The Quantitative Reasoning Test is a subsection of the UCAT ANZ exam that evaluates your ability to perform mental calculations in a relatively limited amount of time. Considering time constraints, if you dedicate 40 seconds or longer per question, you may find it hard to finish the section on time.

The UCAT Quantitative Reasoning subtest is numerical in foundation. Therefore, it predominantly expects you to interpret complex graphs and have a broader understanding of mathematical formulas. In addition, the QR question-types, to a certain extent, mimics the basic mathematical calculations you have encountered during high school. Hence, it is important that you have a solid foundation in algebraic and geometric expressions to maximise your precision and efficiency during the test.

We at Frasers know that UCAT preparation can be draining, especially if you are also in your final year of highschool. Let us dive further into QR question types before narrowing in on currency, speed, and acceleration.

The QR subtest is a mathematical-assessment, but it cannot be equated to a basic high school maths test. The UCAT Quantitative Reasoning test discerns your mathematical reasoning ability, with some of the concepts derived from your high school math textbook.

The Quantitative Reasoning test comes third in the UCAT series and consists of 36 questions to be solved over 25 minutes, giving you 40 seconds or less per question. So accuracy and time management skills are very important for this subsection.

The question-types can include studying classic tax bracket questions or something as rudimentary as deducing the mean, median, mode, as well as algebraic equations. As indicated earlier, the ultimate goal of the QR subtest is to critically assess your ability to simplify complex questions and deduce plausible solutions, all whilst racing against a ticking clock.

It may be helpful to understand some of the commonly asked QR questions in the UCAT exam to systemise your preparation and build appropriate techniques.

- Proportionality or Averages - Calculating the mean, median and mode are formulas we have memorized since high school. These are usually simpler calculations that may be present as a sub-concept within a question
- Percentages - The percentage questions are straightforward and expect you to calculate the increase or decrease in percentage value. It usually concerns profit, a relative change in price value (in quantities) etc. It may also involve unit conversions, from percentages to decimals and vice-versa.
- Diagrams and Graphs - Typically, in a graph-related question type, you have to interpret the data from the graph to then derive a solution. These questions can seem tricky as there will be a range of values that you need to study and apply multiple formulas to find the answer.
- Rates and Conversions - This is a frequently asked question theme in the QR subsection. The rates and conversions are typically based on currency exchange rates, speed and acceleration.
- Tax bracket - This question-type is based on your understanding of compound interests and taxable income which includes flat rate and tax rate as well.

One of the commonly asked QR questions involves speed and currency conversion questions. It is important to remember the formulas to attempt these question types at a time-efficient pace. The longer you spend on these calculations, the lower your chances of success in the Quantitative Reasoning subtest.

Suppose you are a self-starter, motivated individual who likes to brush up on skills based on real-life experiences. In that case, currency conversion and speed-based questions will be pretty straightforward for you to evaluate during the UCAT. For instance, to estimate the value of 1 USD in Australian dollars, you may have applied the foreign exchange value to determine:

- The currency value in Australia.
- The exchange rate between Australia and USD;
- And most importantly, the amount of money you require to equate it in other foreign currencies.

Although this approach can only help fine-tune your overall fundamentals and formulas, to understand these questions thoroughly, you should practice questions that are similar to the actual UCAT exam. The UCAT exam will not have straightforward questions wherein you apply a single formula to crack the question.

The real UCAT exam consists of many variations within individual question types, which can be confusing. Therefore, to keep your frequency intact, our UCAT tutors advise you to memorise the formulas and also understand the background behind each concept.

For example, if you are given a mathematical problem that requires you to calculate the speed based on the distance and time, don't blindly assume that question expects you to find the speed. Obviously, you are racing against a clock in the QR subsection, however, if you fail to double-check whether all the values have the same units, your accuracy and calculation method could be incorrect.

Magic Triangles for Quantitative Reasoning

Magic triangles have helped many students in the QR subtest. By utilising the magic triangle, you can quickly memorise the relation between each concept and the formula applicable to calculate a unit value. One way to work out the formula is to set aside the value you wish to evaluate and use the other two values within the triangle to find the solution.

In order to calculate the Distance, you have to consider the values of speed and Time.

**Distance = Speed * Time**

Once you derive the primary formula, the values for Speed and Time can be easily interpreted:

**Speed = Distance / Time**

**Time = Distance / Speed**

The same approach follows for currency conversion as well:

**Currency rate = Money after exchange / Money before exchange**

*Now apply the *Distance-Speed-Time *relationship process to the currency conversion and figure out ‘Money after exchange value' and 'Money before exchange' value' on your own.

A good tip you can follow during the exam is to use the whiteboard and pen extensively. In cases where formulas can be confusing, like this one, you can draw the magic triangle on the white paper to refer to it if and when you encounter conversion question-types. On this basis, you don't need prolonged minutes to recollect the formula and can concentrate more on the calculation itself.

Now that we have simplified the formula for currency conversions and speed based equations, we also want to highlight that the QR subsection is unique in nature and can be tricky to solve if your foundation in maths isn’t strong. In your preparation, for all QR questions types, it could be worthwhile to maintain a notebook that has a range of applicable formulas to solve algebraic expressions, geometric equations, anf complex tax questions.

Make sure you revisit these formulas at least once per day so that they become second nature to you. Also seek help from your peers or parents to question you on different formula sets so that you become more fluent in solving equations in the actual UCAT exam.

Alternatively, you can take advantage of the freely available resources at Fraser’s. Each article addresses specific UCAT-related themes to streamline your preparation. If you are a parent seeking help for your child who is undertaking the UCAT for the first time, we also have resources for parents to give you insights on the UCAT exam and its purpose.

Here are some core articles to get you started on your UCAT journey in 2022: