We have separated each UMAT section into different categories. You can think of these as sub-sections that we organise similar questions into. This guide goes through each of these categories, offering examples, and tips on how to solve the type of questions.

We recommend reading through it section by section, and then doing a practice quiz on that section.

Section 1: Logical Reasoning and Problem Solving

This section aims to test how well you can draw logical conclusions, identify facts, analyse information and test hypotheses from written or graphical information.

We separate this section into a few different categories: analysing arguments, numerical reasoning, rule-based reasoning, graph analysis, data table analysis, experiments & studies, image-based questions. On the surface, the categories are quite different, but in fact all can be solved with logical reasoning.

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Numerical Reasoning questions require the most in-depth analysis of the data provided. Here's an example:


A vote is carried out at a board meeting on whether to ban smoking at work. Not everyone present is in favour of the ban. Half the attendees are smokers, half are not.

Twenty percent of the attendees are against the ban. Of this twenty percent, six in every fifteen are smokers. All other attendees support the ban.

Which of the following is true?

A The proportion of people for the ban that are non-smokers is 89 out of 100.
B The proportion of people for the ban that are non-smokers is six in fifteen.
C The proportion of people for the ban that are smokers is 50%.
D The proportion of people against the ban that are smokers is sixteen in forty.
You rarely need to be completely precise in your calculations!

Often, the maths will be too complex to do precisely within the 80 seconds you should take per question. You can usually use rough estimates, or round the numbers up/down to make it easier. The difficulty in this type of question is in identifying the numbers you need, and what you need to do with them.

Here are some quick tips:

  • Know your unit conversions. It seems obvious, but make sure that you know that, for example, 1 ton = 1000 kilograms = 1000000 grams, etc.
  • Estimate divisions. Dividing mentally is harder than adding, subtracting or multiplying, but make it easier by rounding up/down to estimate the answer. For example, if you need to divide 39 by 4, round the 39 up to 40, which makes finding the result extremely easy. Usually, this should still allow you to pick out the correct answer. If it does not, then only go over the relevant divisions again with higher precision.
  • Know your percentages. Again, this may seem obvious but can often catch students out. A common error is to convert, for example, 8% to 0.8 instead of 0.08.
  • Double check! Actually double check. Usually, answers are written so that they may seem correct if the student makes some common mistake. So, look at answers similar to yours, and try to work backwards from them. This will help you to see if you have missed any steps. For example, if your answer is '100' and '1000' is another answer, you would have needed to multiply your answer by 10 to get 1000. Ask yourself why you did not - it could help you find any mistakes you have made.

This category is the most common in Section 1. We separate this category further into three different types of question: rule-based questions, hierarchy questions and category questions. They test your ability to identify facts and rules, require you to hold a large number of related facts in your head, and draw conclusions from them.

Rule-based question

This type of question describes a large set of rules, which you will need to apply logically. Here's an example:


Your sock drawer contains ten pairs of white socks and ten pairs of black socks.

If you’re only allowed to take one sock from the drawer at a time and you can’t see what colour sock you’re taking until you’ve taken it, how many socks do you have to take before you’re guaranteed to have at least one matching pair?

A 2.
B 3.
C 10.
D 20.

Most often, but not always, there will be around four possible outcomes from applying the rules - usually each possibility corresponding to an answer. The quickest approach is often to eliminate three answers.

Here are some helpful tips to consider:

  • Symmetry. If the problem is somewhat symmetrical, like the example, you often only need to work through half the possibilities. In the example, working through the possibilities for picking a white sock first will be symmetrical to picking a black sock first. So, there is no need to work through both of these.
  • Venn diagrams. Use these when the rules given are to do with categories, and the categories overlap. For example, if you are asked about a group of 30 people, and told that 20 have black hair and all have blue eyes, then there is an overlap: some people must have both blue eyes and black hair, and others do not. Of course, a real UMAT question will have many more rules.
  • Tree diagrams. A tree diagram would be appropriate for the example given above. Use these when you need to map out a process - such as taking socks out of the drawer.
  • Tables. A table is another tool that can be used. When you need to track many different possibilities, such as in the example above, you will not reliably be able to track these in your head. Writing them down in a structured way lets you easily keep track of them.

