INTRODUCTION TO SECTION 1

STRUCTURE AND CONTENT Section 1 of the UMAT has 44 questions and you will have 65 minutes in which to complete them. That is approximately 88-89 seconds per question. The questions can be broadly divided into:

Logical reasoning questions Problem solving questions

Many of the passages in Section 1 are medicine / science / research-based, but you will not need any prior knowledge to answer the questions. All of the information you need will be provided in the question booklet. However, a basic understanding of research methods is useful (this guide covers such concepts). Many of the questions involve data presented in tables, graphs and / or diagrams. Therefore, a section in this guide is dedicated to data interpretation. Some questions are individual i.e. only one question is based on a particular stimulus. Other questions will be grouped into units and will be based on a larger amount of information / data. To aid learning, this guide is divided into various sections. Remember, however, that in the UMAT questions will often require you to combine skills discussed. For example, you may need to interpret data and research methods in a logical reasoning question.

WHAT DOES IT TEST? According to the UMAT booklet, section 1 tests: Your ability to comprehend, draw logical conclusions, reach solutions by identifying relevant facts, evaluate information, pinpoint additional or missing information, and generate and test plausible hypotheses. Essentially, section 1 tests how well you can solve problems and how fast you can interpret and critically analyse data and information.

HOW IS IT RELEVANT TO BEING A HEALTH PROFESSIONAL? Logical and critical thinking is a vital skill for any health professional. As a health professional, you will be bombarded with information from various sources, for example, government departments, the media, research papers and pharmaceutical companies. You will need to be able to critically appraise data, arguments and new research every day in order to provide patients with the most accurate, effective and up-to-date treatment and advice. Section 1 tests your capacity to do this. It is important to note that the fields of medicine, dentistry and other health sciences are variable and ambiguous there is often no right answer or best treatment that will apply to every patient. Similarly, section 1 will include questions where alternatives are often imperfect. You will need to select the best answer in each case. Problem solving is the basis of any health professionals work. As a health professional, you will need to gather information about the patients medical history, presenting complaint and other pertinent information and use it to develop treatment plans. Often patients will present with multiple and multifaceted problems, which complicates the picture further. Often also you will need to interpret information and data quickly to make a decision. Section 1 tests these skills.

WHAT SHOULD I EXPECT? There are very few easy questions in Section 1 and many people find this section the hardest to finish. However, keep in mind that you can still get an excellent score if you do not finish every question perfectly. Your aim should be to complete as many questions as possible as accurately as possible. Section 1 questions are the first UMAT questions you will be exposed to. Many people find that the first few questions of section 1 are very difficult, possibly because they have not yet got into the UMAT mindset. It is important not to get flustered, but realise that the questions will get easier. Do not be afraid to skip the first question if you find it difficult. The major difficulty of section 1 lies not in the amount of information, but complexity of the passages. This is why mere speed reading will not help you. Woody Allen once said: I took a speed-reading course and read War and Peace in twenty minutes. It involves Russia! This illustrates that it is not just about reading quickly, it is about thinking quickly.

TEN CRUCIAL TIPS FOR SECTION 1 1. The most crucial strategy to remember for section 1 questions is to approach each question with the

aim of

Understanding the stimulus, rather than remembering parts of it

Questions will require you to use (manipulate, rearrange, comprehend, analyse) information. Unlike 'reading comprehension' style questions, they will not simply require you to parrot back bits of information.

2. Use methods such as underlining, annotating and drawing diagrams to ensure that you actively

interpret the information. In section 1 you may also find it helpful to visualise information.

3. It is vital to realise that the UMAT is testing your skills, not your knowledge, so you must

Avoid bringing in your own biases

You should analyse what is presented to you, not anything from your previous knowledge (except the strictly factual, such as the meaning of scientific terms).

4. Read carefully and think quickly. Do not simply skim over parts of the stimulus.

5. Realise that you often need to invest some time in interpreting a stimulus. In year 12 exams, you

often either know the answer or do not. In the UMAT, you need to think about the material. If you slow down and consider the material, it is less likely that you will have to read the information over and over again. Try to crack the question open the first time.

6. Previewing the question stem is particularly important for section 1 questions. This will help you sift through the not-so-relevant information and pull out that which is pertinent.

7. Subvocalising (reading individual words in your mind) can be very useful, especially with more complex stimuli. It allows you to emphasise certain words and aids understanding. Contrary to popular belief, it is usually not a hindrance.

8. When you are looking for the best answer (usually logical reasoning / critical thinking questions), make sure you read and carefully consider all the options. When you are looking for the right answer (usually problem solving questions) there is no need to consider other options. As soon as you arrive at the answer, move on.

9. Learn to deal with ambiguity! Most of the time you will not be presented with a perfect answer, and more than one answer may seem correct.

10. Problem solving questions can be solved using various techniques. Make sure you are familiar with these techniques and know when to apply them.

LOGICAL REASONING

INTRODUCTION In logical reasoning questions, you will be presented with a series of statements (with or without additional data) and will be asked to select the response that can be most logically drawn from the information provided. Keep in mind that a response does not have to be perfect. In fact, most conclusions have some degree of faulty reasoning involved. The test-writers are simply asking you to choose the best possible answer.

CRASH COURSE IN LOGICAL REASONING

What is logic?

Logic is concerned with distinguishing correct reasoning from reasoning that is incorrect. It is the cognitive process we go through to discover the truth. We use logic subconsciously every day in evaluating claims made by the media, advertising and people around us. When you hear something that employs incorrect logical reasoning, you may think to yourself that doesnt sound right or that doesnt necessarily follow. The UMAT tests your ability to use these skills thoroughly, quickly and strategically in the context of a strictly timed, multiple-choice test.

As a health professional, it is vital that your skills in logical reasoning are highly developed. The job of a health professional is ultimately to discover truth and avoid error, which is the essence of logical reasoning.

What is logic applied to?

We know that logic is a way of discovering the truth. But what are these things that we call true and false? These things may be:

Statements Sets of statements Arguments

Statements

A statement is a claim made by a person. For example, a claim may be almost one in four Australians aged 25 years or older has diabetes. Strangely enough, in logic (and in the UMAT) we do not worry whether a particular statement is factually true or false. Instead, we are concerned with whether the statement is logically true or false. While we do not need to go into details, there are two main criteria for judging whether a statement is logically true: 1. Statements must be either true or false (there is no middle ground) 2. No statement can be both true and false For the purposes of the UMAT, all you need to know is that you should accept each statement as fact and proceed accordingly. You should not dispute the factual accuracy of a statement, or bring in your own opinions, you should proceed as if each statement were true.

Sets of statements

A set of statement is a group of statements that we have decided to view together as one unit. Unlike single statements, we never evaluate sets of statements as logically true or logically false. Instead, we only evaluate them in terms of whether they are consistent or inconsistent. What we mean by consistent is whether all the statements in the set are true together. For example, the following set is consistent:

Jake loves Michelle Michelle loves Bob Bob loves Jake A set is inconsistent if it is impossible for all the statements in the set to be true together. The following set is inconsistent: Jake is taller than Michelle Michelle is taller than Bob Bob is taller than Jake Why is this useful? Sometimes want to know if all the claims someone has made could be true. If we discover that they could not all be true together, we know that at least one claim they have made is false.

Arguments

The main concern of logic is how statements are connected with each other. Therefore, we usually consider a group of statements that are related in some way. Compare this with sets of statements, which are isolated units. Arguments are statements that are related to each other in a very precise manner. Because arguments are such as major part of the UMAT, we will consider them in more detail in the following section.

Arguments

An argument in logic is not the same as people arguing. In logic, an argument is a series of statements, where one statement (the conclusion) follows from the others (the premises). We call the single statement that is being argued for the conclusion of the argument, and we call each statement that provides evidence to establish the conclusion a premise of the argument. (Note that in logic the term 'conclusion' does not necessarily mean a 'summary statement' eg. the conclusion of an essay.) It is often helpful to identify conclusions and premises to orient yourself. Premises usually appear first and conclusions often appear later. Certain words and phrases can also provide cues. 'Because', 'since' and 'it has been found that' suggest premises, and phrases such as 'therefore', 'it follows that', 'thus' and 'so' alert you to conclusions.

The transition or movement from premises to conclusion (the logical connection between them) is the inference upon which the argument relies.

There are two main types of inference:

Deductive inference

When the truth of an arguments premises guarantees the truth of its conclusion, it involves a deductive inference. The conclusion follows with certainty from the evidence/premises presented (assuming the evidence is correct). Deductive reasoning holds a very high standard of correctness.

Heres a basic example:

Premises: All dogs are mammals. All mammals are warm blooded.

Conclusion: Therefore, all dogs are warm blooded.

In this case, if we assume that the premises are right, the conclusion must be right. The premises provide absolute and complete support for the conclusion. This is a deductive argument.

Inductive inference

When the truth of an arguments premises makes it likely or probable that its conclusion is also true, it is an inductive inference. The standard of correctness for inductive reasoning is much more flexible than that for deduction. An inductive argument succeeds whenever its premises provide some legitimate evidence or support for the truth of its conclusion. Take a look at this one:

Premises: Johns mailbox is empty. The door to Johns house is unlocked.

Conclusion: Therefore, Johns wife is probably home. This argument is an inductive argument. The conclusion does not follow with certainty it is not guaranteed. The premises might be correct, but the conclusion is not necessarily correct. The conclusion does seem likely, but it might be possible that Johns son is home instead, or John didnt get any mail and forgot to lock his house. Compare this with deductive arguments, where the conclusion necessarily follows from the premises.

In the UMAT, you will often be asked to select the option that can be concluded with most certainty from the information provided. Therefore you should look favourably upon answers that use deductive reasoning to reach the conclusion and be more wary of answers that rely on inductive reasoning.

FLAWS IN LOGICAL REASONING

In the UMAT, you are most often expected to select which conclusion follows most logically from the information presented. In order to do this, you need to have a good understanding of common errors in logic. This section describes those that most commonly arise in UMAT.

Assumptions

An assumption is a premise, usually one that is hidden or unstated. It is often something we assume to be true, so we see no point in stating it explicitly. However, it is important to avoid making assumptions in the UMAT, especially those that are unwarranted. Lets try a simple example. Robbery is an action that hurts another person. Therefore, robbery is immoral. Let's start by dentifying the components of the argument:

Premises: Robbery is an action that hurts another person.

Conclusion: Therefore, robbery is immoral. Assumption: (Actions that hurt others are immoral)

It seems unnecessary to state Actions that hurt others are immoral because most people believe this statement to be true. However, some assumptions are more questionable. Try to identify the assumption(s) in the following passage:

The governments decision to require doctors to prescribe generic alternatives to brand name drugs, when an alternative is available, is an excellent one. Now patients will be able to save a lot of money and yet get the same medical treatment.

The most important assumption here is that generic alternatives will have the same effect as brand name drugs. Otherwise patients will not pay less for the same treatment. But there are other assumptions, for example, that the difference in cost between brand name and generic drugs is sufficient to make a significant difference (so patients will be able to save a lot of money).

The key point is to be wary of assumptions and avoid making assumptions when you select your conclusion.

Scope

The scope of the argument is the limits to what it says. Consider the statement:

Mrs Jones occasionally suffers from migraine headaches after consuming red wine. From this statement alone, you cannot conclude that Mrs Jones always has migraine headaches after consuming red wine. To determine the scope of the argument, you often need to look for key qualifiers. Qualifiers may be words like some, none, never, always, everywhere and sometimes. These words can play a critical role in precisely specifying the facts to be used in your reasoning.

Qualifiers can also be words such as cities (not countries) and vehicles (rather than just motorcycles or cars). For example:

Statement 1: When an otherwise healthy person has a bacterial infection, the white cell count always increases. Statement 2: When a person has an infection, the white cell count always increases.

Statement 2 cannot be determined from statement 1, since it is outside the scope of the argument. Firstly, statement 1 refers to otherwise healthy [people] only. Secondly, it refers to bacterial infections, not infections in general (which could, for example, include viral, fungal and parasitic infections).

Take a look at this argument:

No other major department store offers you a low price and a 14 month warranty on parts and labour on this special edition of the Z-51 Panasonic television.

At first, this advertisement sounds pretty impressive. But when you pull it apart, the claim being made is limited. First, the advertisement is restricted to a comparison with department stores, and major ones at that. It is possible that a small shop or an electronics store has the same deal. Second, other stores may offer a better deal on the product, with a lower price or longer warranty, and the claim would still stand so long as no one else offered exactly a 14 month warranty. Finally, the advertisement is restricted to a special edition of the television.

This example illustrates how the scope of an argument can be dramatically limited by only a few key words.

When answering a question in the UMAT, choose a response that stays within the scope of the argument. One way of doing this is to favour words like could, perhaps and may over more definitive words such as must, only and will.

Further, it is important to pay special attention to the question stem, as this may limit the scope of the question. For example:

From the information above it can be concluded that in the city of Melbourne in 2006

Here the conclusion needs to (1) be valid, and (2) be valid for the city of Melbourne in 2006.

Personal bias

In the UMAT, it is important that you consider the information presented in an objective manner. It is vital that you do not bring in your personal preconceptions. This is important in work as a health professional, when you must avoid your beliefs and views influencing your decisions.

Consider this example:

Every day, areas of rainforest 50 times the size of the MCG are cleared. At this rate, there will be little rainforest left in 30 years.

In this case you cannot definitively conclude that the author wants to find a solution to this problem or even thinks it is a problem. You (along with most people) probably believe rainforest clearing to is highly undesirable, and are used to reading articles that argue that it is undesirable. However, this particular author may be from a logging company and believe such action is a positive move. It is important not to assume that the author shares the same views as you or the majority of citizens.

You must not bring your preconceptions and biases into the UMAT.

Correlation and causation

A cause-effect relationship is the connection between an actions disturbance (cause) and its effect on the environment. This relationship lies at the heart of medical research, which aims to find links between certain causes (eg. disease, drugs, diet, exposures) and certain effects (eg. illness, disability life-expectancy). This concept is tested time and time again in the UMAT.

In every day life (and in the UMAT) it is common to find instances where there is a logical flaw related to the cause-effect relationship. The two most common flaws are:

Correlation is erroneously equated with causation The cause-effect relationship is confused

Equating correlation with causation

If you have studied psychology or research methods, you will be familiar with this type of flaw. For those who have not, it basically means that if two things happen together, it does not necessarily mean one causes another. For example:

The life expectancy of Aboriginal people is low. Therefore, being Aboriginal causes people to die early.

Here, two phenomena (being Aboriginal and having a low life expectancy) are joined in a cause-effect relationship that may not exist. Low life expectancy among Aboriginal people is likely to be caused by other factors, such as social issues, poor health facilities and substandard living conditions, not the pure fact of being Aboriginal.

Confusing the cause-effect relationship

In the following example, the cause-effect relationship is reversed:

Every time the doorbell rings there is someone at the door. Therefore, the doorbell must call people to my door.

Following is another example:

People who have high blood pressure are more likely to suffer stroke than those with normal or low blood pressure. Therefore, stroke increases the likelihood of having high blood pressure.

In this example, the cause-effect relationship is fallaciously confused. The cause is actually high blood pressure, and the effect is stroke, not the other way around.

Generalization

In everyday life, it is common to find examples of generalization. Human beings have a natural tendency to classify objects and people to make the world simpler to understand. However, in this process some of the complexity and subtlety of life is lost. One example of over-generalization is stereotyping, which involves describing a phenomena and then fallaciously applying it to an individual case. For example:

Most people cry when they start school, therefore my child will cry when he starts school.

Other examples of over-generalisation may involve generalising the results of a survey or experiment to a population. There is nothing wrong with this, as long as the sample is representative of the population and the investigation surveyed a sufficiently large and diverse group. For example:

Every household interviewed on this block responded that crime is a serious problem in this area. Therefore, residents in this neighbourhood believe that crime is a serious problem here.

The problem with this argument is the sample group (those living on this block) is not necessarily representative of the population to which the results are being generalised (this neighbourhood).

In the UMAT, be wary of responses that over-generalise.

Irrelevance

If something is not discussed in a passage, chances are it is incorrect. Although it is usually quite easy to spot an option that is totally irrelevant, it becomes more difficult when time is limited and you only have time to skim over the passage. Other people who get caught out on irrelevance are those who do not leave their personal knowledge and biases behind and are therefore caught out by distracter that include material not discussed in a passage. For example:

The Australian sharemarket is expected to open lower for the last week of the financial year, after the price of oil neared a record $US60 a barrel. Fears about rising energy costs hit Wall Street on Friday, amid fears that the high price of oil could also damp consumer spending and in turn hamper economic growth. Current world oil prices suggest that the average petrol price is heading to $1.20 a litre. But for the economy as a whole it is not so bad to the extent that Australia benefits as a net energy producer. Energy-related stocks could get a lift if oil continues to march higher, but other sectors, particularly airlines and transport, could suffer.

