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17 UCAT Quantitative Reasoning Tips (From A Top 1% Scorer)

17 UCAT Quantitative Reasoning Tips (From A Top 1% Scorer)

Updated on: December 3, 2023
Photo of author
Written By Dr Ollie

Every article is fact-checked by a medical professional. However, inaccuracies may still persist.

With these UCAT Quantitative Reasoning tips, you’ll easily be able to crank your score up a level.

Even if you’re allergic to maths and the thought of Quantitative Reasoning causes you to break out in a red blotchy rash, these tips are going to turn your most feared section into a guaranteed strength.

In this article, I’m going to cover 17 of the most important tips you need to know to master this section and put your mathematical fears to bed.

These are the exact strategies I used to get an overall score of 3210 when I was applying to medical school.

1. Understand What Quantitative Reasoning Is Testing

My first tip is pretty simple; you’re never going to do well in the section if you don’t actually understand what you’re being tested on.

Quantitative Reasoning is the third section in the UCAT and it’s all about using mathematics in real-world contexts to solve problems.

But, Quantitative Reasoning isn’t just a fancy way of saying ‘maths test.’

Although, as the UCAT Consortium puts it, you’re going to be using numerical skills, this section isn’t just about answering complicated maths problems.

UCAT Quantitative Reasoning Maths Test
Studying for the UCAT Quantitative Reasoning section

What sets Quantitative Reasoning apart from maths quizzes is that it tests your critical thinking.

Quantitative Reasoning gets you to analyse and draw conclusions from real-world contexts through the application of basic mathematical skills.

Sound scary?

Well, it shouldn’t. The good news is the actual maths tested is only at a basic level- a GCSE passing grade.

What they’re really trying to test are your critical thinking and problem-solving abilities. So even if maths isn’t your strongest subject you can still excel in this section.

2. Get To Grips With Why It’s Being Tested

Understanding the reason why you’re being challenged with Quantitative Reasoning (when you’re just trying to apply to medical school) can give you the extra 1% drive over someone who doesn’t.

I’ve always found I’m far more motivated to succeed at something if I understand the reasons behind why I’m doing it.

The reality is, without a solid foundation in basic mathematical skills, a doctor would pose a serious risk to patient safety.

Drug dose calculation errors can have grave implications.

A Quantitative Reasoning skillset is also invaluable to be able to interpret and analyse data from research or the latest publications.

The gold standard for modern medicine is to be entirely evidence-based. So you need to know how to interpret that evidence to be able to best treat your patients as a doctor.

3. Learn Some Quantitative Reasoning Stats

Here’s the thing: if you were given questions from the Quantitative Reasoning section as a piece of homework, you’d get a top grade.

That’s because you’re a bright student and the vast majority of questions in the section aren’t too difficult.

What makes them difficult is the time pressure.

In the Quantitative Reasoning section, you have:

  • 25 minutes to complete the section
  • Which includes 36 questions
  • Averaging at 42 seconds per question

At only forty-two seconds per question, you don’t have the time to triple check your answers on a fancy scientific calculator.

UCAT Quantitative Reasoning Calculator Mastery
Using a calculator during UCAT revision

At forty-two seconds per question, you’re forced to cut corners to try and maximise your marks in the shortest amount of time possible.

By memorising these key stats about the section, you’ll be able to judge your progress as you’re going through the exam, allowing you to speed up or slow down as required.

4. Be 100% Comfortable With Percentages

Percentages come up in many different forms in the UCAT. I’d try and make sure you’re comfortable with each of the following:

Equivalence To Decimals

A survey is carried out on local shoppers. They were asked about how often they bought certain items of clothes.

The survey concluded for every one pound spent on t-shirts, an average person would spent £0.255 on jumpers.

What’s this as a percentage?

Converting between decimals and percentages is really easy once you know the trick.

To take a decimal to a percentage you literally just times it by 100.

So 0.255 x 100 = 25.5%

Percentage Change

A new clothing company, in their third year of business, is comparing their t-shirt sales to last year.

