Medic Mind Decision Making

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Theory & Technique

Mock Questions

Step-by-Step Guide

Detailed Explanations

Decision Making

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Lesson

Page

Lesson 1: Introduction to Decision Making

3 Lesson 2: Syllogisms I

5 Lesson 3: Syllogisms II

5 Lesson 4: Venn Diagrams I

21 Lesson 5: Venn Diagrams II

21 Lesson 6: Probabilistic Reasoning I

35 Lesson 7: Probabilistic Reasoning II

35 Lesson 8: Logical Puzzles I

42 Lesson 9: Logical Puzzles II

42 Lesson 10: Interpreting Information I

54 Lesson 11: Interpreting Information II

54 Lesson 12: Recognising Assumptions I

64 Lesson 13: Recognising Assumptions II

64 Lesson 14: Summary and Overview

68 Decision Making Mock 1

69 Decision Making Mock 2

84 Answers and Explanations - Tutorial Questions

98 Answers and Explanations - Mock Test 1

114

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What is Decision Making?

The Decision Making subtest assesses your ability to apply logic to reach a conclusion or decision, as well as analysing statistical information and evaluating arguments successfully.

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Why do they test it?

Making decisions in complex situations is a scenario faced by doctors and dentists everyday. Being able to comprehend large amounts of information to manage risks and deal with uncertainty is vital, and requires a numerous problem solving skills.

What are the different question types?

• Syllogisms - when you are given two or more statements and have to use logical reasoning to decide which conclusions follow.

Introduction to Decision Making

Lesson 1 + 2

To gain an understanding of this new section in the UKCAT, and the

timing involved.

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• Venn Diagrams - you may be presented with a set of statements and a set of different Venn Diagrams as response options. You will need to select the diagram that best represents the information provided.

• Probabilistic Reasoning - you will be required to select the best possible response out of four statements regarding a probability scenario.

• Logical Puzzles - you are given a series of statements that you need to infer information from. The statements may not make real-life logical sense, but try to deduce the

conclusions you can gauge from the information provided.

• Interpreting Information - you will be given information in the form of graphs, charts or written passages. You will be required to read this information and interpret it in a

manner which enables you to decide the conclusions that follow best.

• Recognising Assumptions - this will test your ability to evaluate the strength of an argument in support of or against a solution to a particular problem.

Introduction to Decision Making

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What are syllogisms?

Syllogisms contain two or more statements and

these statements are followed by a series of conclusions. You have to use logical reasoning to deduce which conclusions follow from the information given.

When you are presented with the information, it can appear extremely confusing,

especially because the sentences will not make actual sense. For example, you might get a syllogism that says all bananas are vegetables ad all vegetables are desserts. This is not strictly true, and so you must not use any factual knowledge, even if it is as basic as

knowing that bananas are fruits!

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Medic Mind Technique for Syllogisms

Once you crack the technique for syllogisms, it becomes much easier. There is no chronological technique as it varies from question to question, but here are some crucial tips:

1. Read the information multiple times until it begins to make logical sense. It may seem mundane and tedious to read all the information, but it is crucial to read it until it makes sense.

2. Pay special attention to key words such as ‘some’ ‘none’ ‘all’ and ‘only’.

3. Do not make assumptions about the information - this includes using external knowledge.

4. Work out the conditions and draw a Venn diagram wherever possible.

5. Take each option independently and judge whether it fits in with the information presented or the Venn diagram you have drawn. 

Syllogisms

Lesson 2 + 3

Be able to tackle syllogism questions by drawing appropriate Venn

Diagrams and analysing carefully the wording of the syllogism.

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The Venn Approach

The best method of answering these questions is to use Venn diagrams. The alternative using deductive reasoning from just the text.

For syllogisms, the Venn Diagrams may not be as

straightforward as the ones you may use in a mathematics exam, or for other Decision Making questions which are based purely on Venn Diagrams (which we will discuss in the next tutorial).

We will now go through the different types of Venn Diagrams and when to use them. 

Syllogisms I and II

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PATTERN 1 : Some A are B

General Pattern

This is the simplest form of syllogism question you will be presented with.

What can be deduced? 

• Some A are not B • Some B are not A • Some A are B • Some B are A

Example: Some Giraffes are Sharks

For this sort of pattern, the Venn diagram that is drawn will have two circles representing

giraffes and sharks with a section of overlap What can be deduced?

• Some giraffes are not sharks • Some sharks are not giraffes • Some giraffes are sharks • Some sharks are giraffes  

Syllogisms I and II

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PATTERN 2 : All A are B

General Pattern

For these questions, you will draw an atypical Venn Diagram.

What can be deduced?

• All A are B • Some B are A • Some B are not A

Example: All Beaches are Sights What can be deduced?

• All beaches are sights • Some sights are beaches • Some sights are not beaches

Syllogisms I and II

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PATTERN 3: Some A are not B

General Example

For this pattern, we know that some A are not B, but we don’t know about the rest of A - could it also be B? Let’s explain this with a Venn Diagram:

Qualification: A and B overlap may be 0.

For certain Venn Diagrams you need to write a Qualification if you are unsure whether an overlap exists. For example, here we know that an overlap between A and B could exist, but do not know that it does.

• Some A is not B • Some B is not A • Some A could be B

Example: Some Snakes are not Reptiles

• Some Snakes are not Reptiles • Some snakes could be Reptiles

Syllogisms I and II

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PATTERN 4 : No A are B

General Example

• No A is B

• No B is A

Example: No pizza is pineapple

• No pizza is pineapple • No pineapple is pizza

Medic Mind Tip: Whenever you see the word no in a syllogism, ‘some A is not B’ and

‘some B is not A’ will always present no matter what circumstances.

Syllogisms I and II

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PATTERN 5: Some A are B, and some B are C

General Example

Qualification: A and C might have a

relationship, meaning the Venn would have three overlapping circles (with possibly even some in A, B, and C.

Between A and B Between B and C Between A and C

Some A are B Some B are C Could be relationship Some B are A Some C are B

Example: Some Buildings are Skyscrapers. Some Skyscrapers are Tower

Qualification: Buildings and Towers

might have a relationship, meaning the Venn would have three

overlapping circles (with possibly even some structures which are all three).