What can be concluded from the passage?

Distracter: Middle East tensions have contributed to the rise in petrol price

The distracter provides a plausible explanation for oil price rises and one that may be true. However, the passage has nothing to do with Middle East tensions. It is amazing how many people would pick a distracter such as this.

You should aim to quickly identify irrelevant distracters and discard them.

Lack of proof does not disprove

It is important to realise that the mere fact that there is not enough evidence for something does not mean that it is untrue. For example:

A recent study failed to find an association between smoking less than five cigarettes per day and heart disease. Therefore, smoking moderate numbers of cigarettes is safe for the heart.

This argument is unsound for many reasons, one of which is that just because this study has found there is no increase in the risk of heart disease, does not mean the association doesn't exist. Maybe the study was carried out inaccurately, maybe there weren't enough participants to pick up the association, maybe the measures used were not adequate... the list goes on.

Circular arguments

In a circular argument, the premise is used to prove the conclusion and the conclusion is used to prove the premise. For example:

I am not lying. Since I am not lying, I am telling the truth.

Here, the argument is assuming the very thing that it aims to prove that the author is telling the truth. These arguments have no substance behind their reasoning and are usually easy to identify.

Worked examples

Worked example 1

Early this century, the doctor was a comforter, expected to predict the progress of a disease or to help the patient cope with a struggle or imminent defeat, but not to work miracles. This situation changed with the coming of such drugs as penicillin, insulin, and antibiotics. Add the rapid technological developments of contemporary medicine, and we find the medical professional under pressure to defeat every disease, correct every physical defect, and maximize the patients quality of life. Society no longer is satisfied with the dedicated efforts of human beings; it now demands perfect performance of technicians as foolproof as the most sophisticated machines.

Which one of the following can be most reasonably inferred from the passage?

A) The patient today expects results rather than sympathy from his or her physician B) Medical incompetence is more widespread today than it was in the early twentieth century

C) As medical technology has advanced, health care workers have become less sensitive to the feelings of their patients

D) Because doctors cannot meet the often unrealistic expectations of their patients, they are subjected to an ever-increasing number of malpractice suits

Answer: A

Solution: The question stem asks you to make a reasonable inference from the passage. The passage is a brief history of societys changing view of physicians. Option A is essentially a summarized version of the idea expressed in the last sentence of the paragraph. The competence of physicians is not discussed in the passage (i.e. it is irrelevant) and therefore option B is not a valid conclusion. Option C goes too far. There is no suggestion that healthcare workers have become less sensitive; the emphasis of the passage is on the patients expectations. Option D is beyond the scope of the passage, as malpractice suits are not mentioned in the passage.

Worked example 2

Chocolate is derived from the beans of the tropical New World tree Theobroma cacao. When chocolate arrived in Europe around 1500, it was consumed only as a hot drink. In the mid-1800s, however, the Swiss invented the first method for producing it in a solid edible form. Today, millions more kilograms of chocolate are

produced for eating than for drinking. Which of the following can be inferred from the statements above?

A) Today, Theobroma cacao is grown only in the tropical New World

B) The number of kilograms of chocolate made for eating today is greater than the number of kilograms of chocolate that were made for drinking during the 1800s

C) Chocolate was not consumed in a solid form in the New World in the 1500s

D) If the Swiss had not invented a method for producing chocolate in a solid edible form, chocolate would not have become as popular as it is today

Answer: C

Solution: The stimulus tells us that Theobroma cacao is a tropical new world tree, but we cannot infer that this tree only grows in the tropical New World. The tree might exist in other countries. We know from the passage that more kilograms of chocolate are produced for eating than for drinking, but we have no information about how the amount of drinking chocolate in the 1800s compares to the amount of solid edible chocolate produced today. Although we may believe (from our own knowledge or intuition) that option B is true, it cannot be inferred from the passage. It is merely an assumption. Option C is valid. If the Swiss invented the first way to produce solid edible chocolate in the 1800s, then solid edible chocolate was not consumed anywhere in the 1500s. Option D is entirely unsupported by the passage. Just because the Swiss made chocolate into a solid, does not mean that nobody else would have done so if the Swiss had not. This is another unwarranted assumption.

SUMMARY OF STRATEGIES FOR LOGICAL REASONING Accept every fact in the stimulus as true. Only eliminate an answer option if a flaw in logical reasoning can be found. Use only the information in the passage as the basis for accepting or rejecting any response choices. Do not allow any outside knowledge to influence your thinking and do not make assumptions.

Pay careful attention to the question stem, especially for thought reversers (eg. cannot, not)

Pay special attention to words in the stimulus that identify the scope of the argument (eg. all participants , none of the countries). Also pay attention to words and statements in the question stem that limit or expand the scope of the question (eg. 'always true', 'may be false'). In general, be wary response choices that contain absolutes that are extreme such as all or none. They require a much higher level of evidence to be valid.

Be wary of answer options that involve

- Assumptions - Going beyond the scope - Personal bias - Confusion of correlation and causation - Over-generalisation - Irrelevance - Circular arguments If you encounter a question that is difficult to understand, try drawing diagrams and breaking it up into parts.

Briefly try to predict an answer (if possible).

Read all responses carefully before selecting the best answer.

PROBLEM SOLVING

WHAT IS IT?

Problem solving is a complex activity that involves the manipulation of information to arrive at a solution. There are no strict rules for solving problems, and tests such as the UMAT may present problem solving questions in a number of forms. However, general techniques for approaching problems can facilitate the problem solving process. Such techniques are discussed below. Note that problem solving questions in the UMAT do not require you to have knowledge of complex mathematics or other specialised skills.

