Medic Mind Decision Making
Short Description
Medic Mind Decision Making www.medicmind.co.uk/ukcat...
Description
Decision Making UKCAT Course Book
Theory & Technique
Mock Questions
Step-by-Step Guide
Detailed Explanations
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Table of Contents
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
Answers and Explanations - Mock Test 2
137
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Introduction to Decision Making Lesson 1 + 2 To gain an understanding of this new section in the UKCAT, and the timing involved.
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. !
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.
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Introduction to Decision Making Lesson 1 • 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.
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Syllogisms Lesson 2 + 3 Be able to tackle syllogism questions by drawing appropriate Venn Diagrams and analysing carefully the wording of the syllogism.
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! !
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.
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Syllogisms I and II Lessons 2 + 3
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.
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Syllogisms I and II Lessons 2 + 3
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
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Syllogisms I and II Lessons 2 + 3
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
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Syllogisms I and II Lessons 2 + 3
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. What can be deduced? • Some A is not B • Some B is not A • Some A could be B Example: Some Snakes are not Reptiles What can be deduced? • Some Snakes are not Reptiles • Some snakes could be Reptiles
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Syllogisms I and II Lessons 2 + 3
PATTERN 4 : No A are B General Example What can be deduced? • No A is B • No B is A Example: No pizza is pineapple
What can be deduced?
• 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.
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Syllogisms I and II Lessons 2 + 3
PATTERN 5: Some A are B, and some B are C General Example What can be deduced?
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 A
Some B are C Some C are B
Could be relationship
Example: Some Buildings are Skyscrapers. Some Skyscrapers are Tower What can be deduced? 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
Skyscrapers & Towers
Buildings & Towers
Some buildings are skyscrapers
Some skyscrapers are towers
No relationship
Some skyscrapers are buildings
Some towers are skyscrapers
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Syllogisms I and II Lessons 2 + 3
PATTERN 6 - All A is B, and all B is C General Example What can be deduced?
Between A and B
Between B and C
Between A and C
All A are B Some B are A
All B are C Some C are B
All A are C Some C are A
Example: All Cities are Countries, and all Countries are Continents. What can be deduced?
Cities & Countries
Countries & Continents
Cities & Continents
All cities are countries Some countries are cities
All countries are continents Some continents are countries
All cities are continents Some continents are cities
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Syllogisms I and II Lessons 2 + 3
PATTERN 7 - Some A is B, and all B is C General Example What can be deduced?
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.
Between A and B
Between B and C
Between A and C
Some A are B Some B are A
All B are C Some B are C Some C are B
Some A are C Some C are A
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
Slippers and Footwear
Shoes and Footwear
Some shoes are slippers Some slippers are shoes
All slippers are footwear Some footwear are slippers
Some shoes are footwear Some footwear are shoes
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Syllogisms I and II Lessons 2 + 3
PATTERN 8 - All A are B, and some B are C
General Example What can be deduced?
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.
Between A and B
Between B and C
Between A and C
All A are B Some B are A
Some B are C Some C are B
Could be relationship
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
Gadgets and Portables
All mobiles are gadgets Some gadgets are mobiles
Some gadgets are portables Some portables are gadgets
Mobiles and Portables
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Could be relationship
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Syllogisms I and II Lessons 2 + 3
PATTERN 9 - All B are A and all C are A General Example What can be deduced?
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.
Between A and B
Between B and C
Between A and C
All B are A Some A are B
Could be relationship
All C are A 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
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Lorries and Trucks All lorries are trucks Some trucks are lorries
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Syllogisms I and II Lessons 2 + 3
PATTERN 10 - All A are B, and no B are C
General Example What can be deduced?
Between A and B
Between B and C
Between A and C
All A are B Some B are A
No B are C No C are B
No A are C 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
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Syllogisms I and II Lessons 2 + 3
PATTERN 11- All A are B, and no A are C
General Example What can be deduced?
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.
Between A and B
Between B and C
Between A and C
All A are B Some B are A
Some B are not C Some B could be C
No A are C No C are A
Example: All Dresses are Skirts, and no Dresses are Playsuits
What can be deduced?
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
Skirts and Playsuits
Dresses and Playsuits
All dresses are skirts Some desserts are skirts
Some skirts are not playsuits. Could be a relationship.
No dresses are playsuits No playsuits are dresses
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Syllogisms I and II Lessons 2 + 3
PATTERN 12 - Some A are B, and no B are C General Example What can be deduced?
Qualification: There could still be a relationship between A and C. We know some As (the Bs) cannot be Cs.
Between A and B
Between B and C
Between A and C
Some A are B Some B are A
No B are C No C are B
Some A are not C
Example: Some Psychology Students are Graduates, and no Graduates are Mathematicians What can be deduced? 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
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Syllogisms I and II Lessons 2 + 3
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
Question 1 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.
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Syllogisms I and II Lessons 2 + 3
Question 2 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 3 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
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Venn Diagrams Lesson 4 + 5
Understand what the different Venn Diagram questions are, including Euler diagram questions and be able to answer them effectively
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. !
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. !
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.
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Venn Diagrams Lessons 4 + 5 1
Text to Venn
“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:
Worked Example 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.
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
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Venn Diagrams Lessons 4 + 5 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.
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Venn Diagrams Lessons 4 + 5
2
Implicit Text to Venn
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.
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. B. C. D.
51 55 45 40
Explanation 1. Draw the Venn diagram. Before you do anything, draw the Venn diagram and label each circle before it gets confusing.
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Venn Diagrams Lessons 4 + 5 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.
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✔
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 Lessons 4 + 5 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.
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Venn Diagrams Lessons 4 + 5
3
Euler Diagrams
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.
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
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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 Italian Food
Plants Forest Trees
Glass
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.
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Venn Diagrams Lessons 4 + 5
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).
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Venn Diagrams Lessons 4 + 5 4
Venn to Text
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.
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. B. C. D.
There are more gardens that have tulips than roses. There are exactly 21 gardens with only one type of flower. The number of gardens with all four flowers can be calculated There are more gardens that have roses than daffodils.
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.
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Venn Diagrams Lessons 4 + 5 • 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
=
19 + X + Y
Gardens with tulips: 2+3+6+8+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:
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Venn Diagrams Lessons 4 + 5 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) Roses
-
(15 + X) Daffodils
=
11 + Y
There are 11 + Y more roses than daffodils This means that D is the correct answer.
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Venn Diagrams Lessons 4 + 5
5
Non-Circular Venn Diagrams
The same rules apply to non-circular Venn diagram questions as circular ones.
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. B. C. D.
6 7 8 13
Explanation Sweet potato pie - 7 + 5 + 6 + 2 = 20
Chicken Breast - 5 + 2 = 7
20 - 7 = 13 = D
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Venn Diagrams Lessons 4 + 5
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.
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Probabilistic Reasoning Lesson 6 + 7 To be able to use fractions, data and decimals to calculate probabilities for scenarios.