This year they sold 1,184 t-shirts compared to last year’s 872.

What’s the percentage increase in their t-shirt sales from last year?

So to work out the percentage increase we’ve first got to find the difference.

So let’s do 1,184 – 872 = 312

So we know they sold 312 more t-shirts than last year. Now to get this as a percentage of last year’s sales we do:

312 ÷ 872 = 0.358 to three significant figures

That is, as a percentage, a 35.8% increase in sales.

Reverse Percentages

The clothing company decides to try and increase jumper sales by running a 25% off sale.

The price of the jumper in the sale is £84.

What was the original price of the jumper?

Reverse percentages just means working out an original value with just the percentage change given to us

So we know that £84 represents 75% of the jumper’s original value (because it’s 25% off).

So to find out the original value we’re just going to do:

84 ÷ 0.75 = 112

So the jumper originally cost £112

UCAT Quantitative Reasoning Jumper
£112 for a jumper does seem a bit steep…

5. Make Sure You’re Happy With Proportionality

The UCAT frequently tests both direct and inverse proportionality. Here’s an example of each:

Direct Proportionality

The fuel consumption of Car A is 20 litres of petrol per 140 miles.

What distance could the car travel with 7 litres of petrol?

First, let’s figure out how far the car goes per litre of petrol.

So we’ll do 140 ÷ 20 = 7

So for every litre, Car A can travel 7 miles.

Therefore with 7 litres, the car could go:

7 x 7 = 49 miles

Indirect Proportionality

The fuel efficiency of Car A is inversely proportional to its age.

For every five years older the car gets it reduces in efficiency by 2 miles per litre.

If when Car A was five years old it could travel 14 miles per litre, how far could it go per litre in 12 years time?

By doing 12 ÷ 5 = we know 12 is 2.4 5-year blocks.

So the car will have reduced in efficiency by

2.4 x 2 = 4.8 miles per litre

So if at the five year mark it could travel 14 miles per litre it could now do

14 – 4.8 = 9.2 miles per litre

6. Rates Always Come Up In Quantitative Reasoning

They love using rates in questions. Rate of distance over time (speed), rate of change of speed (acceleration), rates of flow… You name it.

Here are two examples- one for speed and one for rates of flow:

Speed

A train is travelling from Point A to Point D. Along the way it stops at Points B and C.

-It sets off from Point A at 10am.
-It arrives at Point B after a twenty minute journey and spends 7 minutes there.
-Following departure from Point B, it arrives at Point C after a thirteen minute journey.
-The train only idles at Point C for 5 minutes.
-The journey from Point C to Point D takes 32 minutes.

If the total distance between Point A and Point D was 53km, what was the train’s average speed?

Remember the trusty formula speed = distance ÷ time?

So to work out the average speed we just need the total distance covered over the total time.

We’re given the total distance- 53km.

It just becomes a matter of adding up the total time then:

  • 20 minute journey to B
  • 7 minute idle
  • 13 minutes to Point C
  • 5 minute idle
  • 32 minute journey to D

So total time is 20 + 7 + 13 +5 + 32 = 77 minutes

Speed = distance ÷ time = 53 ÷ 77 = 0.688 km per minute

or 41.3 km per hour

Rate of Flow

A hole in the train’s fuel line is slowly leaking fuel throughout the journey.

If the fuel flows out at a rate of 12cm³ per second, how long would it take to lose 500ml of fuel?

This is where being able to convert between units really comes in handy.

I know one litre is the same as 1000 cm³.

So, 500 ml is 500 cm³.

So to find the time to lose 500 ml we’d do:

500 ÷ 12 = 41.7 seconds

I’d really recommend learning some basic formulas for converting between these sorts of units, it will make your life way easier:

Conversion Table
1 ml1 cm³
1000 ml or 1 Litre1000 cm³

7. Don’t Be Average At Averages

Put in the work here and there’ll be nothing average about your quantitative reasoning score (sorry not sorry).

You’ll need to have a firm grasp on concepts such as means, combined samples and putting averages to predictive use.

