INTRODUCTION TO SECTION 3

STRUCTURE Section 3 of the UMAT has 30 questions. You will have 40 minutes in which to complete them. That is 80 seconds per question. Historically, there have been two main types of question:

1. Shapes 2. Patterns and sequences

Shapes questions involve finding a particular shape from amongst a pattern of extraneous information. They no longer form part of UMAT. Patterns and sequences questions involve examining the pattern, finding a rule and applying that rule to find the answer.

WHAT DOES IT TEST? Section 3 tests non-verbal reasoning and 'visuo-spatial reasoning'. The first two sections of the UMAT require a reasonable grasp of language and vocabulary, but in this section, the idea is to test the non-verbal aspects of intelligence and aptitude. The UMAT guide states that this section is designed to assess 'your ability to reason in the abstract and solve problems in non-verbal contexts'. The types of questions in section 3 are often referred to as culture-free or culture-fair tests because, theoretically, ones culture should not affect ones performance.

HOW IS IT RELEVANT TO BEING A HEALTH PROFESSIONAL? Section 3 is often criticised by UMAT test takers because it seems to test skills that have no relevance to practice as a health professional.

Some suggest that section 3 tests your ability to identify relevant information from a large amount of irrelevant data. Some believe it tests your ability to identify patterns and trends (indeed, 'pattern recognition' forms a major part of the decision making process of an experienced health practitioner). Some think it is just another way of testing intelligence. Whatever your opinion on this section, in the end, the perceived relevance of section 3 really doesnt matter. Your job is to do well in Section 3 by working through this guide, completing our practice exams, and honing your skills with drills and Eureka! - our section 3 trainer.

PATTERNS AND SEQUENCES

INTRODUCTION

What does it test?

All questions of this type require you to logically reason with non-verbal cues. This involves: Finding logical pattern(s) within figures that are presented to you Using the logical pattern that you have found to answer the question

What should I expect? There are many kinds of patterns and sequences questions. This guide will cover the kinds of questions that are often tested in non-verbal sequence tests such as section 3 of the UMAT.

However, your aim should be to improve your non-verbal reasoning, visuo-spatial reasoning and logic, not to learn each type of question in a rigid fashion.

COMPLETE THE SEQUENCE

This is a very common type of question within in the patterns and sequences genre.

What does it test? This type of question tests your ability to:

Find a logical pattern between the series figures provided Extend this logical pattern to find the next figure in the series

The Approach There are a few crucial steps in solving a complete the sequence problem: 1. Identify the components of the sequence 2. Examine each component individually

Is there a pattern? What is the pattern? Extend the pattern Re-examine the alternatives and eliminate the wrong ones

3. Keep a global view of the pattern 4. When your answer does not match with any provided, look at the differences between the answer

alternatives for some inspiration Lets look at an example: Select the one answer that would logically be the next figure in the series

A) B) C)

The first step in solving these problems is to identify the different components of the sequence. In this case, there are two components: 1. Outer shape (the square / diamond) 2. The arrow

The next step is to look at each of the components separately and see whether a pattern emerges: 1. The outer shape Let us examine the movement of the outer shape alone:

You should be able to see a fairly obvious pattern stated formally, it might sound like this: The outer shape alternates between a square and a diamond or The outer shape is rotated 45o each move. We now have to ask ourselves: if this pattern were extended, what would the next one look like? Answer: A square So we now know that the answer must have a square (not a diamond) as the outer shape. Let us re-examine the alternatives:

D) E)

A)

B)

C)

D)

E)

From this o piece of information, we were able to exclude two out of the five alternatives. Even if we take a

ets continue

. The arrow

ow let us examine the movement of the arrow alone:

Here again there is a fairly obvious pattern: The arrow moves around in a clockwise direction 45o each move.

e now have to ask ourselves: if this pattern were extended, what would the next one look like?

Answer:

ets re-examine the alternatives again:

learly, option B is the right answer.

ets try another one.