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. !
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. Number of desired outcomes Probability of an event happening is:
Total number of outcomes
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
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Probabilistic Reasoning Lessons 6 + 7
Estimating the Frequency of an Event Expected Frequency = Probability x Number of Repeats 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.
!
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
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
This is when the same event occurs three times and the probability of each event does not change one after the other.
Probability of A three times =
Probability of A x Probability of A x Probability of A
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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. B. C. D.
0 1 / 16 1 / 64 1 / 256
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.
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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.
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. Probability of A or B
=
Probability of A
+
Probability of B
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.
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Probabilistic Reasoning Lessons 6 + 7 Probability of 3 or 4
=
Probability of 3 or 4
=
Probability of rolling 3
+
1/6
Probability of rolling 4
+
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.
Probability of A or B
=
1
-
Probability of neither happening
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?
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 Probability of Yogi not wearing a black T shirt Probability of neither happening
=
3/4 x
Probability of either happening
=
1
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-
= = 2/3 1/2
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3/4 2/3 = =
6/12
=
1/2
1/2
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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
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 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
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Probabilistic Reasoning Lessons 6 + 7
Summary: Probability Probability of an event occurring Number of wanted outcomes Total number of outcomes 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 At least one of two events: Probability of A or B = Probability of A
x
+
Probability of B
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.
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Logical Puzzles Lesson 8 + 9 To tackle logical puzzles using the Fill In method or the Cross Hatch method, or any appropriate alternative.
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.
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Category Questions
1
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
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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. Muzdu
Cargo
Maths
✖
✖
Geography
Medicine
✖
Jack Ole
Hudu
✖
✖
Matthew Maths
✔
Geography Medicine
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
Cargo
Maths
Geography
Medicine
✖
Jack Ole
Hudu
✖
✔
✖
✔
✖
✔
✖
✔
Matthew Maths
✔
Geography Medicine
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Logical Puzzles Lessons 8 + 9
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 Name
Jack
Subject Car
N (Hudu)
Ole
Matthew
N (Maths)
N (Medicine)
N (Cargo), N (Muzdu)
Ole must have a Hudu because he cannot have a Cargo or Muzdu. Name
Jack
Subject Car
N (Hudu)
Ole
Matthew
N (Maths)
N(Medicine)
Hudu
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The Geography student has a Hudu, which means that Ole studies Geography. Name
Jack
Subject Car
N (Hudu)
Ole
Matthew
Geography
N(Medicine)
Hudu
The two subjects left are Maths and Medicine. If Matthew cannot study Medicine, he must study maths. Matthew therefore studies Maths.
Name
Jack
Subject Car
N (Hudu)
Ole
Matthew
Geography
Maths
Hudu
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.
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Logical Puzzles Lessons 8 + 9
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.
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.
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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.
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
Method 2: Fill-in Method Adrian wore yellow boots. Player
Socks
Boots
Adrian
Yellow
Shivam Sergio Adrian
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Logical Puzzles Lessons 8 + 9
Shivam wore green socks and Sergio wore yellow socks. Player
Socks
Boots
Adrian
Yellow
Shivam
Green
Sergio
Yellow
Adrian
Player
Socks
Boots
Adrian
Yellow
Shivam
Green
Sergio
Yellow
Adrian
Red
Blue
Player
Socks
Boots
Adrian
Yellow
Shivam
Green
Sergio
Yellow
(Not Red)
Adrian
Red
Blue
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.
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Logical Puzzles Lessons 8 + 9
Ordered Questions
2
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.
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. B. C. D.
50kg 63kg 78kg 83kg
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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: Name
Heart Rate
Jing
73
Weight
Diastolic BP
Sathu Geran
67
Zolt
77
Farah
70
63
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
83
85
Sathu
75
50
110
Geran
65
78
67
Zolt
67
72
77
Farah
70
63
99
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Logical Puzzles Lessons 8 + 9 3
Tabular Diagrams
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.
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.
Team
Played
England Scotland
Wins
Drawn
Lost
Tries Scored Tries Conceded
2
4
2
1
Wales
1
1
0
Which of the following statements is true? 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.
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.
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Logical Puzzles Lessons 8 + 9 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.
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Interpreting Information Lesson 10 + 11 Learn how to tackle different types of graphical questions including scatter, pie, line, bar, text and table charts.
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.
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Interpreting Information Lessons 10 + 11
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.
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Interpreting Information Lessons 10 + 11 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.
Troopinder Robbie
5
DT
4
3 Mohammed Claude 1
0
0
2
4
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Interpreting Information
Lessons 10 + 11 2
Pie Charts
Question 11 Read the following information. It is displaying the length of time customers visit in two separate museums. 0-9 minutes 20-29 minutes 40-49 minutes
10-19 minutes 30-39 minutes 50-59 minutes
Science Museum
1300 visitors
19%
Mathematics Museum
1050 visitors
9%
10%
19%
12% 24% 14% 15% 15%
20%
27% 16%
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.
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Interpreting Information Lessons 10 + 11
3
Line Charts
Question 12 The following graph shows rainfall in the months of April - July in Manchester and Bristol. Manchester
Bristol
100
Rainfall (mm)
75
50
25
0
April
May
June
July
Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. a) b) c) d)
Manchester had a bigger range in rainfall than Bristol did It is likely that Manchester had a higher temperature in July than Bristol did. Manchester had greater rainfall overall in the months displayed than Bristol did. August would have had a similar pattern as seen in July
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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. Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow.
Labour
Conservative
100
75
50
25
0
18-25
26-35
36-45
46+
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
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Interpreting Multiple Graphs
5
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.
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.
Cardiff
London
Chocolate
Vanilla
Strawberry
100
18%
000s
75 50
19% 63%
25 0 April
May
June
July
Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. 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
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Interpreting Information Lessons 10 + 11
Maps
6
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.
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. B. C. D.
Trapezium Pentagon Semi-circle Triangle
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Interpreting Information Lessons 10 + 11
7
Text Passages
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.
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. Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. 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
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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
Book
Magazine 1
Magazine 2
Magazine 3
Normal
36
41
61
Deluxe Edition (+100 pages)
29
25
27
Which of the following statements is true? 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.
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Recognising Assumptions Lesson 12 + 13 To understand statement questions and work to eliminate the statements that do not address the argument correctly.
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. C. No. It will not affect the number of women that are raped. D. No. Every foetus has a right to life, and abortion takes away from this.
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Question 19 Should British citizens have the right to bear a gun to protect themselves? A. Yes, all muggings in Islington could have been prevented if all citizens had a gun. B. Yes, it has been found that psychologically bearing a gun can improve selfconfidence. C. No, it is estimated that states in the US with loose gun bearing laws have a 12% higher crime rate than those with a stricter gun bearing policy. D. No, bearing a gun will mean people will be more paranoid.