Means

AthleteLap 1Lap 2Lap 3Finish
A50.1552.2254.5946.54
B52.4851.2356.1248.31
C49.2353.5052.2149.22

The data above represents the lap times for three different athletes, A, B, and C, completing an 800m footrace.

Their times for each 200m lap of the five lap race was recorded.

What was the mean split time for the final lap for the three athletes?

To calculate the mean we simply need to add up all the final lap times, then divide by the number of athletes.

So the total time for the final lap is:

46.54 + 48.31 + 49.22 = 144.07 seconds

Then divide that by three:

144.07 ÷ 3 =48.02 seconds

Combined Samples

AthleteLap 1Lap 2Lap 3Finish
D51.1352.5753.3647.48

A fourth athlete, Athlete D, did not compete in the race due to injury.

Her lap split times from a recent training session are shown above.

If she had competed, assuming her race times would have been as above, would it have increased or decreased the mean finish time?

This question is going to require a little more work as it needs race finish times, as opposed to just the splits.

So first off we need to determine the mean race finish time without Athlete D included.

Total time for Athlete A is: 50.15 +52.22 + 54.59 + 46.54 = 203.50 seconds

Total time for Athlete B is: 52.48 + 51.23 + 56.12 +48.31 = 208.14 seconds

Total time for Athlete C is: 49.23 + 53.50 + 52.21 + 49.22 = 204.16 seconds

Then the mean time will be (203.50 + 208.14 + 204.16) ÷ 3 = 205.27

Now let’s look at Athlete D’s time: 51.13 + 52.57 + 53.36 + 47.48 = 204.54

Here we can see Athlete D’s finish time was quicker than the mean finish time of Athletes A, B and C.

Therefore, Athlete D would have decreased the mean finish time.

Predictive Use

If a fifth athlete, Athlete E, ran a 1500m race with the same average pace as the original 800m race, what would be his finish time?

From our working out above we know the average finish time for the three athletes for 800m was 205.27 seconds.

So their combined average split for a 100m stretch was:

205.27 ÷ 8 = 25.65875

Times this by fifteen to get Athlete E’s finish time:

25.65875 x 15 = 384.88 seconds or 6 minutes and 24.88 seconds

UCAT Quantitative Reasoning Runner
World record pace for the 1500m is just under 3 minutes 30 seconds

8. Be A Mental Maths Magician

Yes, you’ve got access to a calculator for the entirety of the UCAT exam.

But ironically, in many ways, the best way to use the calculator is… to not use it!

In your preparation for quantitative reasoning, you’ve got to become a mental maths magician.

Even though you’re only losing a small handful of seconds each time you type in something like ‘6 x 8 = 48’, over the course of the entire section that could be time for a whole extra question.

If you can, it’s best to avoid just double checking your mental calculations with the calculator. You’re now spending time doing both the mental and calculator sums.

Get into good habits early on in your preparation and start flexing your mental arithmetic muscles.

If you feel the need, supplement your quantitative reasoning prep with some times tables revision or something similar.

It’s all the little things that will add up to get you that top score in the section (pun intended!).

9. Hone Your UCAT Guesstimation Game

As opposed to a maths GCSE paper you might sit, the UCAT is multiple choice.

And you can play that fact to your advantage massively. 

You know the correct answer is on the screen. Because of this, you can halve your time on some questions through guesstimation.

Let’s look at an example:

Imagine as part of a question you need to work out the area of a rectangular field.

You know the dimensions of the field are 65.3m by 22.1m. Your multiple choice options are:

743.79m²
5672.45m²
1443.13m²
134.4m²
10900.22m²

They’re relatively big, complicated numbers. So time to stick them in the calculator right?

Well, using guesstimation we can do some quick and dirty maths. 22.1 is pretty close to 20. So lets think about 20 x 65.

To do this calculation I find it easiest to think about 10 x 65 then times it by two.

So 10 x 65 = 650, doubled, is 1300.

Looking at our available answers there’s only one even vaguely close to 1300.