Buildings & Skyscrapers

Some buildings are skyscrapers

Some skyscrapers are buildings

Skyscrapers & Towers

Some skyscrapers are towers

Some towers are skyscrapers

Buildings & Towers

No relationship

Syllogisms I and II

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PATTERN 6 - All A is B, and all B is C

General Example What can be deduced?

All A are B All B are C All A are C Some B are A Some C are B Some C are A

Example: All Cities are Countries, and all Countries are Continents. What can be deduced?

Cities & Countries

All cities are countries Some countries are cities

Countries & Continents

All countries are continents Some continents are countries

Cities & Continents

All cities are continents Some continents are cities  

Syllogisms I and II

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PATTERN 7 - Some A is B, and all B is C

General Example

Qualification: There may or may not be

some items which are exclusively A and C, without B, so the overlap in this Venn Diagram could have 0 items.

Some A are B All B are C Some A are C Some B are A Some B are C Some C are A

Some C are B

Example: Some Shoes are Slippers, and all Slippers are Footwear What can be deduced?

Qualification: There may or may not be

some Shoes which are Footwear but not Slippers. Therefore the overlap between Shoes and Footwear could have 0 items.

Shoes and Slippers

Some shoes are slippers Some slippers are shoes

Slippers and Footwear

All slippers are footwear Some footwear are slippers

Shoes and Footwear

Some shoes are footwear Some footwear are shoes  

Syllogisms I and II

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PATTERN 8 - All A are B, and some B are C  

Qualification: There may or

may not be a relationship between A and C. The B items which are C could also be As. It is impossible to have an item which is A and C without B.

All A are B Some B are C Could be relationship Some B are A Some C are B

Example: All Mobiles are Gadgets, and some Gadgets are Portable What can be deduced?

Qualification: There may or

may not be a relationship between Portables and Mobiles. The Gad gets which are Portable could also be Mobiles. It is impossible to have a Portable Mobile which is not a Gadget.

Mobiles and Gadgets

All mobiles are gadgets Some gadgets are mobiles

Gadgets and Portables

Some gadgets are portables Some portables are gadgets

Mobiles and Portables

Could be relationship  

Syllogisms I and II

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PATTERN 9 - All B are A and all C are A

Qualification: There could be a relationship between B

and C. You cannot have an item which is just B and C, it has to be A too.

All B are A Could be relationship All C are A

Some A are B Some A are C

Example: All cars are trucks and all lorries are trucks What can be deduced? 

Cars and Trucks

All cars are trucks Some trucks are cars

Cars and Lorries

No relationship

Lorries and Trucks

All lorries are trucks Some trucks are lorries 

Syllogisms I and II

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PATTERN 10 - All A are B, and no B are C

General Example What can be deduced?  

All A are B No B are C No A are C Some B are A No C are B No C are A

Example: All Symphonies are Trumpets and no Trumpets are Clarinets What can be deduced?

Symphonies and Trumpets

All symphonies are trumpets Some trumpets are symphonies

Trumpets and Clarinets

No trumpets are clarinets No clarinets are trumpets

Symphonies and Clarinets

No symphonies are clarinets

Syllogisms I and II

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PATTERN 11- All A are B, and no A are C  

General Example

Qualification: There may or may not be a

relationship between B and C. The

overlapping region might have 0 items. We know that some B (the As) are not C.

All A are B Some B are not C No A are C Some B are A Some B could be C No C are A

Example: All Dresses are Skirts, and no Dresses are Playsuits  

Qualification: there may or may not be a relationship between Dresses and Playsuits. The overlapping region might have 0 items. We know that some of the Skirts (the dresses) are not Playsuits.

Dresses and Skirts

All dresses are skirts Some desserts are skirts

Skirts and Playsuits

Some skirts are not playsuits. Could be a relationship.

Dresses and Playsuits

No dresses are playsuits No playsuits are dresses 

Syllogisms I and II

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PATTERN 12 - Some A are B, and no B are C

Qualification: There could still be a

relationship between A and C. We know some As (the Bs) cannot be Cs.

Some A are B No B are C Some A are not C Some B are A No C are B

Example: Some Psychology Students are Graduates, and no Graduates are Mathematicians

Psychology Students and Graduates

Some psychology students are graduates Some graduates are psychology students

Graduates and Mathematicians

No graduates are mathematicians No mathematicians are graduates

Psychology Students and Mathematicians

Some psychology students are not mathematicians

There could be some psychology students studying mathematics

Syllogisms I and II

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Syllogisms: General Rules

The UKCAT likes to ask syllogism questions which involve several patterns. When you are given the question it will involve 2 or 3 statements, so you will have to draw several Venn Diagrams on your whiteboard.

Try and take the approach of the question being a riddle. Break down each line of working, and draw a Venn for each sentence.

Here are some shortcuts that we recommend when you are pressured for time: No x + No y —> No relationship

All x + All y —> All connected

All x + Some y —> No immediate conclusion Some x + All y —> Some relationship

Some x + No y —> Some are not related

Some x + Some y —> No immediate conclusion

A group of friends at Cambridge university are from either London or Manchester. They study either Geography or Economics. Some of the students are from London and the rest of the students study Economics

Place ‘Yes’ if the conclusion does follow Place ‘No’ if the conclusion does not follow

A. All of the Economic students are from Manchester. B. None of the students from London study Economics. C. Some of the students from London study Economics. D. None of the Economic students are from London. E. Some of the Manchester students study Economics.

F. There is a possibility that there are both Economics and Geography students are from London.

Question 1

Syllogisms I and II

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Some cockroaches are crocodiles. All crocodiles are strawberries.

Place ‘Yes’ if the conclusion does follow Place ‘No if the conclusion does not follow A. All the cockroaches are crocodiles. B. Some cockroaches are strawberries. C. Some crocodiles are strawberries. D. All the cockroaches are strawberries.

Question 2

Some cupboards are trees. Some trees are leaves. All leaves are jungles.

Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does not follow. A. Some leaves are cupboards

B. Some jungles are cupboards C. All trees are leaves

D. Some trees are jungles

Question 3

Syllogisms I and II

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Venn Diagrams

In Venn Diagram questions you may be presented with a group of statements and a set of different Venn Diagrams as response options. You will need to select the Venn Diagram that best represents the information provided.