GENERAL APPROACH

Following is a series of techniques that are a useful general approach in answering problem solving questions.

Preview the question stem so you know what you are looking for

If the problem is complex, break it up into manageable parts

Identify the components of the problem

Assign the symbols to various parts of the problem

Note down what you know - identify the conditions

Determine the implications of conditions to find other hidden conditions

Eliminate answers

Examine remaining answers for clues

Draw a table or diagram to help organise information

Use trial and error We will use the following example to work through parts of this guide:

Robert, James, Henry and Philip are sprinters. Philip can outrun Henry, James will always beat Philip in a race and Robert will always be beaten by Philip.

COMPONENTS OF THE PUZZLE

The Units The units are the objects, people or events that are bound by rules in the problem solving question. In the example above, the units are:

Robert James

Henry Philip

The other units in this scenario are the positions of the sprinters:

Position 1 Position 2 Position 3 Position 4

The Conditions If we consider the problem solving questions a game, the conditions of the problem are the rules of the game. In the example above, the conditions are as follows:

Philip can outrun Henry James will always beat Philip Robert will always be beaten b y Philip

It is important to identify the rules of the problem and understand how they interrelate. Therefore, time should be spent understanding the rules, not reading over them without analysis.

ASSIGN SYMBOLS TO THE UNITS OF THE PROBLEM In this case we could do the following:

Robert R Position 1 1 James J Position 2 2 Henry H Position 3 3 Philip P Position 4 4

You should use whichever symbols / letters / numbers that you feel comfortable with but ensure that each unit has a unique symbol.

NOTE DOWN WHAT YOU KNOW In problem solving questions in the UMAT, you will often be presented with large amounts of data. It is important to note these down in a simple, easily understandable form. In our example, we know that

P>H (P is faster than H) J>P (J is faster than P) P>R (P is faster than R)

Notice the use of shorthand here. It doesnt matter what kind of shorthand you use as long as it is clear and works for you.

IMPLICATIONS Examine the conditions that you have noted and look for any implications, or hidden rules. Usually, these appear when the same unit is apparent in different conditions. For our example:

P>H and J>P, therefore J>H J>P and P>R, therefore J>R

This can be presented in another form: 1. J 2. P 3. H, R

ELIMINATE ANSWER CHOICES WHICH CONTRADICT CONDITIONS Look at the options in the question to determine whether any of them contradict the conditions weve established. Lets look at our question:

Which of the following can be concluded? A) Henry is faster than Philip

B) Robert is faster than Henry

C) Henry is faster than Robert

D) James is faster than Henry

It is best to start the elimination process with your most basic conditions, as stated in the question.

P>H (P is faster than H) J>P (J is faster than P) P>R (P is faster than R)

Option A clearly contradicts one of our basic conditions (P>H), and can therefore be eliminated. Now lets look at the conditions we made based on implications.

J>H J>R

From this, we can see that option D is correct.

DRAW A TABLE OR DIAGRAM

Drawing a diagram Drawing a diagram is one of the most useful techniques for problem solving and can dramatically clarify a seemingly difficult question. For example:

Some toppies are loppies; all soppies are loppies; no soppies are toppies.

I. Some toppies are not loppies II. Loppies are either soppies or toppies III. Some soppies are not loppies

Which of the statements above can be concluded?

A) I only B) II only C) III only D) I and II only

Answer: A Solution: In this situation, a Venn diagram is very useful. An example of one is shown below:

Loppies

Toppies

Soppies

The question now becomes very simple. From the diagram, it can be seen that there are some toppies that are not loppies (I). It can also be seen that there may be loppies that are neither toppies or soppies (so II is wrong). Further, all soppies are loppies (so III is wrong). Venn diagrams are often useful tools in the UMAT. Venn diagrams are used for questions when sets of objects have overlapping characteristics. The basic idea is to draw regions representing different sets, with interlocking regions representing overlap. In the example above, since some toppies are loppies, the toppy region and loppy region should overlap. Other diagrams, such as the simple diagram in our previous example: 1. J 2. P 3. H, R can also be useful in organising information. Drawing a table Drawing a table may also be helpful. For example,

Bob, Kelly and David each have different occupations. One is a builder, one is in business and one is a journalist. Kelly hates writing and would never be a journalist. The builder is male. David does not like physical labour, and is not a builder.

Which of the following shows the occupations of the three?

Kelly Bob David

A) Builder Journalist Businessman

B) Businesswoman Builder Journalist

C) Businesswoman Journalist Builder

D) Journalist Businessman Builder

Answer: B Solution: This question may be solved using a table. If we take the first two rules:

Kelly is a journalist The builder is male

And fill in the following table?

Kelly Bob David

Journalist NO

Builder NO

Businessperson

Therefore, Kelly must be the businessperson. Logically then, no one else can be the businessperson:

Kelly Bob David

Journalist NO

Builder NO

Businessperson YES NO NO

The last rule, David is not the builder completes the table:

Kelly Bob David

Journalist NO NO YES

Builder NO YES NO

Businessperson YES NO NO

From this, we can clearly see that option B is correct. A final note on diagrams and tables When a question is confusing you, you should always try and draw a diagram or table. You should use your judgement in deciding which one is best.

TRIAL AND ERROR Trial and error is often seen as a last resort: a technique that people use only when they cannot answer a question using logic. However, some questions are most easily solved using trial and error. For example:

Four people make the following statements: Adam: Ben is the winner

Ben: Cassie is the winner

Cassie: I am not the winner David: I am not the winner If only one of these statements is true, then who is the winner?