Select the one answer that would logically be the next figure in the series

newild guess now, we have increased our chances of getting the right answer from 20% (1/5) to 33% (1/3). L 2 N

W

L

A) B) C)

C L

D) E)

Identify the components: 1. Long thick line 2. Long thin line 3. Short thin line(s)

Examine each component individually: 1. Long thick line

Ask yourself: Is there are pattern? Pattern: Long thick line alternates between bottom-left to top-right orientation and top-left to bottom-right orientation.

Extend the pattern: The next figure will be top-left to bottom-right orientation:

Re-examine the alternatives and eliminate the wrong ones:

A) B) C) E) D)

2. Long thin line

A) B) C) E) D)

Ask yourself: Is there are pattern? Pattern: The long thin line appears to be moving around an imaginary square in the clockwise direction. i.e:

Extend the pattern:

Re-examine the alternatives and eliminate the wrong ones:

3. Short thin line

Ask yourself: Is there are pattern? Pattern: The number of short thin lines increases by one each time. They also flip each move so that they are orientated in alternate directions. Extend the pattern: In the next figure, there will be four short thin lines and they will look like this::

Re-examine the alternatives and cut out the wrong ones:

Thus the right answer is option E! Remember that it is important to always keep a global view of the question. For example, in the previous question, the thin small lines were always on the thick long line. Thus, in the answer, the thin small lines would have to be on the thick long line. Keeping a global eye on the question means that although it is crucial to examine the components individually, it is also important to look at the figures with the relationships between components in mind.

A) B) C) E) D)

A) B) C) E) D)

When none of the answers appear to match your answer, it is often useful to look at the answers and see how they differ. For example, in example 3.2.1 above, these were the answers:

A) B) C)

You could ask yourself the question how do these answers differ from each other?. The answer is that 1) they are either a square or a diamond and 2) they have arrows pointing in different directions. This directs you to the pattern.

PICK THE MIDDLE

What does it test? This type of question tests your ability to:

Find a logical pattern between the series of disordered figures Order the presented figures according to the logical pattern that you have found Choose the middle figure in the ordered sequence

The Approach This type of question may seem difficult at first. However, if you apply some general principles, they will seem much easier.

1. Identify the components of the figures 2. Look for the 3-2 situation 3. Examine how the components of the figures are moving/changing 4. Use clues from (3) to find a pattern within the components

What is the 3-2 situation? The 3-2 situation is where three of the five figures provided have a common feature (lets call them the 3 figures) and the other two have a different common feature (lets call them the 2 figures). When this occurs, one of the 3 figures is going to be the middle figure. i.e. if we are to order these figures:

This is the only order they can have if they are to be in sequence or pattern:

D)

3 2 2 3 3

The 3 figures occupy positions 1, 3 and 5, while the 2 figures occupy positions 2 and 4. Identifying this situation makes it easier to solve these problems. Lets try a simple example: Identify the figure that would be in the middle after the figures are ordered in sequence.

1. Identify the components of the figures The figures have one component circles. 2. Look for the 3-2 situation Not present. 3. Examine how the components of the figures are moving / changing The components in the five figures change only in number. Option A has 1 circle, option B has 4 circles, option C has 2 circles, option D has 5 circles and option E has 3 circles. 4. Use clues from (3) to try and find a pattern within the components If we order the options in terms of circles, we get: A(1), C(2), E(3), B(4) and D(5). Of course, we could also have the reverse sequence (starting with D). Either way, option E is in the middle and is thus the answer. Let us try a more complex example. Identify the figure that would be in the middle after the figures are ordered in sequence.

A)

B)

C)

D)

E)

3

2

3

2

3

A) B)

Without knowledge of how to approach these questions, this would be a fairly difficult question. Lets follow the steps: 1. Identify the components of the figures There are two main components in this question the outer shape (which remains constant in all five figures and is thus not part of any pattern); and the inner shape that is either a circle or a smiley face. 2. Look for the 3-2 situation The 3-2 situation is present in this question. We know that the options that hold positions 1, 3 and 5 in the series are (C), (D) and (E) but not necessarily in that order. We now have to find the order. 3. Examine how the components of the figures are moving/changing It is clear that the face changes to the circle and then back again. Furthermore, the position of the face / circle in the larger shape moves. If we draw a simple diagram, it becomes apparent that:

From this diagram, we can see that each of the options takes a different vertice (or corner) of the octagon. 4. Use clues from (3) to try and find a pattern within the components From the diagram, it is clear that the order should be (C), (A), (E), (B) and (D) (the reverse is true also). Thus the middle figure is option E.