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Types of Venn Diagram Questions

Venn to Text

They give you… a Venn Diagram.

They ask you… which of the four statements matches the diagram. Text to Ven

They give you… a passage of information.

They ask you… to provide a conclusion or select the correct Venn Diagram.

We will look closely in detail at both by working through several worked examples.

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Text to Venn Questions

With Text to Venn Diagram questions, it is important to read the information line-by line and see which line gives information about the most categories.

In other words, if the Venn diagram involves 3 categories, a sentence which tells us about categories A, B and C is more valuable than a sentence telling us about just A and B. Always start with the centre of the Venn if you can. This is the region involving the most Sets.  

Venn Diagrams

Lesson 4 + 5

Understand what the different Venn Diagram questions are, including Euler diagram questions and be able to answer them effectively

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“Which diagram best represents the information?”

Here you will be given some text with four associated Venn Diagrams, and asked to select the Venn Diagram which best represents the information. Let’s work through an example:

Explanation

Step 1 - Check the total number of cakes

When you are given a Type 1 question with Venn diagrams as answer options, like in this example, a good thing to check would be that they add up to the total mentioned in the question text.

“Hilary is making 16 cakes”

When counting up the numbers for each Venn diagram we find: A - 16 B - 19 C - 16 D - 16

This means we can rule out B

1 Text to Venn

Which diagram best represents the information?

Hilary is making 16 cakes for her tea party. She is putting toppings on them - sprinkles, smarties and cookies. 7 contain sprinkles, 3 contain all three toppings, 2 cakes contain 2 toppings. The same number of cakes have smarties only as those that have only cookies.

Worked Example

Venn Diagrams

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Step 2 - Use information involving 3 categories

Now, as we said, try to use the information that tells us about the most categories.

“3 contain all 3 toppings”

Looking at all four options, all have 3 in the middle so this does not help us.

Step 3 - Use information involving 2 categories

Next we look at information that tells us about 2 categories

“2 cakes contain 2 toppings”

We need to count the sum of the regions with just two Venns overlapping. Unfortunately, this does not help us either as all four diagrams have a 2 in between two circles!

Step 4 - Cakes with only sprinkles and only cookies are equal

Normally, we would now look at information that tells us about 1 category, but we are given an extra piece of information

“The same number of cakes have only sprinkles as those that have only cookies.”

We want to focus on the regions with only one Venn present, with no overlaps. There are three of these regions, one for only sprinkles, one for only cakes, and one for only cookies. Two of the regions need to have the same value in them.

A - Yes C - Yes D - No This rules out D.

Step 5 - Use the information involving 1 category

We are now left with A and C. From afar, they both look the same, as they have the same numbers just in different arrangements. But remember, the question writers are not giving you extra information for the sake of it - use every line possible. We have used

information about 3 toppings and 2 toppings, so now let’s look at the leftover information which is about one topping only.

“7 contain sprinkles”

Now you should check that in each Venn diagram, at least one each enclosed region adds up to 7.

A - Yes

C - No This leaves A.

Venn Diagrams

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In Implicit Text to Venn questions they do not give you or ask you to draw a Venn Diagram. However, to answer the question most effectively you need to draw one.

So, how do you know when to draw a Venn Diagram if the question doesn’t tell you? The easiest way to spot this is if they give you two or more categories (such as A and B) and tell you how many people are in each category. This is a classic trigger for an Implicit Text to Venn question.

Explanation

1. Draw the Venn diagram. Before you do anything, draw the Venn diagram and label each circle before it gets confusing. 

2 Implicit Text to Venn

Worked Example

The local council were doing a survey of how many people have electronic gadgets. They surveyed 100 people in total.

7 people have TVs, tablets and mobile phones 11 people have TVs and tablets

8 people have tablets and mobile phones. 26 people have TVs and mobile phones

33 people have TVs, 30 people have mobile phones, and 27 people have tablets.

How many people had neither tablets or mobile phones?

A. 51 B. 55 C. 45 D. 40

Venn Diagrams

Lessons 4 + 5

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2. Remember, always start with the information that tells us about the most

categories.  

7 people have TVs, tablets and mobile phones.  

This means we put a 7 in the middle.

3. Next, move on to information that tells us about two categories. 11 people have tablets and mobile phones

8 people have tablets and mobile phones 26 people have TVs and mobile phones

Now, an easy trap that many pupils fall into is putting the numbers straight in. However, remember the number of people who have tablets and mobile phones also includes the 7 that have all three gadgets. We want the people that have only tablets and mobile phones, thus we need to subtract 7 from 11 to give us 4.

Repeat this procedure for the other two combinations.

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Venn Diagrams

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4. Look at the information with the third most categories. Next, move onto the

information that tells us about each single category.

33 people have TVs

30 people have mobile phones 27 people have tablets

5. Consider the items outside the Venns. Remember, this is not the end. There are people that do not have any out of tablets, TVs and mobile phones. To find this out we need to add up all the numbers in the circles and subtract it from the total that have been surveyed.

They surveyed 100 people in total.

15 + 4 + 7 + 1 + 3 + 19 + 3 = 52 100 - 52 = 48

6. Work out the answer. We now know that 48 people did not have any of the 3 gadgets. We still need to factor in the people that had no tablets or mobile phones, but who had just a TV - 3 people

48 + 3 = 51

This means that the answer is A = 51. 

Venn Diagrams

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A Venn diagram shows all possible logical relationships between a series of sets. But an Euler diagram only shows relationships that exist in real world.

For example, in a Venn question they might tell you ‘bananas are chairs’. In a Euler question they expect you to draw on your real life knowledge to picture Venn Diagrams. For Euler questions, you need to understand the relationship between different categories. Based on these relationships, try to draw your own Venn diagram instead of trying to see which of the options fits best with your deductive reasoning. They may present this information in the form of text or a flow diagram.

3 Euler Diagrams

Worked Example

Which of the following Venn diagrams correctly represents the existing relationship between cakes, Italian food, plants, forest, trees, and glass?

A B

C D

Venn Diagrams

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Explanation

For Euler Diagrams, form categories and lists based on the items. Here, we can group the two foods, three vegetations, and then glass on its own.