A) Adam B) Ben C) Cassie D) David

In this question, trial and error is probably the easiest method to use. We'll take each alternative, in turn, to be true and see what would follow:

1. Adam is the winner This would make Adam's statement false, Ben's false, Cassie's true and David's true. Thus this is the wrong answer (2 truths, 2 falses) 2. Ben is the winner This would make Adam's statement true, Ben's false, Cassie's true and David's true. Thus this is the wrong answer (3 truths, 1 falses) 3. Cassie is the winner This would make Adam's statement false, Ben's true, Cassie's false and David's true. Thus this is the wrong answer (2 truths, 2 falses) 4. David is the winner This would make Adam's statement false, Ben's false, Cassie's true and David's false. Thus this is the right answer (1 truth, 3 falses)

Here is another question can be answered by trial and error. If only one of the contestant's statements is false, then who is the winner?

A) Adam

B) Ben

C) Cassie

D) David

We can use the working from the previous problem to solve this, we can see that if there is to be 3 true statements and 1 false statement, then Ben must be the winner.

FIGURES & STATISTICS

Some section 1 questions may require you to interpret and manipulate statistics, ratios, percentages and proportions. While the calculations themselves will not be challenging, and will not require the use of a calculator, the manipulations may be difficult.

Following are some general strategies.

Be clear what the numbers refer to. Does the figure relate to the whole population, a subset of the population, or something else? If you are not clear what the number refers to, you will have difficulty answering the question

Look for short cuts. Remember you will not be required to engage in complex mathematics. For example, 54% is approximately

Calculate only what you have to. You can spend several minutes calculating everything perfectly, but often it is not necessary and is simply a waste of time. Examine the answer alternatives to see how accurate you have to be.

It may be helpful to assign symbols to unknown values eg. x, y. This can help when you manipulate the data

Let's go through a worked example.

Houses in the city of Westland have a high rate of termite infestation. In response, many home-owners have purchased TermOut, a chemical which prevents houses from becoming infested. Westland contains 20,000 houses, and 60% of those are protected with TermOut.

Of houses protected with TermOut, only 1 in 2000 will become infested in the following year. For unprotected houses, 16% will become infested in the following year.

7.1 Question

In the statement An unprotected houses is X times as likely to become infested in the following year compared to a protected house, what is the correct value for X?

A 16

B 320

C 16,000

D 32,000

7.1 Worked solution

Although this may seem like an easy question at first, it is easy to get mixed up with numbers such as those in this question (especially when there is significant time pressure). We should try to explain it to ourselves in statements of fact and make all of the percentages/numbers/fractions in one format. I.e:

1. For houses protected with TermOut, 1 in 2000 will become infested in the following year.

2. For unprotected houses, 16% will become infested in the following year. This is equivalent to [(16/100) x 2000] = 320 in 2000 houses.

When we put the ratios in the same format (i.e "... out of 2000 houses") it becomes easy to compare and thus answer the question. Thus an unprotected house is 320 times as likely to become infested as a protected house (answer B).

7.2 Question

How many of Westlands houses will typically become infested in the following year?

A 1,280

B 1,286

C 3,200

D 3,210

7.2 Worked Solution

Once again, let's firstly identify the relevant pieces of information in the passage:

1. Westland has 12,000 houses (60% of 20,000) protected with TermOut.

2. Westland also has 8,000 houses (the remainder) that are not protected with TermOut.

3. Of the protected houses, only 1 in 2000 will become infested in the following year.

4. Of the unprotected houses, 16% will become infested in teh following year.

Using (1) and (3), we can see that (1/2000) x 12000 = 6 infestations. Using (2) and (4), we can see that (16/100) x 8000 = 1280 infestations. Therefore, the total number of infestations will be 1,280 + 6 = 1,286 (answer B).

Unfortunately, some people are allergic to TermOut, and experience allergic reactions of varying severity. In most cases, they are unable to use TermOut in their house, although in some cases (if the reaction is sufficiently mild) TermOut can still be used. Assume that 1 in 8 households includes a person who is allergic to TermOut, and that 1 in 10 of these households nevertheless uses TermOut to protect their house.

Question 7.3

The percentage of houses that are unprotected and include an allergic occupant is closest to?

A 5%

B 8%

C 10%

D 11%

7.3 Worked Solution

Information that is relevant:

1. 1 in 8 houses, or 12.5% includes an allergic occupant.

2. Of these, 9 in 10 are unprotected.

Therefore, (1/8) x (9/10) = 9/80. To change into a percent, multiply by 100. Therefore, 900/80 = 90/8 which is around 11% (answer D).

Question 7.4

How many houses in Westland are unprotected but do NOT have an allergic occupant?

A 250

B 5,500

C 5,750

D 7,000

7.4 Worked Example

1. There are 20,000 houses in Westland

2. 2,500 (1 in 8) of these have occupants who are allergic to TermOut.

3. Of these, 250 (1 in 10) are protected with TermOut.

4. That leaves 2,500 250 = 2,250 houses that are unprotected and DO have an allergic occupant.

5. There are a total of 8,000 unprotected houses in Westland (of the 20,000 houses, 60% are protected).

It follows that 8,000 2,250 = 5,750 houses are unprotected and DONT have an allergic occupant (answer C).

Because a termite infestation in a given house represents a threat to other nearby houses, the mayor of Westland decides to offer a $300 cash payment to anyone who protects their house with TermOut. His advisors believe that this will result in 20% of currently unprotected houses becoming protected.

Question 7.5

Assuming that the mayors advisors are correct, what percentage of Westlands houses will remain unprotected?