So the answer must be 1443.13m².

Admittedly, this technique isn’t going to work on every question.

You need relatively spaced out multiple choice answers and you need a quick way to be able to do the mental maths.

But when it does work, you can get to the answer in seconds compared to potentially minutes.

10. Skim Quantitative Reasoning Data First

Some of the quantitative reasoning questions can be accompanied by really complex graphs, tables or even paragraphs of text.

Instead of diving straight into interpenetrating trends or checking details, I’d have a quick skim through to get the gist, then read through the questions. 

Knowing what you’re going to be asked can then guide where you focus your attention.

Example Quantitative Reasoning graph in the UCAT

In this graph for example there are three different lines plotted. And you may only need to interpret one!

By reading through the question first (after a quick skim) you’ll know exactly where you need to be looking and won’t waste any extra time.

Bonus tip: if there are a couple of lines of text associated with a graph or table always read them. The UCAT question writers love to hide important information in them.

11. Tactically Use The UCAT Whiteboard

The whiteboard is a really powerful tool in the UCAT.

You can:

  • Write down mid calculation numbers to save time on future questions
  • Use it for formal working out on more complex questions
  • Jot down key bits of information from longer question stems
  • Draw a sad face if you don’t know the answer

As with all these things though, it’s about using it efficiently.

You don’t want to be writing out each step of your calculations if you can help it. Unlike in a GCSE exam, there are no marks for working out.

I’d try and keep whiteboard usage to a minimum.

That being said, if you have to use it, use it.

Writing down important mid-calculation numbers for example can genuinely save you loads of time over the next three questions if you don’t have to keep working out that mid-point number again.

12. Flag Your Way To Success In The UCAT

Making good use of the flagging function is always going to be important in time-pressured sections.

And guess what, unfortunately, the entire UCAT is time-pressured.

My strategy for Quantitative Reasoning is this:

  1. I go through the section answering as many questions as I can
  2. If I feel myself getting bogged down, or the question is too difficult for me, I first put down an educated guess
  3. Then I flag the question and move on
  4. When there’s one minute remaining on the clock I whizz through and put down guesses for any questions remaining
  5. If I’ve got time at the end I will then review my flagged questions

Using this strategy you’ll be sure to have answers down for every question when the timer runs out.

If you don’t, you’re just throwing potential marks away due to the fact there’s no negative marking.

13. Only Use Highly Targeted Revision

If you think to revise for Quantitative Reasoning you’ve got to plough through a maths textbook as thick as your head, you’ve got it all wrong.

The UCAT Consortium actually give you a curriculum for the Quantitative Reasoning section.

It’s not in any way detailed, it’s essentially just the four key areas that make up the question topics:

  • Percentages
  • Proportionality
  • Rates
  • Averages

As you begin your preparation I’d recommend making a note of which Quantitative Reasoning question topics trip you up the most often.

This could be in a ‘UCAT diary’ or just a notes app on your phone.

You may start to see a trend of one particular question topic or format.

Once you’ve got this information you can then go and do a small amount of highly targeted maths revision, focusing only on what’s causing you problems.

That way you’ll work on your weaknesses with clear aims as opposed to wanting to improve quantitative reasoning so going and revising ‘maths’.

14. Use A Variety Of UCAT Resources

The problem with anything not produced by the UCAT Consortium is it’s not going to be exactly like your UCAT exam.

They can be pretty close, but no third party is going to be able to exactly replicate the style and difficulty of official questions.

This difference is most apparent in Quantitative Reasoning questions.

And that’s why it’s the section where it’s most important to use a variety of resources to prepare for.

UCAT Quantitative Reasoning Variety Resources
Preparing for the UCAT Quantitative Reasoning

I’ve found that the difficulty of Quantitative Reasoning questions can vary wildly from one resource to the next.

Some will be too difficult, some will be too easy. By using a variety of resources you’ll have exposure to both.

This will protect you from a nasty shock on exam day when your dialled-in section is completely thrown off by a huge difference in question writing.