Cakes Plants Glass

Italian Food Forest Trees

From this we calculate the Venn type we need. There are three different categories so we need three separate regions, let’s call them Regions 1-3:

• In Region 1, we have cake and Italian food. You can get Italian cakes, but also cakes of different origin and Italian food that is not cake, so we want two overlapping circles. • In Region 2, we have plants, forests, and trees. We know that all trees are plants, and

that some trees are forests. This needs one circle (trees) inside another circle (plants), with the first circle (trees) overlapping another circle (forests). These will all be separate to Regions 1 and 3.

• In Region 3, we have glass is in its own category. This means it needs its own circle separate from Regions 1 and 2.

Based on this information, we need to look for a diagram that has: 1. Region 1- r one circle overlapping another circle.

2. Region 2 - one circle inside another circle and one circle overlapping another circle. 3. Region 3 - Its own separate circle

Step By Step Guide

1. Count the total number of categories. Usually, we advise against counting but it will not take long to ensure that there are the right number of circles for categories.  

Venn Diagrams

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There are 6 circles for every option apart from C which has 7. This means we can rule it out.

2. Eliminate those with less than 3 regions. Remember always use process of

elimination. Try to rule out the option that is easiest to eliminate. This will probably be the one that does not contain the third criterion. This means we rule out D.

3. Eliminate those with more than 3 regions. This leaves A and B. The answer is B because A puts cake and Italian Food in two separate categories (thus making 4 regions).  

Venn Diagrams

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Certain questions will give you a Venn Diagram, perhaps with some information missing. You will be given four statements related to the Venn diagram and you will have to choose one that is most suitable for the Venn diagram.

For these questions, work by elimination to rule out statements step by step.

Explanation

First of all, we can see there are two missing values that are X and Y. It is a good idea to write down what these values represent:

• X represents the number of gardens with daffodils, tulips, roses but not dandelions.

4 Venn to Text

Worked Example

The following diagram displays the number of flowers in the gardens of 100 citizens in Berkshire. Every home has at least one flower.

Which of the following statements is true?

A. There are more gardens that have tulips than roses. B. There are exactly 21 gardens with only one type of flower. C. The number of gardens with all four flowers can be calculated D. There are more gardens that have roses than daffodils.

Venn Diagrams

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• Y represents the number of gardens with tulips, roses but not daffodils and dandelions.

Statement C

Looking at these statements, the easiest to rule out is C because there is no region with all 4 flowers overlapping.

Statement B

The second easiest to rule out is B because we just have to add up the regions that have no overlaps.

4 + 3 + 7 + 6 = 20

Statement A

Gardens with roses is:

9 + X + Y + 6 + 8 + 3 = 26 + X + Y Gardens with tulips:

2 + 3 + 6 + 8 + X + Y = 19 + X + Y Gardens with roses - gardens with tulips: (26 + X + Y) - (19 + X + Y) = 7

There are 7 more gardens with tulips than roses, so A is false.

Statement D

Gardens with daffodils is:

Venn Diagrams

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4 + 2 + 9 + X = 15 + X Gardens with roses is:

9 + X + Y + 6 + 8 + 3 = 26 + X + Y

We do not know the value of X or Y, but we know that both equations have X, so to work out the difference between them:

(26 + X + Y) - (15 + X) = 11 + Y Roses Daffodils

There are 11 + Y more roses than daffodils This means that D is the correct answer.

Venn Diagrams

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The same rules apply to non-circular Venn diagram questions as circular ones.

Explanation

Sweet potato pie - 7 + 5 + 6 + 2 = 20 Chicken Breast - 5 + 2 = 7 20 - 7 = 13 = D

5 Non-Circular Venn Diagrams

Worked Example

The Venn Diagram below shows lunch options chosen by Medic Mind staff.

How many more people have a meal with at least sweet potato pie than at least chicken breast?

A. 6 B. 7 C. 8 D. 13

Venn Diagrams

Lessons 4 + 5

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Venn Diagrams: Summary

• When you are presented with questions that do not already have a Venn diagram presented to you, draw your own

• Do not fall for the trap of just putting the numbers in the Venn without calculating them properly

• Read over the information as many times as you need.

• If it is a Euler diagram question, try and think of as many possible conditions as possible.

Venn Diagrams

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Probabilistic Reasoning

You will be required to select the best possible response out of four statements regarding a probability scenario.

It will require you to use the basic principles of probability which we will now go over. These three pages cover all you need to know about probability in the UKCAT.

The questions will be more likely to ask your reasoning behind a certain answer. This will meant that you will have to work out the answer, and display the step by step working that you have used.

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Basic Probability

You express a probability as either: • A decimal between 0 and 1

• A percentage between 0 and 100% • A fraction between 0 and 1

0 means that an event is impossible. 1 means that an event is guaranteed.

Probability of an event happening is:

E.g. What is the probability of rolling a 3 on a normal dice?

Number of desired outcomes - 1 (There is only one face with a 3 on the dice) Total number of outcomes - 6

Probability = 1/6

Number of desired outcomes Total number of outcomes

Probabilistic Reasoning

Lesson 6 + 7

To be able to use fractions, data and decimals to calculate

probabilities for scenarios.

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Estimating the Frequency of an Event

This is when you are given a probability question over a certain period of time or involving several repeats. Always use the rule below when trying to estimate the frequency of an event. 

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Double Probabilities

Sometimes you are faced with double events, so you have to consider how probabilities interact. All of the below examples assume that the two events are mutually exclusive - one event does not affect the chance of the other event happens.

1. Repeat of same events

This is when the same event occurs three times and the probability of each event does not change one after the other.

Expected Frequency = Probability x Number of Repeats

Probability of A three times = Probability of A x Probability of A x Probability of A

Question 4

Is it likely to be sunny for over three days over a two week period if the probability of it being sunny on any given day is 1/7?