SIMILARITIES

What does it test? This type of question tests your ability to:

Find the relationship between an original figure and a transposed figure Apply the relationship found on another figure to find a new transposed figure

The Approach To attack this type of problem, use the following steps:

C) D) E)

D

A

B

C E

1. Identify the different components in the original figure the original components 2. Find the original components in the transposed figure how have they changed? 3. Look for any new components in the transposed figure how to they relate to the original components? 4. Define rules for how each of the components have changed 5. Apply the rules to the components in the question

Lets take a simple example:

as is to is to

Identify the figure that completes the relationship. 1. Identify the different components in the original figure the original components In this example, there is only one original component the shape in the original figure (rectangle). 2. Find the original components in the transposed how have they changed? Comparing the transposed figure to the original component, it becomes apparent that the original component has shrunk in half to get the transposed figure. 3. Look for any new components in the transposed figure how to they relate to the original components? There are no new components. 4. Define rules for how each of the components changed The rule could be defined in this way: the original component is squashed vertically by half to get the transposed figure. 4. Apply the rules to the components in the question The component in the question is the triangle. If we are to apply the same rule to the question, the transposed figure should look like the same triangle but squashed vertically by half. We can see that option B is the right answer. Now lets look at a more complex example:

A) B) C)

D) E)

Identify the figure that completes the relationship.

is to

1. Identify the different components in the original figure the original components Triangle facing up. 2. Find the original components in the transposed how have they changed? Original component (triangle facing up) has become black and has been flipped vertically. 3. Look for any new components in the transposed figure how to they relate to the original components? New components: the large pentagon that encompasses the triangle. 3. Define rules for how each of the components changed The original component changes colour (from white to black) and is flipped vertically to get the transposed figure. In addition, a pentagon is added which encompasses the original component that has now been transposed. 4. Apply the rules to the components in the question

The original component in the question is: Therefore, the parallelogram must be flipped vertically, change colour to black and be encompassed by a pentagon to be the transposed figure. The only answer that corresponds is option A.

CIRCULAR SEGMENTS

A)

B)

C)

D)

E)

as is to

What does it test? This type of question tests your ability to:

Find a logical pattern within figures that are arranged in a circular manner (this can be in a circle, or another shape such as a hexagon)

Extend this logical pattern to find the missing figure This type of question is basically one of the other types of questions (presented above) in a different representation.

Variations 1) Sequence type:

Each segment is similar to one of the figures in the complete the sequence questions. There will be one segment missing. The segments change as they move clockwise or anticlockwise in a sequential manner and your task is to find the sequence or pattern and extend it to find the missing figure. These questions can be answered using the same techniques as those in the complete the sequence questions. Please refer to the Complete the Sequence section for the approach. 2) Opposite-side type:

As can be seen above, in this type of question, there is a pattern between the opposite segments of a figure. These questions are basically the same as the Similarities questions and you should refer to that section for techniques on how to solve the questions.

Lets look at an example: Select the answer that would logically complete the picture.

Firstly, we have to recognise this as one of the opposite-side type questions as opposed to the sequence type questions. Next we have to find the opposites from which we can find a relationship.

Then we think of the opposites like the similarities questions

A)

B)

C)

D)

?

E)

?

is to

? as is to&

is to

As you can see, we get two pieces of information instead of one in the similarities questions. Thus this is an easier type of question! Lets approach it like we did the similarities questions: 1. Identify the different components in the original figure the original components

The inner shapes (there may be one or two of these) and the outer oval. 2. Find the original components in the transposed figure how have they changed? In this case, the oval (one of the original components) is lost when it is translated. Also, the inner shapes change from coloured to white. 3. Look for any new components in the transposed figure how to they relate to the original components? The oval is either lost or gained, depending on which way you look at it.

