Complete Guide To UCAT Quantitative Reasoning

Guide To UCAT Quantitative Reasoning

Introduction to Quantitative Reasoning

Quantitative Reasoning section is the third of the five UCAT sections:


Students commonly think they’re going to dislike Quantitative Reasoning because it involves maths. The maths you need to do isn’t actually that hard but learning to apply it to the scenario is a bit more difficult.


Don’t worry though, we have it covered for you. 

Why is Quantitative Reasoning used?

Quantitative reasoning is included in the UCAT because it’s a really important skill to have. As a doctor, you may have to do drug dosage calculations for a patient, so it is important to be able to do calculations so that you do the correct prescriptions in order to keep the patients safer.


In the future you may also want to get involved in medical research and Quantitative Reasoning skills will be super useful for that.

How to time UCAT Quantitative Reasoning Section

In the Quantitative Reasoning section, you will face 36 questions. The section lasts for 24 minutes in addition to 1 minute of reading time. Using our mathematical skills, we can conclude that you will have approximately 40 seconds to do each question.


What are the different Quantitative Reasoning Question Types?

There are a variety of different question types you may face in this section including:



You will recall doing indirect and direct proportionality in maths lessons at school. You may be required to use this in order to solve problems.



This involves manipulating data in order to find mean, median and mode. You should be comfortable with what each of these mean so you know how to interpret data.



This could involve working out the percentage increase or decrease. You will also have to become comfortable doing conversions between fractions, decimals, percentages and ratios as the answer options could be in different formats.

Quantitative Reasoning Worked Example 1

Question Passage:


Tasty treats is a bakery specialising in selling cakes. They offer 4 flavours of cake in 2 different sizes and the option to have custom decorations as well as a special deal where if you buy 1 cake you get a 2nd one for half price (cheaper cake of the two is half price).


8 Inch Cake Cost
10 Inch Cake Cost
Custom Decorations
Red Velvet
+5% of 8 inch cost
+10% of 8 inch cost
+5% of 8 inch cost
+ 5% of 8 inch cost

Question 1

Mrs Smith would like to buy a 10-inch chocolate cake with custom decorations. How much will this cost her?

  • a) $32.50
  • b) $33
  • c) $35
  • d) $38
  • e) $40

Solution 1

D: Chocolate cake base price is $30. The 10-inch cake means you need to add 10% to the base price which is $3. Mrs Smith also wants custom decorations so this is a further $5. Add all these together to get $38.

Question 2

George wants to buy 2 cakes for his twin daughters. He wants to buy one 8 inch chocolate cake without custom decorations as well as one 10 inch lemon cake with custom decorations. How much will this cost him?

  • a) $37.25
  • b) $45.60
  • c) $46.25
  • d) $50.75
  • e) $61.25

Solution 2

C: The chocolate cake costs $30 as this is simply the base price without any additional costs. The lemon cake base price is $25. You have to add 5% for the 10-inch size which is an additional $1.25. The custom decorations also add $5 which means the total for lemon cake is $31.25.


In the question, there is mention of a deal for half price off the cheapest cake which is the chocolate cake. The new price of the chocolate cake is $15 so in total that is $46.25.

Question 3

Rafay bought 10-inch chocolate with custom decorations for his friend’s party. However, the cake was damaged. Tasty treats offered him a 35% discount as a result of the issue. How much did Rafay pay for his cake?

  • a) $24.50
  • b) $25.50
  • c) $26.50
  • d) $27.50
  • e) $28.50

Solution 3

C: You already worked out the cost of a 10-inch chocolate cake in an earlier part to be $38. Having clear workings in your notes will help you in case you need to refer back. The 35% discount is best split by working out 10% as $3.80 and multiplying by 3 = $10.60. 5% is $1.90 so total discount is $12.50. subtract the discount from the original price to get $25.50.

Question 4

Tasty treats bakery is reducing the price of 10-inch vanilla cake with custom decoration to $20.80. Calculate what percentage decrease this is from the old cost.

  • a) 19%
  • b) 20%
  • c) 21%
  • d) 22%
  • e) 23%

Solution 4

B: We need to work out the old price of the 10-inch vanilla cake. The base price is $20. We need to add 5% to this which is an additional $1. We also need to add $5 for custom decorations. So the total is $26. The new price is $20.80. This is $5.20 cheaper which is a 20% decrease.

Quantitative Reasoning Worked Example 2

Question Passage:


A bus company sells bus passes for different costs depending on the length the pass is needed for as well as whether a person gets a student discount. The prices are shown below:


Standard rate (per day)
Student price (per day)
1 day
1 week ( 7 days)
1 month (30 days)

Question 1

Adhithi is a student who has to use the bus daily for 2 weeks in order to attend an internship.