A. Yes, because it will be sunny for 7 days as 14 x 1/2 = 7 B. Yes, because it is more likely to be sunny than not sunny C. No, because it will be sunny for 2 days, as 14 x 1/7 = 2 D. No, because it is less likely to be sunny than not sunny

Probabilistic Reasoning

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2. Different events that are mutually exclusive 

Probability of A and B = Probability of A x Probability of B

Question 6

Kings and UCL take part in a Varsity football match. For each 45 minute half, the probability of UCL scoring at least one goal is 0.2

Both halves of the 90 minute match are independent. The UCL captain believes that, over the course of the entire match, they are more likely to score a goal in the entire match than not.

Is he correct?

A. No because there is an equal likelihood of scoring in either half, so the probability of UCL scoring at least one goal is 0.4

B. Yes because the probability he will score one goal or more is more than 0.5 C. No because the probability of scoring in one half and not scoring in the other

half is 0.32

D. No because the probability of scoring one goal or more is less than 0.5.

Question 5

There are four marbles in a bag. 3 of which are green and one of which is red. What is the probability of picking a red marble from a bag three times if the marble is replaced in the bag after each selection?

A. 0 B. 1 / 16 C. 1 / 64 D. 1 / 256

Probabilistic Reasoning

Lessons 6 + 7

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3. Either One of Two Events (where both cannot happen)

Sometimes you get questions where they ask you to work out the probability of either A or B happening, but both are not possible. For example, if you roll a dice, the probability of getting 1 or 2 is the sum of each individual probability.

What is the probability of rolling a 3 or 4 on a normal dice?

Both events cannot happen, so we can apply the formulae above.

Question 7

The probability of England winning the World Cup is 1/24. Olivier Giroud plays three matches. In each individual match, the probability of him scoring is 1/5.

Is the probability of Olivier Giroud scoring in every match greater than the probability of England winning and Giroud scoring in at least one match.

A. Yes, because the probability of England winning the World Cup and Olivier Giroud scoring is 1/144, and the probability of Giroud scoring in every match is 1/216.

B. Yes, because the probability of England winning the World Cup and Olivier Giroud scoring is 91/5184, and the probability of Giroud scoring in every match is 1/216.

C. No, because the probability of England winning the World Cup and Olivier Giroud scoring is 1 / 144, and the probability of Giroud scoring in every match is 1/216.

D. No, because the probability of England winning the World Cup and Olivier Giroud scoring is equal to the probability of Giroud scoring in every match.

Probability of A or B = Probability of A + Probability of B

Probabilistic Reasoning

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Probability of 3 or 4 = Probability of rolling 3 + Probability of rolling 4

Probability of 3 or 4 = 1/6 + 1/6 = 1/3

4. Either One of Two Events (where both can happen)

If you had separate events which could both happen, the above formula does not work because you need to factor in the possibility that both could happen.

Explanation

To work out the probability of either happening you need to add: • The probability of just Khaled wearing a flowery shirt

• The probability of just Yogi wearing a black t-shirt

• The probability of both Khaled wearing a flowery shirt and Yogi a black t-shirt.

Our original equation (of adding the probabilities of both events) would only factor in the first two possibilities. With this question the easiest way to answer is to work out the probability of neither event happening, and minusing this from 1:.

Probability of Khaled not wearing a flowery shirt = 3/4 Probability of Yogi not wearing a black T shirt = 2/3

Probability of neither happening = 3/4 x 2/3 = 6/12 = 1/2 Probability of either happening = 1 - 1/2 = 1/2

Worked Example

The chance of Khaled wearing a flowery shirt is 1/4, and the chance of Yogi wearing a black t-shirt is 1/3. What is the probability of at least one happening?

Probability of A or B = 1 - Probability of neither happening

Probabilistic Reasoning

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5. Repeat of same events without replacement

If you are calculating the probability of multiple events happening, where one event affects another, then you have to adjust your calculation. A common example of this is the classic marbles from a bag question.

 

Question 8

The probability of Sam winning a contest is 1/10 and the probability of having Italian for dinner is 1/5. Is the probability of either Sam winning a contest or having Italian for dinner greater than 0.5?

A. Yes, because the probability of either winning a contest or having Italian for dinner is 1/3

B. No, because the probability of either winning a contest or having Italian for dinner is 1/10

C. No, because the probability of either winning a contest or having Italian for dinner is 3/10

D. No, because the probability of either winning a contest or having Italian for dinner is 7/25

Question 9

A bag has 6 balls. 3 are red and are blue. If Sam takes out a ball in a bag and doesn’t replace it, what is the chance of getting two red balls in a row?

A. 0.2 because the probability of getting red first time is 0.5 and the second time is 0.4 B. 0.2 because the probability of getting red first time is 0.4 and the second time is 0.5 C. 0.9 because the probability of getting red first time is 0.4 and the second time is 0.5 D. 0.9 because the probability of getting red first time is 0.5 and the second time is 0.4

Probabilistic Reasoning

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Summary: Probability

Probability of an event occurring

Estimating the frequency of an event:

Expected Frequency = Probability x Number of Repeats

Repeat of same events

Probability of A three times = Probability of A x Probability of A x Probability of A

Two different mutually exclusive events:

Probability of A and B = Probability of A x Probability of B

At least one of two events:

Probability of A or B = Probability of A + Probability of B

Do not start the question before you have read through all the options. You may only have to work out a small thing but if you misread the question you will waste lots of time.

These questions ask for your probabilistic reasoning - be able to know why a certain answer is correct or wrong.

Number of wanted outcomes Total number of outcomes

Probabilistic Reasoning

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Logical Puzzles

In Logical Puzzles you are given a series of statements and facts and you need to infer information from this. Thee statements may not make real-life logical sense, but try and deduce what the statements are trying to get at.

Medic Mind recommends sing a step by step process from the first piece of information to the last in order to reach a suitable conclusion.

• Bear in mind that for this section there is only one correct response per question. • You will be presented information which is in the form of a table, text or an alternative

graphic.

• Always try to draw a diagram whenever you are given the information. They will present you with a great deal of information and it may not necessarily be in the most appropriate order. Try and organise the information so it is both concise and chronological.

• The best way to organise information chronologically is to start with known facts that use the word ‘must’, rather than facts that use the word ‘might’.

• Use the process of elimination whenever you can, as it will help reduce the time taken to answer the questions.

• On some occasions, you may only need to figure out a small portion of the entire puzzle therefore in a situation which is already time constrained, try and avoid completing the puzzle when you can. That being said, there will be occasions where it is necessary to complete it.