Question 20 Should animals be used for scientific testing to prevent disease? A. Yes, animal testing has contributed to a large proportion of life-saving cures and treatments. B. Yes, they help increase competition for cosmetic goods. C. No, animal testing is cruel and barbaric. D. No, 95%. of animals used in experiments are not protected by the Animal Welfare Act in the US
Question 21 Should the minimum wage be raised to increase economic activity? A. Yes, it will mean a greater proportion of the population is working and so more productivity B. Yes, it will mean that there is reduced unemployment and so less people on benefits. C. No, it will create greater inequality. D. No, a higher minimum wage will mean people at work become complacent.
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Question 22 Should the drinking age be increased from 18 to 21 to reduce alcohol addiction? A. Yes, it will mean that fewer teenagers drink alcohol. B. Yes, teenagers that drink more become more addicted to alcohol. C. No, it would encourage 18-20 year olds to purchase alcohol illegally, and illegal activity is more likely to lead to addiction. D. No, according to a study by the University of Oxford, cases of alcohol addiction arise at the age of 24 and are not influenced by age of beginning alcohol consumption.
Question 23 Should the government be able to gain access to information on social media accounts? A. No, if the government had access to data on social media they would spend more of the budget on this and less to the National Health Services. B. No, this will be an invasion of privacy which is important to people. C. Yes, it is estimated that 13% of the crime that take place yearly could be identified viewing personal data on social media. D. Yes, all the terrorist attacks occur involve the use of social media.
Question 24 Should Marijuana be legalised to reduce illegal smuggling? A. Yes. It can then be taxed to benefit the economy. B. Yes. Legalising marijuana would allow users to obtain the herb from controlled vendors C. No. The same number of people will smoke marijuana. D. No, if it is legalised then more people will steal it increasing the crime rate which is an illegal offence. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 25 Should the death penalty be reintroduced to reduce crime? A. Yes. It will help reduce prison costs. B. Yes. The death penalty is even easier now with modern technology. C. No. There should be more police to reduce crime. D. No. Murdering someone itself is a crime regardless of the circumstances.
Question 26 Should zoos be stopped because of animal cruelty? A. Yes. Animals do not benefit from it at all. B. Yes. Many animals are taken out of their natural environment and forced to become enslaved. C. No. There are plenty of sanctuaries where animals are kept safe and there is no cruelty. D. No. It will reduce the level of tourism and have an effect on the local economy.
!
Summary: Recognising Assumptions - Use the process of elimination to remove statements that are not related to the topic being debated, or statements that are based on assumptions.
- Pick the statement that involves evidence or fact - Do not use external knowledge - Choose the argument that is strongest and most suitable
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Summary and Overview Lesson 14 Summarise and review each tutorial to achieve your Medic Mind.
Lesson
Objective ?
1 2 3 4 5 6
To gain an understanding of this new section in the UKCAT, and the timing involved. Be able to tackle syllogism questions by drawing appropriate Venn Diagrams and analysing carefully the wording of the syllogism.
To understand the variety in Venn Diagram questions, and tackle each type with the correct technique.
To be able to use fractions, data and decimals to calculate probabilities for scenarios.
7 8
To tackle logical puzzles using the Fill In method or the Cross Hatch method, or any appropriate alternative.
9 10 11 12
Learn how to tackle different types of graphical questions including scatter, pie, line, bar, text and table charts.
To understand statement questions and work to eliminate the statements that do not address the argument correctly.
13
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Question 1 Of all the Nobel prize winners of the past 5 years, none were neuroscientists younger than 25 years old. Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does follow.
a) Only those over 25 won a Nobel prize in the past 5 years. b) There have not been any neuroscientist winners younger than 25 years old. c) No Nobel prize winner in the past 5 years was a neuroscientist younger than 25 years d) All the Nobel prize winners above 25 are neuroscientists. e) There was definitely no neurologist winner below 25 in the past 5 years.
Question 2 Some gram-negative viruses, such as Epstein-Barr virus, cause disease by interfering with the cell’s DNA. Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does follow. a) All viruses are gram-negative. b) Epstein-Barr is gram-negative. c) Most gram-negative viruses interfere with the cell’s DNA. d) Some viruses cause disease. e) If a virus is gram-negative, it can interfere with the cell’s DNA.
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Question 3 The year is 2040 and the 2012 Jamaican Olympic team are having a reunion race for a charity event. They need to establish who is in the present moment the fastest and who is the slowest. They know that right now: Asafa is slower than Usain. Benjamin is slower than Swarley. Gayle is faster than Swarley but slower than Asafa. Swarley is slower than Asafa and Usain. Who are now the fastest and slowest members of the team? A. B. C. D.
Benjamin (fastest) and Gayle (slowest) Usain (fastest) and Benjamin (slowest) Belle (fastest) and Usain (slowest) Cora (fastest) and Belle (slowest)
Question 4 Brighton, Doncaster and Bradford are three cities in the DAHT (Domesticated Animals Hub Trilogy) of the United Kingdom. The whole population of Doncaster has pets, however only 80% have pets in Brighton. No citizens from Bradford have pets. Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does follow. a) Jonathon is from the DAHT and has a pet so he must be from Doncaster. b) No pet category can be owned by householders in all three of the DAHT c) Sam is from one of the cities of the DAHT. He does not have a pet. His neighbour has two pets. He must be from Brighton. d) Everyone in Matthew’s city has no pets. He lives in Bradford. e) The number of pets in Doncaster will always be more than the number of pets in Brighton. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 5 All Year 11 students at Alterif Grammar School studied French, except those who studied German who might or might not have studied French. Some French students passed their French GCSE. All German students passed their other (non-German) GCSEs. Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does follow. a) All Year 11 students study French or German. b) Some German students at Alterif passed their German GCSE. c) It is possible that some students at Alterif studied German and French GCSE. d) The majority of students at Alterif studied French GCSE. e) Harry studied German, Spanish and French GCSE at Alterif. He did not fail his French exam.
Question 6 Some of the Kasya tribe are villagers. All the villagers are hungry. Which of these conclusions are true? 1. All the Kasya tribe are villagers. 2. Some Kasya tribe are hungry. 3. Some villagers are hungry 4. All the Kasya tribe are hungry.
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Question 7 Some treats are ice cream. Some ice creams are desserts. All desserts are sweet. Which of these conclusions are true? 1. Some desserts are treats 2. Some treats are sweet 3. All ice cream are desserts 4. Some ice cream is sweet
Question 8 All elephants are animals. No elephants are chickens, yet some animals are chickens. All sharks are chickens. Which of the following diagrams best represents the information given?
A.
C.
B.
D.