4. Define rules for how each of the components changed Lose the oval on the outside and change the colour of the inner shapes to white. 5. Apply the rules to the components in the question

Therefore, the answer is option E.

PYRAMIDS

What does it test? This type of question tests your ability to:

Find a logical pattern within the figures that are presented to you in a pyramid type formation Extend this logical pattern to find the missing figure

Variations When items are arranged in a pyramid type fashion, there are a number of ways in which patterns can arise:

Within rows:

Between rows:

Within diagonals:

Between diagonals:

For example: a + b = e b + c = f c + d = g h + i = j etc

j

Addition of units:

i

af

h g

e b

c

d

Note: A unit refers to one of the building blocks of the pyramids (eg. one of the circles in the examples above).

The Approach There are three main steps to solving this type of problem:

1. Identify the components in each of the units 2. Find a pattern between the components 3. Extend the pattern

Lets try a simple example: Identify the shape that is missing from the provided figure.

?

1. Identify the components in each of the units In this question, the units only comprise one component (a shape). The shape can be either a triangle or a square. 2. Find a pattern between the units If we keep in mind the many ways patterns can be found in pyramid type structures, it is clear that the most obvious pattern is between rows. The rows alternate between having a square and a triangle as its unit. 3. Extend the pattern To extend the pattern, we simply realise that there should be all triangles in the second row and thus the missing unit is a triangle. Lets try a more difficult example:

Find the missing figure that fits in the rectangle.

?

Using the three step approach: 1. Identify the components in each of the units In this question, the units are the rectangles. There are three components to the units:

A circle that is always in the middle of the rectangle A bottom-left to top-right line A bottom-right to top-left line

2. Find a pattern We should keep in mind the many ways patterns can be found in pyramid type structures. In this example, there is no obvious pattern between or within rows or diagonals (unlike the previous example). If this is the case, a common pattern is the addition of units. Lets examine adjacent units:

These are the three units in the bottom-left of the pyramid. We should ask ourselves, how can the two adjacent triangles add together to get the one on top? It is evident that in this triad of units, when the two adjacent units are added, the common figures disappear and the other figures are carried through. In this example, the bottom-right to top-left line and the circle disappear because they are in both the two adjacent units. However, the bottom-left to top-right line stays because it is not common to both adjacent units. You should now test this hypothesis on other triads in the pyramid. You will see that it works. 3. Extend the pattern Now the question arises:

If we add the two adjacent units together with the rule mentioned above, both lines and the circle will be carried forward because neither is common to the adjacent units:

ODD ONE OUT

What does it test? This type of question tests your ability to:

Find a common feature(s) between a number of presented figures Identify the one figure of those presented that does not have the feature(s)

The Approach To attack this type of question, you may follow these steps:

?

1. Identify the main features of the presented figures 2. Look for similarities between the main features 3. Find the option that does not share the similarity(s)

Lets take an example: Out of the following five figures, find the one that does not belong with the others

1. Identify the main features of the presented figures The main features of the figures are the balls and the square. Also, there are some balls that are coloured. The square is the same in all of the figures so it is irrelevant to this question. 2. Look for similarities between the main features There are four balls in each figure thus the total number of balls cannot be a distinguishing feature. The only feature that is different between the balls is their colour. 3. Find the one that does not share the similarity(s) On closer inspection, all of the figures except one have two coloured balls this one has to be the odd one out.

NUMBER GAMES

What does it test? This type of question tests your ability to:

Find a logical pattern / relationship between a series of numbers Extend this logical pattern / relationship to find the missing number

These questions require basic mathematical operations. Do not stress if you are not great at mathematics you will only need the basics. The UMAT is testing your logic, not your mathematical ability. There are two main types of number games: 1) Series 2) Relationships Series: The Approach Lets first consider series questions. They can be answered by using this method:

1. Look at the differences between numbers 2. Find a pattern between the differences

Lets try an example:

Find the missing number in the sequence 2, 4, 7, 11, ? Difference: +2 +3 +4 Numbers: 2 4 7 11 The differences are +2, +3, +4. The pattern is obvious: the difference rises by +1 each time. The next difference should be +5 so the next number in the sequence is 16 (11+5=16). Relationships: The Approach You can attack these questions by following these steps: 1. Identify the components of the figures

