How to Score Highly in the Quantitative Reasoning Section of the UCAT

The quantitative reasoning (QR) section is the third subtest section in the UCAT. It tests your problem-solving skills. It is not a test of your maths skills but rather how you apply knowledge of some basic maths to solve problems. This section is important as doctors need to have some basic maths skills since they quite often need to quickly calculate doses of drugs and other things. 

This section can be quite hit or miss initially. Maths geniuses are able to whizz through this section with ease but some students who are not the best at maths may find it relatively harder to get through this section. However, the good news is that you do not need to be adept at maths in order to be able to excel in this section.  With the tips given below and plenty of practice, anyone can score good marks in this section.

The average score for this section from the years 2016 to 2021 ranged between 665-690, and ideally, a high score in this section would be considered 700+. Generally speaking, having a score of 700+ in the 4 cognitive sections (abstract reasoning, decision making, quantitative reasoning, and verbal reasoning) or a 2840+ total score with a band 1 in situational judgement would very likely put you in the top 10% of test-takers and put you well above the UCAT cut-offs set by various universities.

About the section

  • This section has 36 questions
  • Time given for the section – 25 minutes
  • Time per question – 41 seconds

In this section, a lot of the questions come in sets of 4 questions with there being a few standalone ones as well. Due to most of the questions being in sets, once you figure out the overarching theme of the main question, you should be able to whizz through the set.

The data will be presented in the form of texts, diagrams or graphs that will need to be interpreted. You will need to choose the correct answer from 5 possible answer choices. Sometimes, you may have to do several calculations to reach the right answer.


Types of questions

There will be various questions focusing on different topics and it is crucial to know what these are to be able to understand and practice properly. While practising, you will start identifying the topics and question types you struggle most with. This will enable you to know where you have to put more of your effort. Some of the most common topics that show up are:

  1. Percentages – Calculating increase and decrease in the percentage 
  2. Chart/Graph reading – Being able to pull data from a graph for calculations
  3. Perimeters, areas and volumes – Be familiar with the formulas for these
  4. Table reading – Being able to interpret the information given in a tabular form
  5. Averages – Mean, median and mode
  6. Rates and converting between rates – Calculating speed, distance and time
  7. Ratios – Calculating ratios of given quantities
  8.  Proportionality – Direct and Inverse

Tips to score highly in QR

Know important formulae

It is crucial to know some of the common formulae required for solving questions in this section. Knowing these will help you reach the correct answer a lot faster.

Speed, distance and time
Speed = distance/time
Acceleration = change in velocity/time

Areas and volumes
Area of a rectangle = (length x width)
Area of a triangle = (1/2 x base x height)
Area of a right-angled triangle = (1/2 x base x height)
Area of a circle = (πrˆ2)
Area of a trapezium = (1/2 (total length of both parallel sides) x height)
Volume of a cylinder = (πrˆ2h)
Volume of a sphere = (4/3 πrˆ3)
Circumference of a circle = (2πr)
Pythagoras’ theorem = (a2 + b2 = c2)


Percentages, ratios and fractions
Percentage change = change in value/original value x 100

Common Percentages

1/8 = 12.5%

3/8 = 37.5%

5/8 = 62.5%

7/8 = 87.5%

1/20 = 5%

1/25 = 4%


Common Minute-hour conversions

15 minutes = 0.25 hrs

20 minutes = 0.333 hrs

30 minutes = 0.5 hrs

40 minutes = 0.667 hrs


Know unit conversions

A great way to save time is to memorise some of the unit conversions. This will ensure that you don’t have to waste time trying to actively work to figure these out in the test as you will already know these like the back of your hand.


1 kilometre 1000 metres
1 metre 100 centimetres
1 centimetre 10 millimetres
1 kilogram 1000 grams
1 gram 1000 milligrams
1 litre 1000 millilitres


Do mental maths

This advice would differ from person to person. Some people might be quite good with mental maths and others might be more prone to making mistakes this way. It is important to try your hand at some basic mental maths such as basic conversion or percentages. During practice tests, try doing as much mental maths as possible to assess your skill with it. This will help you determine what sort of questions you are able to do mentally and what sort of things need to be written down.