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Question 9 Four people are taking part in a weight loss scheme - Jack, Samiha, Marco, Julian and Carlo. On the first day, their weights are 62kg, 66kg, 72kg, 74kg, 76kg (not in any order) and by the end of the scheme their weights were 67kg, 56kg, 63kg, 59kg, and 66kg, respectively (meaning that the person with 62kg ended up with 56kg, and so on). Samiha and Carlo lost the same amount of weight. One out of Jack and Julian gained weight. Jack started off with the second highest weight. Marco ended up with a higher weight than Samiha. Which of the following statements is true? a) Samiha began with 76kg, and Julian ended with 67kg b) Jack began with 66kg and Marco lost 9kg c) Samiha ended with 56kg, and Julian began with 62kg. d) They all lost weight during the programme. e) The sum of Julian and Carlo’s weight loss equals Jack’s weight loss.
Question 10 Should the UK leave the Paris agreement on climate change to overcome the issue of budget restriction? a) Yes, leaving the Paris agreement on climate change will mean that there is greater use of fossil fuels which will benefit the local economies. b) Yes, climate change is only a theory, and there is no scientific evidence for it. c) No, because the Paris agreement helps reduce the cost of advertising campaigns for climate change by NGOs (non-governmental organisations) and the cost of public street maintenance. d) No, because leaving the Paris agreement will lead to greater expenditure on healthcare by the government. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 11
In order to increase accessibility for those who cannot afford it, should university fees that have to be paid by homegrown students at the beginning of university, such as in the United States, be reduced? a) Yes. Students who enter university and borrow money from the government are crippled with debt in their future career. b) Yes. It will mean that income becomes less of a factor in helping someone gain a university qualification, as currently many people might not go university due to lack of funds. c) No. Universities require money and if university fees are reduced it will affect the quality of education. d) No. They can easily study in another country if they wanted to, where they would be offered a bursary.
Question 12 To help small businesses, should there be a cap on the amount a large corporation can earn? a) Yes, a cap on the amount they earn will mean that small business can compete with larger businesses as they will have similar amounts of investment to improve the business. b) Yes, there should be more equality in society, and a cap will mean that all business have the same turnover. c) No, because it discriminates against those who work hard for their business and earn more money. d) No, because it will reduce the productivity of the UK Economy.
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Question 13 A family is passing by a drive-through restaurant. All of the people in the car, except for Sam, want fries. More than one person in the car wants a chicken burger. Everyone orders something. Place ’Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does not follow. a) Sam wants a chicken burger. b) If a person in the car does not want a chicken burger, they must want fries. c) If a person in the car does not want fries, it must be Sam. d) If only two people in the car want a chicken burger, one of them must be Sam. e) Someone in the car wants both fries and a chicken burger
Question 14 Which of the following Venn diagrams best represents this information?
A.
B.
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Question 15 Jack is choosing balls and ribbons from a bag. The balls are coloured red, blue and green, and the ribbons are also coloured red, blue and green. Once a ball is picked out of the bag, it is not put back in. Once a ribbon is picked out of the bag, it is replaced. Jack picks a ball and ribbon together in each round. What is the probability that Jack will choose a ball and ribbon of the same colour twice in a row? A. B. C. D. E.
1/9 1/54 1/3 1/6 2/27
Question 16 John flips a coin every day for 200 days. On any given day, John continues tossing until he lands on tails, when he stops for the day. Using probability, estimate the number of days John will have where he flips exactly three times in the day. A. B. C. D. E.
12 25 50 100 125
Question 17 Lai and Timothy are playing a game called ‘Odds-On’. If they both guess the same number at the same time, they have to complete a dare. They can choose a number between 1 to 100 inclusive. What is the probability that they will both choose the same number, and that the number ends in zero? A. B. C. D. E.
1 / 100 1 / 1000 1 / 10000 1 / 100000 1••••••••••••••••••••••••••••••••••••••••••••••••• / 1000000 Page 76 •••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 18 Charles and Salina are taking part in a darts tournament. There are 3 rounds and for each round the probability of Charles scoring over 100 points is 0.4. All three rounds are completely independent. Charles believes he is more likely than not to score over 100 in at least one round. Is Charles correct? A. Yes, because there is an equal likelihood of scoring over 100 points for 3 rounds, and so the probability of scoring over 100 rounds in at least one round is 1.2 B. Yes, because the probability of scoring over 100 points once is 0.784 C. No, because the probability of scoring over 100 once is 0.064 D. No, because the probability of scoring over 100 once is 0.216
Question 19 The invigilator for A-Level examinations was checking if every pupil in the row was sitting in the right order. Four pupils, named Iresh, Bella, Sheena and Arthur were in the row, and all four were being examined for a different subject – Biology, Chemistry, Art and Philosophy (not in any order). Bella and Iresh were sitting on the ends of the row, B1 and B4 respectively. Iresh was not being examined for Art. The pupil examined for Art was sitting next to Sheena. The pupil sitting on seat B3 was being examined for Chemistry. B1
B2
B3
B4
Which of the following combinations must be true? A. B. C. D.
Arthur studies Chemistry and Sheena studies Art Iresh or Arthur study Art, and Sheena studies Chemistry Bella or Arthur study Chemistry Iresh studies Philosophy and Arthur studies Biology ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 20 Wollyworths has a ‘pick and mix’ section where children can choose different types of sweets and combine them into one product. This diagram below illustrates the possibilities with this.
Key of Shapes
Aaron, a headteacher of a school, picks up 50 different bags for his students. 31 bags include Marshmallows. 25 bags include Smarties. 4 bags have just Brownies. 2 bags have just Strawberries. 3 bags have just Smarties. 13 bags have just Marshmallows. No bags have just Strawberries and Smarties. No bags have just Brownies and Smarties. No bags have just Marshmallows and Brownies. No bags have Strawberries, Brownies and Smarties. 1 bag has just Brownies and Strawberries. 1 bag has just Marshmallows, Smarties and Brownies. How many bags have just Marshmallows and Smarties, and how many have just Smarties and Brownies? Marshmallows and Smarties
Smarties and Brownies
A
17
4
B
18
5
C
18
4
D
17
5
E
13
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Question 21 Chris owns a bakery and records the number of customers he gets on Wednesday, Friday and Sunday. On those three days he had exactly 50 customers. Below are the statistics for the week in general:
• • • • • •
13 customers in total came on at least Wednesday 20 customers in total came on at least Sunday 12 repeat customers came on just Wednesday and Friday 13 repeat customers came on just Friday and Sunday No repeat customers came on just Wednesday and Sunday No repeat customers came on all three days
Based on this information, how many customers did Chris have that only came on Friday? A. 19 B. 14 C. 33
D. 17
Question 22 Rickin asked 60 people which sports they liked from rugby, football and cricket. 8 people like all three sports. 17 people like rugby and football. 13 people like football and cricket. 19 people like rugby and cricket. 35 people like football. 27 people like cricket 30 people like rugby. How many people liked neither rugby, football or cricket? A. B. C. D.
6 7 8 9
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Question 23 The frozen yoghurt shop Moomoo records its sales over the past week. Customers are allowed to have as many combinations of toppings they want.
