember to keep note of whether you’ve rounded up and/or down, as if you’ve rounded up on most values, the true answer should be smaller than the approximation you get, and vice versa.


*“Far apart” is relative. 8753 and 9463 may be further apart than 79 and 43, but depending on the starting values, rounding may or may not be reliable in each case. 

🏃‍♀️ Moving on

Sometimes there will be questions which are confusing to you. As someone from a scientific background, you are used to problem solving to get the answer, even if it takes you a long time. In this test however, it is often best to move on if the data for a scenario, or the specific question is befuddling you. Like the rest of the test, the difficulty of questions in the QR section vary greatly. There will be some questions you can do easily and quickly, and you do not want to be forced to guess them all in the last minute when you don't have time to work them out. 

Instead, if you make no headway on knowing what to do for a question in the first 20 seconds or so, pick a random guess, flag it, and move on to easy ones, to guarantee some points. You may find that in any leftover time you are able to work it out with a fresh pair of eyes. If you do plenty of practise, most question formats and data presentations will be familiar and you should recognise what to do easily.

 

Abstract Reasoning

A good way to think about timing is to aim for 1 minute per 5 questions, leaving a 2 minute buffer at the end for more difficult questions. For type 1 and 4 questions, this gives 1 minute for the set, and for type 2 and 3 questions it gives 12 seconds per question. This will make more sense as you continue to read about question types. Due to the nature of the exam, being strict with yourself on time is one of the most important aspects to your success.

💨 Build up Speed

It is important you build up speed slowly. Jumping into full speed will ultimately stop you being able to succeed, or develop any basics, and learning will actually take longer. Instead use the large number of practise banks out there to practise identifying patterns with no time limit. Some of them may take 5 minutes or more, but I guarantee that once you figure it out, you will always be able to recognise similar patterns. Slowly introduce time limits, and gradually build your speed. Start many weeks before the exam to give yourself the best opportunity to succeed.

🤔 Understand Question Types

There are 4 question types that you will come across, all of which require similar pattern recognition skills, it is important you become familiar with each format to allow you to quickly and easily answer questions. Each type is explained below.

✍️ Question Type 1

This contains 2 sets of 6 ‘Shapes’ (boxes with patterns) labelled ‘Set A’ and ‘Set B’. There will then be 5 question shapes which you must place in either Set A, Set B, or Neither. The pattern within Set A and B are almost always linked in some way, and sometimes even direct opposites of each other.


As you have roughly 1 minute per set, I would recommend allotting 30-35 seconds to determine the patterns within the sets, then allowing 5-6 seconds per question shape to determine which of the sets it fits into. If it is not immediately obvious whether a question shape fits into either of the sets, it is likely to be neither. If you cannot identify a pattern after 40-45 seconds, move on! (Remember if you stick to timings elsewhere, you have that buffer).