Hierarchy questions

This type of question usually provide a list of items that are ranked in a particular order. Then, additional items are provided with information on where they rank relative to items in the current list. Here's an example:


The following fruit are in order of decreasing sweetness. Orange, Watermelon, Melon, Banana, Guava, Apple. A Peach is sweeter than an Apple, but less sweet than a Watermelon. A Nectarine is sweeter than a Peach.

Which of the following is definitely true?

A A Nectarine cannot be sweeter than a Watermelon.
B Oranges are the sweetest fruit.
C If Peaches are less sweet than Melons, Nectarines are less sweet than Watermelons.
D If Nectarines are as sweet as Melon, Peaches could be as sweet as Bananas.

The trick here is there is a lot of ambiguity; there is only enough information to place them relative to some other items but with uncertainty about their exact placement. For example, we cannot tell whether a Peach or a Banana is sweeter from the information provided above.

How we recommend solving this type of problem:

  • Write out the initial list. Leave some space in between the items.
  • Add each 'new' item separately. Add them alongside the original list. Mark all the positions that the item could go in. Add the next 'new' item alongside this, and so on. Now you should be able to place all the items relative to others. Note you do not need to have a definite placement for the items; the questions will generally only ask about whether certain placements are possible.

Here's an example suggesting what to do for the example above:

Orange -
- -
Watermelon Nectarine
- --
Melon --
- --
Banana Peach
- -
Guava -
- -

Category questions

In this type of question, students are provided with a number of categories (e.g. people, houses, species) and items within the category (e.g. Tom, the blue house, golden eagle) There are usually three or four items in each category. Each item is related to one other item in each of the other categories. Here's an example:


Jack, James, Judy and Jess are four medical students. Each has a different brand of smart phone and each travels to university their own way.

Jack does not live near a bus route. James lives next door to Judy so sometimes offers her a lift to Uni. Jess' iPhone needs a new screen. The Motorola was left in the car.

Who takes the bus?

A Jack or Judy.
B James or Jack.
C Jess or Judy.
D Either Jess, Judy or James, but not Jack.

Here are some helpful steps:

  1. Identify the categories and items. There will often be a lot of specialist, unnecessary information in the text. Try and ignore this and focus on the categories and the items. In the example above, the categories will be the name of the student, the brand of phone, and the method of transport. The items that we know about would be iPhone/Apple and Motorola, and bus and car (in a real UMAT question, a near-complete list of items would be given).
  2. Start a table/grid. (see an example grid below) There are a few different types of facts that can be given in the text:
    • Simple facts. These are straightforward, such as 'Jess has an iPhone'. Add these to your grid, and cross off other possibilities.
    • Implied facts. That James offers Judy a lift to Uni implies that James has a car. These can be easy to miss.
    • Constraints. 'Jack does not live near a bus route' does not tell us who takes the bus, but only that it is not Jack. Add only a cross to your grid.
    • Partial Information. The Motorola must belong to either James or Judy, as they use the car. Therefore, we cannot tell who owns the Motorola, but only that Jack and Jess do not. So, add a cross to your grid for them.
JackJamesJudyJess iPhoneSamsungMotorolaGoogle

Continue in this way until you have exhausted the information available to you. Now try and reconcile this with the questions and answers. Given that you only have around 80 seconds to answer a question in the UMAT, you should not be able to completely fill the grid. The questions are designed so that you can answer them with a partial solution. For example, from the grid we can tell that Judy or Jess take the bus, which might be enough to answer a question.

  • Re-use the same grid for multiple questions. UMAT questions are designed so that the first one in a set may take more than 80 seconds to solve, but the second and third will be easier (because you have already processed much of the information).
  • Don't get lost in the grid! Read the question before you start; you do not want to waste valuable time on filling in information that you do not need.
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Section 2: Understanding People

This section aims to test how you think and understand people, their thoughts, relationships and feelings.

While we can separate this section into three categories (pure dialogue, pure narration, and mixed dialogue and narration), they are in fact extremely similar. So, instead of looking at each category, we look at each type of question.

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One of the most common questions in Section 2 will ask you to choose between sets of adjectives describing how a character feels (sometimes only one adjective). You need to determine which set is most applicable. Here's an example:

Brittany's approach to the situation can be best described as
A calm and defiant.
B concerned and reserved.
C passive and composed.
D grudging and sour.