How much cheaper is it for her to buy 2 of the 1 week passes at student price instead of 14 of the 1-day standard rate passes?

  • a) $28
  • b) $42
  • c) $55
  • d) $70
  • e) $66

Solution 1

B: The prices in the table are shown per day. So for 2 weeks at the student price using the 1-week contract, you would need 2 x 14 = $28. The 1 day contracts costs $5 x 14 = $70. The difference is $42.

Question 2

The bus company is giving a 15% discount to new customers. How much does it cost for Mike to buy a 1-month contract at a standard rate for himself and a 1-month contract at a student rate for his son if they are new customers?

  • a) $60.25
  • b) $74.75
  • c) $89.25
  • d) $94.50
  • e) $105

Solution 2

C: The 1 month contract is 30 days so for Mike it will be 30 x 2 = $60. At the student price for his son it will be 30 x 1.5 = $45. The total is $105. The discount is 15% of $105 – $15.75 so the new total is $89.25

Question 3

The bus company starts a new promotion where you only need to pay for 6 days of the 1-week contract and get the 7th day free. How much would it cost for someone to buy at this rate one 1 week contract at the standard rate and a 1-month contract at the standard rate?

  • a) $18
  • b) $60
  • c) $72
  • d) $78
  • e) $81

Solution 3

D: As you are only paying for 6 days on a one week contract that will be 6 x 3 = $18. In addition to the one month contract which is 30 x 2 = $60. In total this will be $78.

Question 4

A taxi company opens up nearby and charges $9 per day for use. Marie needs to go to school on 4 days. How much cheaper is it for her to use the bus one day contract at student price instead of a taxi?

  • a) $19
  • b) $20
  • c) $21
  • d) $22
  • e) $23

Solution 4

B: The taxi will cost 4 x 9 = $36 for the journeys. At student price it will be 4 x 4 = $16. This is $20 cheaper.

Quantitative Reasoning Scoring and Marking

In the Quantitative Reasoning section, each question is worth 1 mark. This means regardless of how difficult the question is you will only get 1 mark for a correct answer and no extra marks are given for showing working out.

In this section, you can receive a score between 300 and 900. The average score for Quantitative Reasoning in UCAT  2019 was 663 and 662 in the UK. In 2020 the average ANZ score was 671 but 664 in the UK. You can find more information on results in our Complete Guide to UCAT ANZ Scoring.

You can see from this that Quantitative Reasoning is one of the higher scoring sections on average and as such you should look to get a good score here to help boost your overall score to meet university criteria.

Top Tips for Quantitative Reasoning

Here are some tips to improve your quantitative reasoning score:

1). Practice using the calculator


You might be used to scientific calculators but for the UCAT you need to get used to the onscreen calculator because it’s very basic. You can use basic functions on it but it’s also very time consuming to use the calculator.


Get used to using the keypad because it’s quicker to type the numbers than it is to individually click on the buttons of the calculator.

2). Know when you need to do a multiple-step calculation


These questions can take ages to do so you should flag them for review and come back to them at the end. You get the same number of marks for each question you do so you don’t want to waste lots of time doing one question.


If the question looks complicated or requires you to use different pieces of data in multiple steps just ignore the question. There’ll be easier questions that you can do first before coming back to these harder questions.

3). Know which maths topics you will see a lot in UCAT


By doing more practise questions you’ll see which questions appear a lot and what kind of maths they require. For example, percentages and fractions appear a lot so it’s a good idea to practice these topics in order to become more confident in them. Knowledge of graphs also comes up so make sure you know how to read graphs properly.

4). Estimate


If the answer options you are given are quite different to each other, you can make an estimate of the answer. By rounding numbers in the question, you’ll be able to make the calculation easier so you’ll complete the question quicker. Then you just need to choose the answer option that’s closest to your estimate.

5). Don’t overuse the whiteboard


Usually in maths, you get credit for working out but that’s not the case with UCAT. Each question is worth 1 mark and that mark is for the answer.


Only write down key numbers on the whiteboard that you need to remember for your calculation and don’t write out all your working as this will waste time.

Final Words For UCAT Quantitative Reasoning

Overall Quantitative Reasoning can be done quite easily if you manage your time well and it doesn’t require too much prior knowledge. Make sure on test day that you stick carefully to the timings and you’ll be able to get a good score. Remember to work swiftly but avoid making silly mistakes that cause you to lose easy marks. This section is all about practice so remember to do as many practice questions as you can.

By Sharon Daniel

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