A 8

B 20

C 32

D 80

7.5 Worked Solution

1. Initially, Westland had 12,000 protected houses (60% of 20,000) and 8,000 unprotected houses (the remainder).

2. Another 1,600 houses (20% of the currently unprotected houses) will become protected after the cash payment is offered

Therefore, there will be 8000 - 1600 = 6,400 unprotected houses after the cash payment is offered. That is, [(6400/2000)x100]= 32% of Westlands houses will remain unprotected.

DATA INTERPRETATION

INTRODUCTION In the UMAT, you are unlikely to be asked to simply read information from a graph or table. However, many UMAT questions require you to analyse data that is presented in tabular, graphical or diagrammatical format. Data interpretation questions test your ability to extract relevant information and apply that information to solve problems, draw conclusions or make interpretations. These questions will not require you to have extensive mathematical skills but may require you to have basic skills in estimation, percentages and simple calculation.

GENERAL STRATEGIES

Look at the data from a birds eye perspective what is the stimulus as a whole describing, examining, telling you?

Identify headings, labels and axes eg. dates, time periods If there is more than one graph / table / diagram, ask yourself: how are they interrelated? Is the data provided as percentages or raw data? What are the units?

Look for annotations, small print, etc Can you make any immediate connections or interpretations from the data? Can you identify any

trends? Following is an example of some data that is presented to you in tabular format.

Life Expectancy in 2001 Total population Males Females

WHO* Member State At birth 2000

At birth 2001

At birth

At age 60

At birth

At age 60

1 Afghanistan 33.8 33.4 31.1 4.9 35.7 8.7 2 Albania 58.6 58.7 55.9 8.8 61.5 12.7 3 Algeria 57.5 57.8 55.8 10.3 59.9 12.2 4 Andorra 70.8 70.9 68.8 15.8 73.0 18.5 5 Angola 28.9 28.7 25.7 5.8 31.7 9.2 6 Antigua and Barbuda 59.7 59.7 56.9 10.3 62.6 13.4 7 Argentina 62.9 63.1 60.6 11.9 65.7 15.1 8 Armenia 57.9 58.3 55.4 9.2 61.1 12.2 9 Australia 71.4 71.6 70.1 16.4 73.2 18.8

10 Austria 70.7 71.0 68.9 15.7 73.0 18.5 * WHO: World Health Organisation ** This is an excerpt from the full WHO listing which comprises of 191 member states

Look at the data from a birds eye perspective The data describes:

The first 10 member states of the WHO (in alphabetical order) Life expectancy in the year 2001

The total population statistics as well as only male and only female Life expectancy at birth and life expectancy at age 60

Identify headings, labels, axes

Headings: Life Expectancy in 2001, Member state, Male, Female, At birth 2000, At birth 2001, At age 60.

If there is more than one graph / table / diagram, ask yourself: are they interrelated? There is not more than one table, rather there are elements within a table.

Is the data provided as percents or raw data? What are the units? Raw data. The units are 'years'.

Look for annotations, small print, etc

WHO: World Health Organisation This is an excerpt from the full WHO listing which comprises of 191 member states

Can you make any immediate connections or interpretations from the data? Can you identify any trends?

This table illustrates the life expectancies of the first 10 alphabetically listed member states from the

WHO It provides data on the overall population in terms of life expectancy at birth if born in 2000 and 2001 It provides data for males only and females only in terms of life expectancy at birth and further life

expectancy at age 60 Lets look at a question: What can be concluded from the table presented above?

A) Life expectancy rose in all the countries between 2000 and 2001 B) Australia has the highest life expectancy of the WHO member states

C) In general, females have a higher life expectancy than males

D) Those who get to age 60 have a shorter life expectancy than average

Answer: C Solution: Notice the word all in option A. This should alert you because the only thing you need to do to refute this statement is find one of the countries in which the life expectancy dropped between 2000 and 2001. All of the countries life expectancies rose between 2000 and 2001 except Afghanistan which dropped from 33.8 to 33.4. Thus option A is wrong. Although Australia has the highest life expectancy from the member states presented, it is clear from the data that there are many other WHO members that are not presented. These may or may not have higher life expectancies than Australia we do not know. Therefore, we cannot conclude option B. From the data presented, we can conclude option C because, in general, females do have a higher life expectancy than males. If option C were phrased in all WHO member states, females have a higher life expectancy than males or all females will live longer than males in the 10 countries presented, it would be false because this would make conclusions that are beyond the scope of the material presented. Option D is a misunderstanding of the data in the table the values in columns that represent At age 60 are lower than the

at birth columns but this is because these people are already 60 years old. In fact, the table shows that once they reach 60, people live longer than the average life expectancy.

RESEARCH METHODS

WHY RESEARCH METHODS? Even though the UMAT does not require you to have knowledge of research methods, many of the passages and much of the data presented are in the form of research trials or investigations. If you understand some basic concepts before you go into the UMAT, youll spend less time interpreting them in the exam and thus have more time to answer the questions.

DEFINITIONS Here are some common words that are used in research methods that you should familiarise yourself with.

Participants / Subjects Participants are people / animals that are involved in the experiment. They are often divided into groups and either given a treatment / intervention or a placebo.

Population A population is a well-defined group in which members have particular characteristics (for example, male office workers living in Australia). Participants in a study are taken from a particular population.

Control Group The participants in the control group are used for comparison with the experimental group. For example, lets say that Drug A is being tested for its usefulness in preventing heart disease. The participants of the trial might be divided into two groups the control group and the experimental group. The experimental group would be given Drug A while the control group would be given no treatment or a placebo. At the end of the trial, the two groups are compared to see whether Drug A helped prevent heart disease.

Experimental Group The participants in the experimental group receive the treatment, drug or intervention that is being investigated. See control group for an example of an experimental group.

Placebo A placebo is a substance that looks like the treatment / intervention but is actually inert. For example, when the treatment is a drug pill, a sugar pill could be the placebo. In many experiments, the participants in the control group are given a placebo.