There are two main types of logical puzzles that are presented in the UKCAT. They are based on the method of solving them. These are the ‘fill-in’ grid and the ‘crosshatch’

grid. We will begin with the ‘fill-in’ grid method.

Logical Puzzles

Lesson 8 + 9

To tackle logical puzzles using the Fill In method or the Cross Hatch

method, or any appropriate alternative.

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We recommend using the fill-in method. In addition to this, you should:

1. Write down the information that you know into a more concise format. It does not necessarily have to make sense but put it in a format that can be converted to

something which helps solve the puzzle.

2. Use information. Any information is good information. If something tells that someone cannot be something or have something - it is still crucial, and necessary to include in your fill-in grid.

3. Keep using each statement as a clue. Work step by step through each piece of

information. 

Worked Example

Jack and two of his friends each own a car. They all study different subjects. • Arnold, a Maths student, a Geography student and the Muzdu owner are

members of the Car Appreciation Society at University. • Ole doesn’t own a Cargo.

• Jack doesn’t own a Hudu

• The Medical student, who also doesn’t own a Cargo is best friends with Matthew, one of the friends.

• Ole who doesn’t study Maths also does not have a Muzdu. • The Geography student has a Hudu.

Which subject does Matthew study?

A. Medicine B. Geography C. Maths

D. This cannot be determined

1 Category Questions

Logical Puzzles

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Explanation

We will walk through the two methods that are used to answer these questions. Both are usually just as effective, but it depends on what you find most time-efficient.

Method 1: Cross-Hatch Method

For crosshatches, we recommend using a cross and tick method.

Based on this, we know that Ole has to have a Hudu because he can’t have the other two cars, Muzdu and Cargo. Hence we know that Ole has a Hudu, and the person with a Hudu studies Geography. Therefore Ole studies Geography.

We are left with the subjects Maths and Medicine for Matthew. We know that Matthew can’t study Medicine, since he is friends with the Medical Student. Also, we know that Ole is studying Geography. Therefore Matthew is a Maths student.

Muzdu Hudu Cargo Maths Geography Medicine

Jack

✖

Ole

✖

Matthew

✖

Maths Geography ✔ Medicine

Muzdu Hudu Cargo Maths Geography Medicine

Jack

✖

_✔ Ole

✖

_✔

✖

_✔ Matthew _✔

✖

Maths Geography _✔ Medicine

Logical Puzzles

Lessons 8 + 9

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Method 2: Fill-in Method

Name ______ ______ ______ ______

Subject ______ ______ ______ ______

Car ______ ______ ______ ______

Let’s fill it in with the information we know so far. These do not correspond with each other at the moment. We need to work out what Matthew studies.

Name Jack Ole Matthew

Subject Maths Geography Medicine

Car Muzdu Hudu Cargo

Let’s now fill in what we know each person cannot study or own. N means not. We know all of these for a fact, but we can work out that:

• Matthew doesn’t study medicine because his best friend does which is either Jack or Ole.

• Jack doesn’t own a Hudu and the person that doesn’t own the Hudu

Subject N (Maths) N (Medicine)

Car N (Hudu) N (Cargo), N (Muzdu)

Ole must have a Hudu because he cannot have a Cargo or Muzdu.

Subject N (Maths) N(Medicine)

Car N (Hudu) Hudu

Logical Puzzles

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The Geography student has a Hudu, which means that Ole studies Geography.

Subject Geography N(Medicine)

The two subjects left are Maths and Medicine. If Matthew cannot study Medicine, he must study maths. Matthew therefore studies Maths.

Subject Geography Maths

Here, we could work out further information but it will waste time. Do not try and complete the puzzle when you do not need to. 

Logical Puzzles

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Explanation

Method 1: Cross-Hatch Method

Go through each statement one by one to fill in the table (see next page). • Adrian wore yellow boots.

• Shivam wore green socks and Sergio wore yellow socks. • The person wearing red socks wore blue boots.

• The person wearing yellow socks did not wear red boots A. Adrian wore red socks.

No, the person wearing red socks wore blue boots. Adrian is wearing yellow boots.

B. Sergio wore yellow boots. No, Adrian wore yellow boots.

Worked Example

Two teams with red and blue bibs were playing a four a side football match. The winning team was made up of the players Aaron, Shivam, Adrian and Sergio. All four of them were wearing different coloured boots and different coloured socks. One of them was wearing red boots, another yellow boots, another green boots and

another blue boots. One of them was wearing red socks, another blue socks, another green socks and one of them yellow socks.

• Adrian wore yellow boots.

• Shivam wore green socks and Sergio wore yellow socks. • The person wearing red socks wore blue boots.

• The person wearing yellow socks did not wear red boots

Which of the following MUST be true?

A. Adrian wore red socks. B. Sergio wore yellow boots.

C. Shivam did not wear blue boots. D. Sergio wore red boots.

Logical Puzzles

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C. Shivam did not wear blue boots.

Yes, this is possible. The person wearing blue boots wore red socks, but Shivam wore green socks. So Shivam could not have worn blue boots.

D. Sergio wore red boots.

We know that Sergio wore yellow socks, and that the person wearing yellow socks wore red boots. This therefore is not possible either.

Method 2: Fill-in Method

Adrian wore yellow boots.

Red Boots Green Boots Yellow Boots Blue Boots Red Socks Green Socks Yellow Socks Blue Socks Adrian _✔ Shivam ✔ Sergio

✖

_✔ Aaron Red Socks ✔ Green Socks Yellow Socks

✖

Blue Socks

Player Socks Boots

Adrian Yellow Shivam Sergio Adrian

Logical Puzzles

Lessons 8 + 9

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Shivam wore green socks and Sergio wore yellow socks.

The person wearing red socks wore blue boots. 

The person wearing yellow socks did not wear red boots.

The answer must be C, Shivam did not wear blue boots.  

Adrian Yellow

Shivam Green

Sergio Yellow

Adrian

Adrian Yellow

Shivam Green Sergio Yellow

Adrian Red Blue

Adrian Yellow

Shivam Green

Sergio Yellow (Not Red)

Adrian Red Blue

Logical Puzzles

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These questions will be based on a group of people who are ordered based on an activity such as racing or on something measurable such as weight or height. For these questions, we recommend writing down the information in a way that is as close to chronological or ordered as possible.