Being proficient in mental maths can save you a great deal of time which can result in having more time for some of the harder questions and ultimately getting a high score.

Estimate when required

To maximise your time, you can sometimes estimate the numbers given in the data. Depending on the type of question and data given, it may be appropriate to round off the numbers to the nearest 10 or 100. This could make the calculations easier and perhaps even make it easier for you to do some mental maths that you may not have been able to do otherwise. Once you have done this and have an answer, you can make an educated guess to see which answer choice your answer is the closest to. However, remember that this might not always be the wisest choice especially when the answer choices are quite similar in terms of the number to each other. In such cases, you would want an exact answer, so approximation would not be recommended. 

Master the keyboard shortcuts

  • Use Alt+C to open and close the calculator.
  • Use the Backspace button for ON/C (clearing the calculator)
  • Use the keyboard (+,,*,/) for addition, subtraction, multiplication and division.

Make use of the tools provided

Make sure to practice using the whiteboard as this is what you will be using during the actual exam. This can also help you visualise some of the data given in tabular or graph form better. Practice writing down key points while solving questions and learning how to keep track of all the data you write down. It would also be helpful to be familiar with the calculator function as using this could make some of the questions a lot quicker and more accurate but be careful to not fall into the trap of using this function too often for even just the basic calculations as this can be time-consuming and slow you down.

Make use of the memory function on the calculator

The ‘M’ buttons on the calculator are memory functions.

  • Press M+ to add a number to the memory
  • Press M- to remove the stored number
  • Press MRC to recall the stored number

This is often useful for multi-step questions.

You can try out the UCAT calculator here.

Use the ‘flag’ function when needed

What works for one may not work for everyone, but it is strongly advised to not spend too much time on 1 question. If after 60 seconds you are still struggling and are nowhere near figuring out the answer, it might be worth choosing a random answer (as you do not get marked down for wrong answers), flagging the question and moving on. Once you’ve finished all the questions, you can always come back to the flagged questions and review them. What you don’t want happening is that you’ve spent 5 minutes on just a single question and then towards the end, you know how to answer the question but simply don’t have enough time.

Don’t stress!!

You are a lot more likely to make careless mistakes due to stress in this section than in any other section. This is because something as small as a decimal point being misplaced can cause the whole sum to go wrong. This is why it is crucial to get into the zone of doing these types of questions and stay calm. Even if you’ve messed up in some other section or a previous question in QR, it is important to not worry about it while solving a new question.

Remember that these questions are no harder than GCSE maths and that you can easily tackle these with the right mindset and practice.



Quantitative reasoning can be a daunting section, especially for those who are not the biggest fans of maths. However, with enough practice and memorisation of important conversions and formulae, this section can be easily conquered.

As mentioned earlier on in the article, a competitive UCAT score would be getting 700+ in all 4 sections (verbal reasoning, decision making, quantitative reasoning, abstract reasoning) and a band 1 in SJT. If you want to have a competitive score on your UCAT, check out our brand new ‘Ace the UCAT’ course, which includes:

  • 200+ lessons
  • 20 hours of video lessons
  • 350+ practice questions, with Dr Hilton walking you through the answers and the best way to tackle them
  • Lots of support and help with the UCAT
  • UCAT advice

If you want help getting into your dream university then also be sure to check out our Elite Coaching Programme. As part of this programme, you will get in-depth help with the entire application process from whatever stage you join at till you get into the medical school of your choice. This is done through 1-on-1 mentoring and the founder of the course, Dr Ashley Hilton is always available for any questions. You can find out more about the Elite Programme here. 


However, if you choose not to join the FutureDoc team and this article is the last time you engage with us then best of luck for the future and I hope you’re able to get into the medical school of your choice!


Written by Muskaan Sharma