Based on this diagram, how many customers had a combination of just strawberry, chocolate chips, and smarties? A. B. C. D. E.
4 9 11 18 13
Question 24 A group of 20 friends are asking each other what countries they’ve visited in their life. 11 have visited France, 11 have visited Germany and 14 have visited Spain. 6 have visited Spain and Germany and of these 3 have visited France as well. Which of the following diagrams best represents the above data?
B.
A.
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Question 25 This diagram below shows a proposed plan for building a school. Each building has its own unique shape, and they are reserved for the departments of Biology, Chemistry, Maths, Physics and German.
•
The trapezoid is not allocated to Maths.
•
The Maths classroom is as far way from Biology as possible, because of the lack of timetable clashes.
•
Maths is equidistant from Chemistry and Physics.
•
Physics is closer to Biology than Chemistry.
Which classroom is represented by the circle? A. B. C. D.
Biology German Maths Physics
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Question 26 A tour company called Rurre runs a tour in South America to Las Pampas. They asked their customers to review their tours and found that 8 in every 10 would recommend the Rurre Las Pampas tour to a friend. Rurre write on their website that 80% of their customers would recommend their company. Was this claim justified? A. Yes, because they asked their customers themselves. B. Yes, because 8 in every 10 is the same as 80% C. No, as some of the customers would have done the Las Pampas tour with another company. D. No, because they are generalising from a sample.
Question 27 An after school club has 30 pupils that are in Year 11 and Year 12. There are 6 more boys than girls. 18 pupils are in Year 12, and 13 of these are boys. How many Year 11 boys are there in this after school club? A. B. C. D. E.
5 7 8 9 10
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Question 28 Liam, Naomi, Beth and Georgee went to a funfair. There were four stalls and they participated in the four stalls: Go-Karting, Whack-A-Mole, Teacup Ride and a Merry Go Round. They cost £3, £5, £6, £8 (not in any order). • • • •
Naomi didn’t go on the Go-Karts but her stall costs less than Georgee’s. Liam did not spend the most money, but he did spend £2 more than than Beth. Beth chose to took part on the Merry Go Round. Liam did not go on the Teacup Ride.
Who spent £8 for their activity? A. B. C. D.
Liam Naomi Beth Georgee
Question 29 Sam has a sandwich everyday. In this sandwich, his mum lets him have no more than 2 fillings out of Beetroot and Cucumber. One day, his Mum also buys Halloumi filling, which he hasn’t tried before. Sam says “now that I have Halloumi, I can make 6 different combinations of sandwiches using a maximum of 2 fillings per Sandwich”. Is he correct? A. Yes, because it will be 6 combinations with the addition of the previous 3 and another 3 B. Yes, because there will be 4 additional combinations from original 2 combinations he had. C. No, because it will be still be 3 combinations and one extra option doesn’t make a difference. D. No, because it will a total of 8 combinations.
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Question 1 All petrol stations are shops and all ice cream vans are shops. Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. A. B. C. D. E.
All petrol stations are ice cream vans Some petrol stations are shops Some petrol stations are ice cream vans Some ice cream vans are not shops There is a chance that a petrol station could possibly be an ice cream van.
Question 2 All rivers are meanders and no meanders are ox-bow lakes. Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. A. B. C. D. E.
Some meanders are rivers Some ox-bow lakes are rivers Some rivers are not ox-bow lakes Some meanders are not ox-bow lakes No ox-bow lakes are rivers
Question 3 All buildings are towers and some towers are landmarks. Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. A. B. C. D.
Some buildings are landmarks All towers are buildings Some landmarks are towers Some towers are buildings ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 4 Should all 18 year olds receive a free travel card for the whole of Europe to improve their cultural understanding of other countries? A. Yes. Travel is very expensive, and many students cannot afford it. A free travel card will help this. B. Yes. If 18 year olds go travelling around Europe, they will come back as better people and more employable individuals. C. No. The government’s budget does not have sufficient money to finance this. D. No. It is not vital to travel to understand the culture of different countries, as it can be done via other means such as reading.
Question 5 Should medicine tuition fees be scrapped to encourage more applicants? A. Yes. Some of the brightest applicants are put off medicine because they are afraid of the burden of student debt when they are older. B. Yes. If tuition fees are scrapped for medicine, there will be more doctors so more lives will be saved. C. No. If medicine tuition fees are scrapped, then anyone and everyone would apply meaning there will be incompetent and incapable doctors. D. No. Tuition fees are needed by universities to maintain their funding.
Question 6 Should children get free school meals to encourage healthy eating? A. Yes. It will only cost the government £1.3 billion, which can be invested in school meals instead of the military. B. Yes. It is estimated that school meals are 33% healthier than ordinary meals. C. No. School meals are not expensive and parents should be able to afford them for their children. D. No. It will mean that children eat more, since the food is free and so will lead to obesity problems. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 7 Tom and Salah are playing air hockey. •
Salah is playing the Cuban version, where you can only score 5 or 1. He plays for 3 rounds, and for each round, the probability of Salah scoring 5 points is 1/3.
•
Tom is playing the Swiss version, where you can only score 8 or 0. Tom plays for 6 rounds, and for each round, the probability of Tom scoring 8 points is 1/2.
•
All rounds of the game completely independent.
Salah believes that he is more likely to score 15 than Tom is to score over 30. Is Salah correct? A. Yes, because the probability of Salah scoring 15 is 1/27 and the probability of Tom scoring 40 or over is 6/64 B. Yes, because the probability of Salah scoring 15 is 1/27 and the probability of Tom scoring 40 or over is 7/64 C. No, because the probability of Salah scoring 15 is 1/27 and the probability of Tom scoring 40 or over is 1/64 D. No, because the probability of Salah scoring 15 is 1/9 and the probability of Tom scoring 40 or over is 7/64.
Question 8 I am rolling a dice 3 times, hoping to get a total score of 16 or more. Is the probability of this happening greater than 1/100? A. Yes, there are 10 possible ways to get 16 or more, and the probability of getting 16 or higher is 10/216. B. Yes, there are 7 possible ways to get 16 or more, and the probability of getting 16 or higher is 7/216. C. No, the probability of rolling any number is 1/6, and 1/6 x 1/6 x 1/6 = 1/216 D. No, there are not enough possible combinations for there to be a larger than 1/100 probability. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 9
(2 marks)
The retail department office are doing a lucky draw for the upcoming World Cup. There is one piece of paper in the draw per team. Once a paper has been picked, it cannot be put back in. The teams are: Brazil, Argentina, Chile, England, Germany, France and Spain. a) Two people go before Amaru. What is the probability that Amaru will pick Chile? A. B. C. D.
1/ 5 36 / 343 1 / 12 1/7
b) Two people go before Amaru. What is the probability that Amaru will be the first one to pick a European team? A. B. C. D.