15. Use An Online UCAT Resource

This tip somewhat follows on from the last- I’d recommend at least one of your UCAT preparation resources to be online.

Now I’m not saying you have to go out and buy membership to one of the online question banks. The UCAT Consortium has loads of great free material.

What I’m saying is just make sure you use one!

You can also then do Quantitative Reasoning revision from your bed…

There really is a big jump between doing paper-based UCAT mocks and completing them on a computer.

By practicing online you’ll get used to the interface, the keyboard shortcuts, the on-screen calculator…

You’ll just generally be much better prepared for the actual thing.

16. Master The UCAT Calculator

Mastering the tools at your disposal in the UCAT is one of the best ways to take your performance to the next level.

The UCAT calculator is just one of those tools.

Although it can be used throughout the exam, it undoubtedly plays its most vital role in the Quantitative Reasoning section.

UCAT Quantitative Reasoning Calculator Full

The Texas Instruments TI-108

To bring up the calculator you can either click the ‘Calculator’ button in the top left of the screen or use the keyboard shortcut CONTROL + C.

Let’s take a look at what each of the buttons on the TI-108 do.

UCAT Quantitative Reasoning Calculator Snip 1

The ON/C Button

You don’t actually have to turn the calculator on- it’s ready to go as soon as you bring it up.

C stands for clear- it clears the display and any previous calculations you’ve entered.

UCAT Quantitative Reasoning Calculator Snip 2

The Numpad

Using the numpad on your keyboard is a much faster way to use the calculator than clicking in the numbers.

Just be sure to press num lock first.

UCAT Quantitative Reasoning Calculator Snip 3

The Operation Keys

You can save time by not clicking these guys either!

Times is ‘ * ‘ (star) and divide is ‘ / ‘ (slash) on the keyboard. Enter is EQUALS.

UCAT Quantitative Reasoning Calculator Snip 4

Technical Keys

+/- toggles either the positive or negative version of the number on the display.
Square-root symbol gives you the square root of a number.
The % key is super useful. See below:

The percentage key gives you a quick, no effort way of calculating equations with percentages.

178% of 24? No problem!

You literally just type in 24 x 178% = 42.72

This is of course the same as 24 x 1.78 but you may find it a quicker and less confusing method.

UCAT Quantitative Reasoning Calculator Snip 5

Memory Function Keys

M+ adds the POSITIVE version of your number to the calculator’s memory.

M- adds the NEGATIVE version of your number to the calculator’s memory.

When the calculator has a number stored in its memory you’ll see an ‘M’ appear in the top left of the display.

To retrieve your stored number you just press MRC. This stands for ‘Memory ReCall’.


Let’s put the memory function to the test in a compound interest problem.

Let’s say you’ve got £139 in the bank accruing 3% interest per year. How much money would you have after four years?

For 3% you’d add 1.03 to the calculator’s memory with M+.

You could then do: 139 x MRC x MRC x MRC x MRC

= £156.45

MUCH quicker than typing out 1.03 four (or more) times!

Some final tips:

  • To clear the memory you can press MRC twice.
  • To clear the display BACKSPACE can be used instead of the ON/C button.
  • To go to the next question you can use ALT + N

17. Have Confidence You’re Going To Do Well

Analysing previous years’ data, the Quantitative Reasoning section is in fact, on average, a candidate’s best scoring section.

This tells us that people do very well in the QR section- and that you more than likely will do as well.

Don’t be put off by the seemingly impossible number of maths questions in such a short period of time.

Everyone’s in the same boat and everyone generally performs well. By implementing the strategies you learn from this article, you will too.

Final Thoughts

You now have all the tips you need to master the UCAT Quantitative Reasoning section.

Although they might not seem like much, those seconds really do count.

Your mental maths, keyboard shortcuts, not double-checking answers, guesstimates and whiteboard use will all add up to equal a higher overall UCAT score.

About the author
After studying medicine at the University of Leicester, Dr Ollie now works as a junior doctor in London. His interests include medical education and expedition medicine, as well as having a strong belief in the importance of widening access to medicine.