2. Find a pattern within one of the provided figures using common operations ( , -, , +, x2 etc) 3. Test the pattern on any other figures provided 4. Apply the relationship to the question Note: The best way to complete step 1 is to have a feel for what operations would be used with certain kinds of numbers. There is no hard and fast rule but basic mathematics should have taught you the way operators interact. For example, if you were to get the numbers 1, 24, 25, you would probably think addition or subtraction is the key operator. On the other hand, if you were to get 5, 6, 30, you would probably think multiplication or division. The difficulty increases with smaller numbers because it becomes harder to distinguish between the use

of or and + or . Lets attempt an example: The numbers in each of the figures are linked through a relationship. The relationship is the same for each figure. Find the missing number.

2

0

6

2

2

9

?

1

8

A) 1 B) 2 C) 3 D) 4 E) 5

3

1

4

1

2

2

1. Identify the components of the figures There is a top number, a left number, a middle number, a right number and a bottom number.

2. Find a pattern within one of the provided figures using common operations ( , -, , +, x2 etc) Lets look for a pattern within the first figure. There are a few different possibilities for patterns. Some patterns are:

left top right +/ bottom = middle left 2 top right bottom = middle top left + bottom right = middle top + left + right + bottom = middle etc

You need to perform this step quickly to find some possibilities and then move to the next step. 3. Test the pattern on any other provided figures The next stage is to test our hypotheses on the second figure. Only the last of our possibilities works. 4. Apply the relationship to the question Now we apply the rule: (top + left + right + bottom = middle) to the figure in question. When we do this, the answer is apparent: 3 or option C. Now try this question for yourself. The numbers in each of the figures are linked through a relationship. The relationship is the same for each figure. Find the missing number.

30

21

3

45

20

5

23

7

?

A) 2 B) 3 C) 4 D) 5 E) 6

Answer: C Explanation: Take away the square of the middle number from the left number to get the right number.

MATRIX

What does it test? This type of question tests your ability to:

Find a logical pattern in a matrix (can be 3x3, 4x4, 5x5 etc)

Extend this logical pattern to find the missing box The Approach In this type of question you should:

1. Look for patterns across rows 2. Look for patterns down columns 3. Define the pattern 4. Extend the pattern to find the missing figure

Lets try an example: Identify the figure that should fit in the missing square.

. Look for patterns across rows

cross a row, there is a small black circle, a big white cross and a small white cross within a big white circle.

here appears to be some kind of pattern here. It seems that the big white cross in column B becomes a small

. Look for patterns down columns

olumn A has all small black figures

large white figures

. Define the pattern

he pattern was the most promising within rows.

A B C

1

2

3

1 A Tblack cross in column C. Similarly, the small black circle in column A becomes a big white circle in column C. 2 CColumn B has all large white figures Column C has all small black figures in 3 T

A) B)

C) D) E)

We could define it as Figures in column A move to column C and change colour from black to white and size from small to large. Figures in column B move to column C and change colour from white to black and size from large to small. 4. Extend the pattern to find the missing figure When we extend the pattern, the small black triangle in the last row and column A should become a large white triangle in column C. Also, the large white diamond in column B should become a small black diamond in column C. Thus option E is the right answer. Lets try another example:

Identify the figure that should fit in the missing square.

1. Look for patterns across rows Across a row, there is always one small black diamond, one small black circle, one cross, one plus, one large white circle and one large white square. 2. Look for patterns down columns Down each column, there is the same situation as across a row (above). 3. Define the pattern The pattern is that across rows and down columns, there must be one small black diamond, one small black circle, one cross, one plus, one large white circle and one large white square. 4. Extend the pattern to find the missing figure In the third row, the missing figures are a large white circle and a small black diamond. Thus (B) is the right answer.

A)

B)

C)

D)

E)

A B C

1

2

3

1. Introduction to Section 3.pdf2. PATTERNS AND SEQUENCES.pdf