7 / 343 1 / 55 2 / 105 1/5
Question 10 All windows are chairs, and no windows are satellites. Which of the following Venn Diagrams best represents this piece of information?
A
C.
B
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Question 11 I flip a coin and roll a dice once a day for six weeks. Using probability, estimate the number of days I will have where I simultaneously roll a six on the dice and flip a head on the coin. A. B. C. D.
1 2 3 5
Question 12 Sukhpreet is popping balloons and has three left to pop - a red, a green and a yellow. However, she only has two needles, so has to leave one unpopped for today. She chooses the balloons at random. What is the probability that she pops the red today? A. B. C. D.
1/6 1/3 1/2 2/3
Question 13 Yoga’s tour company in Bali offers several activities which can be purchased standalone, or as a package deal. Which of the following package deals are not available? A. Scuba diving alone B. Scuba diving and Abseiling C. Fly fishing and abseiling D. Abseiling, scuba diving and snorkelling
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Question 14 Should 18 year olds have to carry out 1 year of compulsory military service to help them in their future career?
A. Yes. Other countries do it, such as Singapore so the UK should follow suit. B. Yes. It is suggested that the military service has helped people gain skills such as leadership and teamwork. C. No. It will delay their working age by one year, which is detrimental as the UK has an ageing population. D. No. If they do military service, it will mean that they are tired when they start university and they will gain a poorer degree.
Question 15 Jonathon is counting up the number of sales of soft drinks at his bar for tonight. 47 people had orange juice 40 people had lemonade 50 people had banana smoothie 27 people had lemonade and banana smoothie 18 people had banana smoothie and orange juice 3 people had all orange juice, lemonade, banana smoothie 20 people had orange juice as their only drink. 4 people had lemonade as their only drink. Based on this information, how many people had both orange juice and lemonade? A. B. C. D. E.
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Question 16 A Geography class is surveying members of the public for their coursework. They find 34 participants (all public travellers), and ask them what mode of transport they use car, bus or tube. They all use at least one form of transport. 22 people use the Tube, 11 people use all three, 6 people use two forms of transport. The same number of people that use bus only as Tube only.
Which diagram best represents the information?
A. 7 1
B. 5
8
6
5
1
C. 5
8
6
5
1
D. 5
7
6
5
1
6 6
4
Question 17 The following diagram displays the details of the items 60 pupils from Brendan’s Vision Academy bought at the tuck-shop. Everyone bought something. Pizza slice
13
Fries
X
Y
Watermelon
11
24
Apple Pie
X
Y
Which of the following statements is true? A. The number of people with two options was greater than the number of people with one item. B. The number of people that had all four options cannot be calculated C. More people had fries than apple pie D. More people had pizza slices than Page watermelon ••••••••••••••••••••••••••••••••••••••••••••••••• 91 •••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 18 Which of the following diagrams correctly represents the relationship between England, Scotland, Wales, the United Kingdom and Great Britain? A
B
C
D
Question 19 Of all the tennis champions of the past 3 years, none were left-handed older than 30 years old. Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. a) Only those over 30 won a Tennis tournament in the past 3 years b) It is unlikely that there will be a left-handed tennis champion next year. c) No Tennis champion in the past 3 years who was left handed was older than 30 years old. d) All the Tennis champions in the past 3 years younger than 30 years old are lefthanded.
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Question 20 The pie charts below show annual statistics about two separate newspapers, and displays what the age distribution of the readers was. 18-24 55-64
25-34 65+
35-44
The Oracle of Information
1376 Readers
10%
45-54
Sign of the Times
1148 Readers
17%
21%
7% 19%
23%
15% 14%
8%
11%
27%
29%
Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. A. A greater number of 65+ year olds read the Oracle of Information than the Sign of the Times B. A larger number of people read the Oracle of Information every single day. C. The Oracle of Information has more readers above 40 than the Sign of the Times does. D. A greater proportion of readers are between 45-54 for the Sign of the Times than for the Oracle of Information.
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Question 21 The following table shows the number of raffle tickets Alex, Bethany and Elizabeth sold for their summer fete at school. The bronze tickets cost £5, the silver tickets cost £10 and the gold tickets cost £15. Alex
Bethany
Elizabeth
Bronze (£5)
11
47
31
Silver (£10)
23
4
15
Gold (£15)
4
0
5
Which of the following statements is true? A. One of Alex’s tickets was the winning ticket. B. Bethany made more money than Alex. C. Elizabeth single-handedly sold the most raffle tickets. D. Elizabeth sold more bronze and silver tickets than Alex sold bronze and silver tickets.
Question 22 The map below was developed to help design a new aircraft. Each aspect has its own unique shape and is reserved for the following: cabin-crew seat, emergency exit, kitchen, toilet and a Wi-Fi router. • The arrow is not allocated to the toilet. • The cabin-crew seat is almost equidistant from the Wi-Fi router and the toilet. • The emergency exit is as far away from the kitchen as possible to help ease confusion. Which of the following shapes represents the Wi-Fi router? A. B. C. D.
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Question 23 JumpingForJoyBeds
ILoveToSleepySleepy
100
The following graph shows the number of beds sold by:
80 60
JumpingForJoyBeds (JFJB) ILoveToSleepySleepy (ILTSS)
40 20 0
April
May
June
July
Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow. a) ILTSS made more sales overall than JFJB b) ILTSS has better beds than JFJB because they had more sales in 3 out of 4 months c) July was the month were most beds were sold in total. d) ILTSS sales figures has a larger mathematical range than JFJB.
Question 24 At Heathrow Airport, there are 4 different flights to 4 different destinations by 4 different airlines. This comprises of a flight by Jetlag Airways, a flight to Bangkok, a flight to Berlin and a flight to Dehli. • Skyline Airways does not fly to Delhi. • The airline which flies to Bangkok is a sister airline to OrangeJet. • The other destination is Toronto. • GlorianAir is flying to Berlin. Where is OrangeJet flying to? A. B. C. D.
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Question 25 Four people are at the opticians. All four of them have different coloured T-shirts to each other, and they also have different coloured glasses as well. One of them was wearing a black T-shirt, another a purple T-shirt, another one a green T-shirt and another an orange T-shirt. One of them was wearing burgundy glasses, another black glasses, another yellow glasses and another red glasses. • Felicity wore black glasses. • Alice wore a purple T-shirt and Sandra wore a green T-shirt. • The person wearing a black T-shirt wore yellow glasses. Which of the following must be true? A. Alice wore burgundy glasses B. Sandra wore red glasses C. Felicity wore a black T-shirt D. Felicity wore an orange T-shirt.
Question 26 Thivu and Anjali are talking about their daily habits. Anjali tells Thivu that:
- “When I go swimming, I have breakfast. If I don’t go swimming, I don’t have -
breakfast”. “When I don’t go swimming, I don’t feel satisfied”. “Today, I am satisfied and have had two great meals!”. “When I nap, I have lunch and I am also satisfied. When I don’t nap I don’t have lunch”.
Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not. A. Today, Anjali is not swimming. B. Today, Anjali is having a nap. C. When Anjali goes swimming, she is satisfied D. If Anjali is not satisfied, it means she is not swimming E. If Anjali is satisfied, it means she had a nap. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 27 The question mark represents two of the same shape. Which shape is this?
A. B. C. D.
Square Triangle Circle Diamond
Question 28 Should laptops be allowed on aircrafts since they post a threat to security? A. Yes. Laptops do not have to be used on aircrafts, as there are several alternative forms of entertainment. B. Yes. Terrorists could use laptops to implement explosive devices such as the failed attempt in 2007. C. No. If people do not use laptops to cause terror, they will find an alternative form anyway. D. No. Airport security is stringent enough to prevent any threat.
Question 9 counts for 2 marks, making 29 in total.
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Question 1 - E and F In this scenario we are told about two groups: • One group from London, which could study either subject • One group who must by default be from Manchester, and who all study Economics. A. No We do not know if any of the first cohort, from London, study Economics. B. No Again, we do not know if any of the first cohort, from London, study Economics. C. No There is a possibility that the students from London could all study Geography. D. No The question is rephrasing the same concept in different ways to confuse you. Again, we do not know if any of the first cohort, from London, study Economics. E. Yes We know that all of the Manchester students study Economics. F. Yes The London cohort could study either subject, and the key word here is ‘possibility’ which makes this statement true.
Question 2 - C
Cockroaches
Crocodiles Strawberries
Qualification: The overlap between cockroaches and strawberries may contain 0 items. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Answers and Explanations Tutorial Scenarios Based on this Venn diagram, we know that: A. False - we do not know this. B. False - this could be the case, but it may not be. C. True - yes all of the crocodiles are strawberries. D. False - all of the crocodiles are strawberries, not cockroaches
Question 3 - D
Qualification: There could be a relationship between cupboards and leaves, cupbaords and jungles, trees and jungles, or cupboards and leaves. A. B. C. D.
No - we cannot tell if there is a relationship, but there could be No - we cannot tell if there is a relationship, but there could be No - this is not true because some trees are leaves, not all. Yes - some trees are leaves, and all leaves are jungles.
Question 4 - C Expected Frequency = Probability x Number of Repeats Probability is 1/7. The number of repeats is the number of days, which is 14. Expected Frequency = 14 x 1/7 = 2 days
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Question 5 - C Remember, because the marbles are replaced each event is independent. Probability of red three times = Probability of red x Probability of red x Probability of red Probability of red three times = 1/4 x 1/4 x 1/4 = 1/64
Question 6 - D The answer is D because the probability of scoring one goal or more = 1 - (probability of scoring in neither half) 1 - (0.8 x 0.8)
=
1 - 0.64
=
0.36
You might get tempted by A, but this is the calculation to work out if a goal happens in either the first or second half. It doesn’t take into account the fact that if they score in both halves, and both events happen, they have still scored ‘at ;east one goal’. You might also be tempted by C, but this answer option does not consider the fact that he could score in both halves.
Question 7 - B This question combines this rule and the repeat of same events rule: Probability of England Winning and Giroud Scoring At Least Once First work out the probability of Giroud scoring at least once: = 1 - probability of him not scoring in any match = 1 - (5/6 x 5/6 x 5/6) = 1 - 125/216 = 91/216
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Answers and Explanations Tutorial Scenarios We need to multiply the probability of England winning by the probability of Giroud scoring at least once: 1/24 x 91/216 = 91/5184 = 1.76% chance Probability of Giroud in Every Match Probability of A x A x A 1/6 x 1/6 x 1/6 = 1/216 = 0.46% chance The probability of Giroud scoring three times is lower than the probability of England winning the World Cup and Olivier Giroud scoring a goal.
Question 8 - D If the probability of winning a contest is 1/10 and the probability of having Italian for dinner is 1/5, the probability of either happening is: 1 - probability of neither happening = 1 - (9/10 x 4/5) = 1 - 36/50 = 14/50
Question 9 -
D
Probability of Red twice = Probability of Red 1st time x Probability of Red 2nd time The probability of getting a red first time is 3/6, as there are 3 red balls out of 6 in total. If Sam picked a red first time, then there will be 2 red balls out of 5 in total for the second pick. Remember, Sam is not replacing the balls. Therefore the probability of getting a red second time is 2/5. Probability of Red twice = 3/6 x 2/5 = 6/30 = 1/5
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Question 10 -
C and D
Let’s go through each statement: a) No. He has the equally smallest dot, and the lowest score for both Maths and English. It is likely that Troopinder’s is the hardest to diagnose. b) No. This graph shows their performance on English, Maths and an IQ test. While there may be a correlation with these three and attendance, there is nothing from the information given to suggest this. Remember do not use external knowledge and do not make any assumptions that do not have any underlying evidence. c) Yes. This is a potential explanation for the results seen on the graph. The key word in this statement is the word ‘plausible’. If it did not contain the phrase “it is plausible” then it is likely that the answer to this question would have been no. Mohammed has an overall higher an IQ but does more poorly on both English and Maths exams. It could be that there are other reasons why the pattern was seen. Linking back to what we learnt in Verbal Reasoning, the statement is quite mild so more likely to be true. d) Yes. This could be true as Troopinder’s scores on the Maths exam was much higher than it was on the English one. Another key word here is potential - the statement does not outright say that he will do better in a Mathematically orientated career, as of course there are several factors that could contribute to the success. e) No. While it can be said that Robbie is better than Mohammed at maths since he performed better on the maths test, he may be weaker in certain aspects than Mohammed is. The answer therefore is no.
Question 11 -
D
D is the correct answer… Science 14 + 15 + 19 = 48% 0.49 x 1300 = 624 (to save time you could estimate it to be 0.5 x 1300 = 650) Mathematics 15 + 14 + 10 = 39%
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Answers and Explanations Tutorial Scenarios 0.39 x 1050 = 409.5 (to save time you could estimate it to be 0.4 x 1000 = 400) Knocking out A… A is false as the Maths museum had 500 visitors per day, compared to the Science museum which had 400 visitors per day. Science 9% + 24% = 33%. 0.33 x 1300 = 429 (to save time you could estimate it to be 0.3 x 1200 = 400) Maths 19% + 27 % = 46%. 0.46 x 1050 = 483 (to save time you could estimate it to be 0.5 x 1000 = 500) This is therefore false. Knocking out B… B - we do not have sufficient amount of information to deduce this. It could just be 1300 visitors were surveyed for the Science Museum and 1050 surveyed for the Mathematics Museum, not the total number of visitors. C - is not necessarily true, as this could mean that some of the visitors that stayed for much longer or much less time are eliminated and therefore could skew the results.
