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BMAT Section 1: Problem Solving with fractions

Updated: Aug 28, 2022

The BMAT has a reputation for long wordy questions, which involve you figuring our what you have to do, as much as they involve doing it. This is as true with Problem Solving, as it is with critical thinking, despite most problem solving questions being Mathematical in nature.

Let’s consider a question, so we can look at and apply strategies for answering it. This question has been taken from the 2020 question paper.

In a cafe, Delicious Tropical drink is one-half orange juice and one-half strawberry juice. Vibrant Sunset drink is two-thirds orange juice and one-third apple juice. Stacy makes a mixture called Tasty Delight which is one quarter Delicious Tropical and three quarters Vibrant Sunset. What is the proportion of orange juice in Tasty Delight?

For many, all of the additional information can be confusing and slow you down. The fractions are written as words and so they are a little harder to pick out and there are five answers, so if you guess you have a 20% chance of getting it right.

The trick is to draw out the information you need, without going over the text too much. Start by reading the question, not the paragraph of text.

We are only interested in the amount of orange juice. So we can look at each drink and simplify question paper something like TD 1/2 and VS 2/3. Draw it out, because it makes it much easier to see, especially as they have given us different fractions and if you aren’t good a fractions you may panic wondering how you will harmonise thirds and quarters.

Lets break it down. Draw out a circle with half filled in, because Delicious Tropical is half orange juice. only a quarter of this is used, so now divide that half into quarters and you can see 1/8 of orange comes from Delicious Tropical.

Now do the same for Vibrant Sunset. Draw your circle with 2/3 and divide those thirds into quarters, 3/4

of 2/3 and divide those thirds into quarters, 3/4 of two thirds is half. My nice infographic didn’t have a 2/3 pizza I could use, so I have done 2/3 x 3/4. But in the exam it is probably easier to start with 2/3 and work out 3/4 (I have done this as a sketch, as my infographic tool, doesn't give me thirds!)

Now it is easy to find 1/4 of a 1/2 and 3/4 of 2/3 and to convert the 1/2 to eighths, the answer is 5/8, answer E. This is a good example of BMAT style questions, where they often look more complicated than they are and the biggest tip you can learn, is to keep calm, read the question and just extract the information you need to do it, without getting to involved in the text.

Giving yourself this visual in the exam will stop you getting confused.

Interesting reading ahead of the BMAT

If you have time, do read "Thinking Fast and Slow" by Daniel Kahneman. He describes system 1 thinking and system 2 thinking. System 1 is the quick conclusions we jump to and system two is slower but in somethings much more accurate. Many of the section 1 questions and often section 2, take advantage of this. Because we are under pressure, we often go for the easy and obvious answer that jumps out at us, or we get stuck in the text thinking about the wrong things.

One of the aims of these lessons are to help you form strategies, which you can put to practice with the free past papers available from There is no substitute for using those papers to practice the strategies for answering questions. This helps prevent getting stuck in the text or lost in all the additional unnecessary information they give you.

Save time during the exam

If you happen to be really good at fractions this question may have been very easy for you. Whether it was or not, you will save precious time on the BMAT if you are conversant with fractions, decimals and percentages and can flip between them quickly and easily.

Good luck!

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