This is how we recommend you solve these questions:

  1. Cross out any adjectives that are obviously incorrect. If, like in the example, you need to choose between pairs of adjectives, both the adjectives must be correct. So, cross out any answers that have even only one incorrect adjective.
  2. Highlight ares of the extract that support each adjective. If the adjectives of one of your remaining answers have significantly larger highlighted areas than the rest, chances are that the well-supported answer is correct.
  3. Really think about the meaning of the adjectives. Think of situations in which they are commonly used, or situations where one may be appropriate but the other would not be. Do not get caught up on one adjective; the first adjectives of two pairs might be equally appropriate, but the second may not be.
  4. Do not read everything at face value. If a character laughs, it does not necessarily mean that he is happy; instead he may be laughing because he is nervious, embarassed or in disbelief.
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Section 3: Non-Verbal Reasoning

This section tests your abstract reasoning, pattern recognition and visual problem solving ability.

Many people consider this the hardest UMAT section. We break it down into three categories: rearranging a sequence, completing a sequence, and three-by-three grids. Within these categories, UMAT questions tend to follow a few simple patterns.

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There are two main types of question: those that follow a sequence along the rows/down the columns, and those where shapes add or cancel out along the rows/down the columns.

Sequence type

In this type of question, the rows or columns follow a sequence (just like 'rearranging a sequence' or 'completing a sequence' questions). The difference is that there are only three images per sequence (each row/column is its own sequence). This would normally make the sequences harder to identify, but the sequence that each row/column follows is related to that followed by the others. Here is an example:

Select the answer that most logically and simply completes the picture.
Example three-by-three grid image with shapes following a sequence

Here are some steps to follow that may help you solve these questions:

  1. Rows or Columns? Usually, this will be made clear by the background images. They will be the same for every picture within a sequence, but different for each sequence. If they are the same, the best strategy may be to check if it follows an 'add/cancel out' pattern. If it does not seem to, it's likely a sequence.
  2. Think about paths. Generally, sequences share movement patterns i.e. in each sequence, one shape will move 2 steps and rotate 45°, and another might move three steps. However, to identify this pattern across the three sequences, you need to know what a 'step' looks like on each background image. As always, the path on each background image will be related to the actual image; if the image is a circle, the path is likely to follow the perimeter of the circle.
  3. Now try and find a movement pattern. Focus on one shape in one of the sequences and find out how much it moves by. Look at another sequence, and search for an image that moves by the same amount. This should confirm whether you correctly identified the movement pattern. Now try and find the corresponding shape in the row/column with the missing picture. You should then be able to predict where this shape should be in the missing image.
  4. Do this for every shape. Double check! You should now be able to identify which answer is correct.

Add/Cancel out type

In this type, the shapes along the rows or columns are adding up or cancelling out. This means that if there are two shapes in the same positions in first two rows/columns, the position will be empty in the third row/column. Here is an example:

Select the answer that most logically and simply completes the picture.
Example three-by-three grid image with shapes cancelling out

After you understand these once, this type of question is very simple to solve. They are used surprisingly often in the official UMAT test. Here are the steps we recommend following:

  1. Rows or Columns? First assess whether shapes are cancelling out along the rows, or down the columns. An easy way to do this is to pick a shape in the top-left image, and see if there is another shape in the same position in the top-middle image or middle-left image. If there is in only the top-middle image, and there is no shape in the top-right image, the shapes must be cancelling out along the rows. If there is in the middle-left image, and there is no shape in the bottom-left image, the shapes must be cancelling out down the columns. If there is a shape in both the top-middle and middle-left image, pick another and run through the same process.
  2. That's basically it! This is why this type of question is so simple. After you tell whether they are cancelling out along the rows or down the columns, systematically go through the shapes in that row/column, and decide whether there needs to be a shape in the same position in the missing image. Once you know exactly what the answer should look like, find it in the answers. If it is not there, you've likely made a mistake - so double check!

Here's a worked example:

Example three-by-three grid image with shapes cancelling out
  • The blue highlights show that the shapes are adding up down the columns.
  • So, we would expect the top-left image and the middle-left image to combine.
  • So, there will be a triangle in the 'top' circle, 'center' cirlce, 'bottom-right' circle and 'left' circle.