2 Ordered Questions

Worked Example

There are five runners competing in a marathon who go for a health-check. Their names are Jing, Sathu, Geran, Zolt and Farah. The nurse measures their heart rate, weight, diastolic blood pressure and blood group.

In no particular order:

- Their heart rate is 66, 67, 70, 73 and 75 - Their weights are 50, 63, 72, 78 and 83.

- Their diastolic blood pressures are 67, 77, 85, 99 and 110

• One person’s has a diastolic blood pressure of 85, and has a heart rate that is 2 more than Jing.

• Farah weighs 63kg and has the 3rd highest heart rate.

• Zolt has a diastolic blood pressure that is 10 more than Geran.

• The person who has the highest diastolic blood pressure has the highest heart rate and a weight that is lower than Farah.

What is Sathu’s weight?

A. 50kg B. 63kg C. 78kg D. 83kg

Logical Puzzles

Lessons 8 + 9

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Explanation

Always start with the clearest information. We are told outright that Farah’s weight is 63kg and we can work out his heart rate being 63 as it is the third highest.

Next look for information where there is a difference between two values. There are only two values that have a difference of 10 between them for blood pressure. These values are 67 and 77. This means that Zolt has a blood pressure of 77, and Geran has a blood pressure of 67.

The only heart rate that has a 2+ gap is 73 and 75. Since this person’s heart rate is 2 more than Jing, Jing’s heart rate must be 73.

This is what we know based on this:

We know that Farah weighs 63 which is the second lowest weight. This means that the same person has a blood pressure of 110 and a weight of 50kg. The only person we do not have the information for both blood pressure and weight is Sathu. This means that his blood pressure is 110 and weight is 50kg. This means that his weight is 50kg. So the answer is therefore A, 50kg.

Name Heart Rate Weight Diastolic BP Jing 73

Sathu

Geran 67

Zolt 77

Farah 70 63

Name Heart Rate Weight Diastolic BP

Jing 73 83 85 Sathu 75 50 110 Geran 65 78 67 Zolt 67 72 77 Farah 70 63 99

Logical Puzzles

Lessons 8 + 9

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For these questions, you will be presented with a table with information missing. You will have to decide which of the four statements are correct based on the information and the information that has been presented.

Explanation

Knock out B…

We know that Wales drew one game and lost the other, which means that they did not win any games. They also did not score any tries, so the draw must have had zero tries. We know that England have won both of their games, so the draw must have been with Scotland, who have been with Scotland.

3 Tabular Diagrams

Worked Example

The table below shows the results of a tri-nation rugby tournament. Each team plays each team once only at a neutral ground.

A. England scored 3 tries in their game against Wales.

B. In Wales’ game with Scotland, there were no tries and the game ended in a draw.

C. Wales only won a single game. D. Scotland beat Wales by 1 try.

Team Played Wins Drawn Lost Tries Scored Tries Conceded

England 2 4

Scotland 2 1

Wales 1 1 0

Logical Puzzles

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Knock out A…

We cannot tell this for sure.

Knock out C…

They did not win a game because there were two games, and so they can’t have won a game since there were only two.

Correct Answer is D…

Scotland and Wales drew.

!

Summary: Logical Puzzles

• Present the information in a format which is chronological and concise.

• Use the process of elimination whenever you can, as it will help reduce the time taken to answer the questions.

• Step by step process from the first piece of information.

• Use either a ‘crosshatch’ grid or ‘fill in’ grid method wherever possible.

Logical Puzzles

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Interpreting Information

In Interpreting Information questions you will be given information in the form of graphs, charts or written passages. You will be required to read this information and interpret it in a manner which enables you to decide which conclusions best follow.

• There could be multiple correct answers to these questions.

• You will be presented with a great deal of information. The best thing to do is decide which of the information is relevant which will enable you to save time.

• You will not be asked to calculate certain values exactly, so rounding and estimating can be useful tools to use which can help save you time and still gain the correct answer.

• Do not use external knowledge as we always advise, and do not assess how strong a conclusion is based on how likely it is. Read the information that has been given to you and decipher whether it supports the conclusion stated or not

Analysing Question Information

Just as other aspects of the decision making section, they are trying to test how well you can deduce the correct answer by using logical reasoning. You are not expected to understand everything that is presented to you. Try and pick the necessary information and go from there.

Sometimes they will ask you to say ‘yes’ if the confusion follows. For these types, ask yourself if there is sufficient information that has been presented for this to be deduced. Often it would require external knowledge, and they are testing your ability to recognise this. They can also have more than one correct answer. This means take each statement individually and do not use the process of elimination.

Interpreting Information

Lesson 10 + 11

Learn how to tackle different types of graphical questions including

scatter, pie, line, bar, text and table charts.

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We will look at the following types of question:  - Interpreting scatter graphs

- Interpreting pie charts - Interpreting line charts - Interpreting bar graphs

- Interpreting multiple charts - Interpreting maps

- Interpreting text - Interpreting tables

Interpreting Graphs

All graph questions require similar techniques. You will have to read the accompanying information to get an idea of what the question is asking, and have a brief scan of the data presented. This will enable you to gain a brief context to the question you are answering, and will also enable you to use guessing and estimation a lot better.

We recommend using estimation wherever possible. This is not the quantitative section, and so is not testing your ability to carry out mathematical arithmetic, rather it is testing how quickly you can interpret information and apply it.

Interpreting Information

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1 Scatter Graphs

Question 10

This grid shows us the Maths and English scores of five pupils at school. The size of the dot indicates their IQ.

Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does not follow.

a) Claude’s overall academic performance is hardest to diagnose b) It is likely that DT has the highest attendance at school.

c) It is plausible that DT spends more time revising for Maths and English exams than Mohammed does.

d) Troopinder has greater potential in a Mathematically-orientated career than an English-orientated career

e) Robbie is better at fractions than Mohammed.

0 1 3 4 5 0 2 4 6 8 DT Mohammed Claude Robbie Troopinder

Interpreting Information

Lessons 10 + 11

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2 Pie Charts

Question 11

Read the following information. It is displaying the length of time customers visit in two separate museums.