Placebo effect The placebo effect occurs when the belief or knowledge that one is being treated can itself have a physiological effect. For example, some people who take a pill that they think is a drug (but which actually has no active substance) can improve in their condition simply due to the belief that they took a drug that would work. This can confound research findings. Single and double blind trials are used to reduce the detrimental effect of this phenomenon on research.

Experimenter bias

Experimenter bias is bias that is introduced by an experimenter, whose expectations about the outcome of the experiment can be subtly communicated to the participants in the experiment. For example, if an experimenter was testing how good Drug E was in helping with depression, his expectations that Drug E would work could be communicated to the patients, thus affecting the outcome of the experiment.

Single blind trial In a single blind trial, participants do not know whether they are in the experimental group or the control group. This helps reduce any errors due to the placebo effect.

Double blind trial In a double blind trial, both participants and experimenters do not know which participants are in the experimental group or the control group. This helps reduce any errors due to the placebo effect as well as any experimenter bias.

Independent Variable An independent variable is the factor(s) whose effects are to be studied and manipulated in an experiment. For example, if an experimenter is examining the way different fertilisers help a plant grow, the independent variable is the type of fertiliser (i.e. the variable(s) that the experimenter changes).

Dependent Variable Dependent variables change in response to changes in the independent variable. For example, if an experimenter is examining the way different fertilisers help a plant grow, the dependent variable is the growth of the plants (i.e. the variable that helps measure the effects of the independent variable).

Hypothesis A hypothesis is a tentative explanation of observed events that can be further tested. It is a prediction of the relationship between an independent variable and dependent variable in an experiment. For example, a hypothesis could be Drug A will reduce the risk of having a heart attack in females above 50 years of age. This can be tested in an experiment. It is important to note that a hypothesis can never be proven. An experiment may show it to be false, but experiments cannot prove it to be absolutely true. However, a well-controlled experiment can help support a hypothesis.

Sampling Sampling is the process of selecting a subgroup of participants from the population so that the subgroup can be used to make generalisations to the population as a whole. In general, the greater the number of participants in the sample and the more effective the selection procedure, the better the sample represents the population as a whole.

Randomisation Randomisation is a technique of assigning patients to experimental and control groups that is based only on chance distribution. By using randomisation, any selection bias is diminished and variables between the experimental and control groups are more effectively controlled. Questions in the UMAT most commonly focus on the concepts of sampling and controlling variables (which include the concepts of the placebo effect and randomisation).

SAMPLING In a research study, it is important to have participants that are representative of the population under investigation so that inferences can be made about the population as a whole. For example, if a drug was being investigated, but the participants in the study were not similar to the population, it would be difficult to recommend that drug to the population, even if the experiment showed it to be successful. Lets take an example:

A researcher wants to investigate the usefulness of drug A in helping male smokers aged 40-45 stop smoking.

Independent variable: Being given Drug A or being given a placebo Dependent variable: Whether or not the participant stops smoking In this case, the population is male smokers aged 40-45 years. Of course, it is impossible to have all males between 40 and 45 years of age as participants in the experiment. A sample needs to be taken from the population. A sample is a subset of people that needs to have similar characteristics to the population. The selection procedure is vital in ensuring that the sample is representative of the population under investigation. For example, if all of your participants were from one suburb in outer Sydney, your sample would not be representative of all smokers aged 40-45 years in Australia. The number of people in the sample is also important. For example, 5000 male smokers aged between 40 and 45 is likely to give a more representative sample than 50 male smokers aged 40 to 45 years.

CONTROLLING VARIABLES Controlling extraneous variables One of the most important elements of experimental design is controlling extraneous variables. For an experiment to be effective, all variables except for the independent variable (the one under investigation) should be kept constant. If this is done, then any changes in the dependent variable can be attributed to the independent variable. Lets consider an example of how an uncontrolled variable can impact on our study. Suppose that the smokers in the control group were given their placebo and told that it contained vitamins. Those in the experimental group were given their drug and told that it would help them quit smoking. When the study was completed, those in the experimental group were found to have a much greater rate of quitting than those in the control group. But what is this difference due to? Is it due to the activity of the drug? Or is it due to the fact that those in the experimental group believed they were being helped? This example illustrates two concepts. Firstly, it demonstrates the importance of the placebo effect in influencing an experiment. Secondly, it shows the degree to which an uncontrolled variable can affect the outcome of an experiment. Extraneous variables therefore need to be controlled and kept constant in order to ensure the effectiveness of the study.

Experimental and control groups One key variable that must be controlled in an experiment is the differences between control and experimental groups. It difference is not minimised, any disparity in results between experimental and control groups could be due to participant characteristics, rather than any treatment. Of course, we cannot guarantee that each of the groups will be identical to each other in every way even twins are different. The best that we can do is allocate participants to different groups randomly. If we do this, the chances are the groups will be similar. In our study, it is important that the experimental and control group had participants that were similar in particular ways. For example, if all of the participants in one group had spouses that smoked, and the other group did not, this may confound the experiment.

THE IDEAL STUDY Here are some components of an ideal study:

Good sampling technique (large number of participants, representative sample) Randomised allocation to control and experimental groups Double-blind procedure to control the placebo effect and experimenter bias

All variables apart from those being manipulated are controlled

It is worthwhile keeping this list in mind when you are reading through a research study. It is also helpful to have a good understanding of what the experimenter is testing or trying to achieve with the study.

1. Introduction to Section 1.pdf2. LOGICAL REASONING.pdf3. PROBLEM SOLVING.pdf4. FIGURES.pdf5. DATA INTERPRETATION.pdf6. research methods.pdf