Which of the following must be true?

A. More people stayed for less than 20 minutes in the science museum than they did for the mathematics museum

B. The science museum had a greater number of visitors per day.

C. If the two museums had the same number of visitors, the number of minutes spent in total by all the tourists would be equal.

D. More people stayed for more than 30 minutes in the science museum than they did for the mathematics museum.

Mathematics Museum   1050 visitors 10% 12% 15% 16% 27% 19% Science Museum   1300 visitors 19% 14% 15% _20% 24% 9% 0-9 minutes 10-19 minutes 20-29 minutes 30-39 minutes 40-49 minutes 50-59 minutes

Interpreting Information

Lessons 10 + 11

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3 Line Charts

The following graph shows rainfall in the months of April - July in Manchester and Bristol.

Place ‘Yes’ if the conclusion follows.

Place ‘No’ if the conclusion does not follow.

a) Manchester had a bigger range in rainfall than Bristol did

b) It is likely that Manchester had a higher temperature in July than Bristol did. c) Manchester had greater rainfall overall in the months displayed than Bristol did. d) August would have had a similar pattern as seen in July

Question 12

R a in fa ll (mm) 0 25 50 75 100

April May June July

Manchester Bristol

Interpreting Information

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4 Bar Charts

Question 13

This graph shows the voting selections of a group of people sampled in North London following the 2017 election.

a) Conservatives were the most popular party in the UK

b) 17 year olds in this group of people will vote Conservative based on evidence from the 18-25 category.

c) In this sampled group, Labour was more popular for those over 36 than Conservative was.

d) The proportional difference in voting between Labour and Conservative in this sample was larger in the 46+ group than in the 36-45 group.

e) More people voted for Conservative than they did for Labour 0 25 50 75 100 18-25 26-35 36-45 46+ Labour Conservative

Interpreting Information

Lessons 10 + 11

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Sometimes, when you are given two types of graphs, it can make it difficult to present information in a concise format that makes it easy for you to answer the questions. We recommend that you look at each of the five statements individually, and ensure you know whether it is asking you to use either the line graph or the pie graph or both, for example. Depending on the answer, you should carry out accordingly.

5 Interpreting Multiple Graphs

Question 14

The charts show the temperature of London and Cardiff throughout the year and the average number of milkshakes bought per day throughout the year.

a) More chocolate milkshakes were bought throughout the year in Cardiff than any other milkshake.

b) London had a higher average of sales of milkshake than Cardiff did c) July was where they had the highest discrepancy of sales

d) Vanilla milkshakes made more profit than strawberry milkshakes

e) It is likely that the hottest month in Cardiff was July since milkshake sales were highest 000s 0 25 50 75 100

April May June July Cardiff London

18%

19%

63%

Chocolate Vanilla Strawberry

Interpreting Information

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You will be presented with a set of shapes and a bit of accompanying information related to it. Usually this is in the form of some sort of arrangement, such as a map of a new city or a seating plan for an examination.

When given this information, know two things throughout - what you are trying to work out and what information is relevant to that. Sometimes, you might find that information that is not directly related to the aspects you are actually trying to work out can be the most useful.

These questions are like a puzzle. They may give you information that is unnecessary but use everything that they give you to guide you to the answer.

6 Maps

Question 15

The layout below was developed for a local park. Each aspect has its own unique shape and is reserved for the following: see-saw, slide, roundabout, monkey bars and a bench.

• The bench is as far away from the monkey bars as possible to avoid people getting hurt.

• The slide is almost equidistant from the see-saw and roundabout. • The monkey bars are not allocated to the heart

• The roundabout is not allocated to the triangle

Which of the following shapes represents monkey bars?

A. Trapezium B. Pentagon C. Semi-circle D. Triangle

Interpreting Information

Lessons 10 + 11

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These questions relate to syllogisms in a way, as they present information on how certain categories are related to one another, however these questions are focused on how you interpret the information presented, and whether certain conclusions can be deduced from the text or not. As we always advise, try and recognise which of the statements are related to the text, and whether some are jumping to conclusions and are extracting facts which are not related or can be extracted from the text at all.

7 Text Passages

Question 16

Not all superheroes wear capes, but all super heroes that wear capes are very fast flyers. It is fair to say that some cape wearing super heroes are unaware of how to properly get from one place to another.

a) Some of the superheroes who know how to get from one place to another are fast.

b) Some of the fast superheroes wear capes or know how to get from one place to another

c) Not all superheroes who are fast know how to get from one place to another. d) All superheroes who know how to get from one place to another and are fast

Interpreting Information

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8 Interpreting Tables

Question 17

The following table shows sales of three separate magazines. There are two versions, the normal version which is 300 pages, and the deluxe edition which is 400 pages. The normal edition costs £8.99 whereas the deluxe edition costs £13.99

A. There were more sales of deluxe edition than normal copies B. Magazine 1 was more popular than Magazine 2 overall

C. Magazine 3 made more revenue through its normal edition than its deluxe edition.

D. The deluxe edition was found to be more cost effective by its customers.

Book Magazine 1 Magazine 2 Magazine 3

Normal 36 41 61

Deluxe Edition

(+100 pages) 29 25 27

Interpreting Information

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Recognising Assumptions

Recognising Assumptions questions test your ability to evaluate how strong an

argument is in support for or against a solution to a particular problem. You will be given four statements, and there will only one which correctly is the strongest argument. It is vital that you do not use external knowledge to make decisions for this.

There are various factors that decide how strong a certain argument is compared to another. You will need to assess the validity of the argument presented purely based on the evidence that is available.

For an argument to be valid:

- It must be strongly related to the topic of the subject

- It cannot be based on assumptions or speculative - This means it cannot presume that something will happen theoretically.

- It is more likely to be related to factual evidence rather than opinion.

If you follow the criteria above, you will have no problem answering these questions. Let’s look at a few examples now.

Question 18

Should abortion be legal to help cases of women being raped and having a child they never planned for?

A. Yes. Contraception does not always work, and abortion is an essential part of healthcare.

B. Yes. A woman has a right to do what she wants with her body, and rape forces many women to have a baby.