Question 12 -
A and C
Let’s go through each statement: a) Yes, this is correct:
A quick method to see this would be to look at the gap between the largest value of Manchester and the lowest value of Manchester and compare this gap with the gap for the corresponding values for Bristol.
Manchester 100 - 35 = 65
Bristol 70 - 20 = 50
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Answers and Explanations Tutorial Scenarios b) No. While this is a plausible possibility, there is insufficient information present for that to be the case.
c) Yes, this is correct:
Manchester 35 + 35 + 50 + 100 = 220
Bristol 20 + 45 + 70 + 60 = 195
d) No. We cannot tell what the pattern is based on the information that has been presented.
Question 13 -
C and E
Let’s go through each statement: a) No. We cannot tell anything about the entire UK population. We only know from a small sample size. This is a Passage Adjustment, as we saw in Verbal Reasoning.
b) No. We cannot know this for sure unless we sample them. Do not make unnecessary assumptions. This is Extreme Language, as we saw in Verbal Reasoning.
c) Yes, this is correct:
Labour Conservative
50 + 95 = 145
70 + 60 = 130
d) No. We can tell from a distance that the largest discrepancies came between 18-25 year olds, or from 46+ year olds. Here, a good method to use would be percentages.
18-25 46+
(55 - 20) / 55 = 64% (95 - 60) / 95 = 37%
This means that the 18-25 difference was the largest.
e) Yes, this is correct:
Labour Conservative
20 + 30 + 50 + 95 = 195 55 + 25 + 70 + 60 = 210
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Question 14 -
A and B
Let’s go through each statement: a) Yes, this is correct: This is true. On average the most popular milkshake was chocolate therefore it is acceptable to suggest that it was the most bought milkshake. b) Yes, this is correct: Cardiff 17 + 26 + 53 + 96 = 192 192/4 = 48 London 55 + 43 + 70 + 58 = 226 226/4 = 56.5 The average amount for London is higher therefore the answer is ‘yes’. Remember, always try and use estimation when you can as it will save time. ~ represents ‘roughly’ Cardiff ~ 20 + 25 + 50 + 100 = 195 = ~ 200 200/4 = 50 London ~ 50 + 40 + 70 + 60 = 220 220/4 = 55 London is still higher. c) No, this is false: 55 - 17 = 38 96 - 58 = 38
They were equal.
d) No. We cannot tell this from the information given, as we do not know about the production cost and selling price of each ice cream as they could be different.
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Answers and Explanations Tutorial Scenarios e) No. There is no evidence to suggest this is the case. The milkshake sales could be due to a large array of factors.
Question 15 -
A
Remember, not all the information they present will be important. We need to work out what is represented by the monkey bars. Looking at the box from afar, we see that three shapes are very close to each other, and two shapes are in the opposite corners. When corroborating with the text, we see why it is useful to look at the box from afar. It is likely that the triangle, semi circle and pentagon all relate to the phrase: “The slide is almost equidistant from the see-saw and roundabout”. This must mean that the semi-circle represents the slide. We know that the triangle and pentagon could both be either see-saw or roundabout. To help us work out which one is which we can use: “The roundabout is not allocated to the triangle”. This means that the roundabout is therefore related to the pentagon, and the see-saw is related to the triangle. We now know the middle three shapes. We are left with bench and monkey bars. We know that “the monkey bars are not allocated to the heart”. This means that the monkey bars must be the trapezium shape, so the answer is A, trapezium.
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Question 16 -
A, B and C
Let’s go through each statement: a) Yes. We know that there are some cape wearing superheroes who do not know how to get from one place to another, and from this we can infer that there are some that do know how to get one place from another and also wear capes. All cape wearing superheroes are fast meaning the answer to this is Yes.
b) Yes. Same reasoning as above, we know that all superheroes that are fast wear capes, and that there must be some superheroes that do know how to get from one place to another.
c) Yes. We know that some cape wearing super heroes cannot get from one place to another. Cape wearing superheroes = fast flyers. This means that some fast flying superheroes do not know how to get from one place to another. The answer is therefore yes.
d) No. We do not know anything about superheroes that do know how to get from one place to another.
Question 17 -
C
C is the correct answer…
Normal Edition 61 x 8.99 = £548.39 (Could estimate by doing 60 x 10 = £600) Deluxe Edition 27 x 13.99 = £377.73 (Could estimate by doing 30 x 14 = £420) Knocking out A… 36 + 41 + 61 = 138 29 + 25 + 27 = 81 Knocking out B…
Magazine 1
36 + 29 = 65
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Answers and Explanations Tutorial Scenarios Magazine 2
41 + 25 = 66
Knocking out D… While it may have more pages, and may be cost effective per page - we do not know what the general consensus of the public is - they may have found that those extra pages did not add much to the quality of the book.
Question 18 -
B
The quickest way to answer these questions is to try and eliminate ones that are not related to the statement at all. Break down each part of the statement and we learn that it is about: Should abortion be legal to help cases of women being raped and having a child they never planned for ? • A does not address all aspects of this. it only addresses the abortion aspect. • C only addresses the rape aspect. • D only addresses the abortion aspect. This means that the answer is B. Not all questions will be as straightforward as this, but it is clear to see that 3 of the 4 options were ruled out just by looking at whether they addressed all aspects of the question.
Question 19 -
C
This is slightly harder, as all of them are potentially viable arguments for having the right to bear a gun. All of them address the aspect of bearing a gun for protection in some form, however the extent to which they relate to the argument is questionable. •
A is based on a small area of the UK, and there is no basis to support the argument that every single citizen could benefit. There is no evidence for the statement either, it could easily be sensationalised.
•
B does not explain why a higher self-confidence will lead to people being more protected.
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D has the same problem. It does not tell us how it exactly relates to a different level of protection.
Question 20 -
A
Remember, always try to eliminate information that does not relate to the statement at all. • •
B is related to cosmetic goods rather than scientific testing. C is a general point and is not specific to scientific testing, but is still a valid point. The reason the answer is not C is because it does not suggest why animal testing being cruel and barbaric is a reason for animals to not be used in scientific testing.
•
D contains scientific evidence which is usually a good sign of a valid argument. However, this does not tell us the significance of animals being used that are part of the Animal Welfare act.
•
A is the correct answer as not only does it directly relate to scientific testing, it addresses the aspect of preventing disease which the other options do not.
Question 21 -
A
•
B does not provide a basis as to how that improves economic activity.
•
C does not address economic activity per say, it is focused on inequality.
•
D is a sensationalised statement based on a lack of evidence.
Question 22 -
D
•
A does not address alcohol addiction.
•
B does not address the issue of age
✓ C is an assumption based on a lack of evidence •
D involves scientific evidence and explains why changing the age limit will not impact alcohol addiction.
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Question 23 -
C
•
A is an assumption.
•
B is an assumption based on a lack of evidence - while it may be true that it is an invasion of privacy there is no evidence to support it.
✓ C is the strongest argument as the reasoning provided is based on evidence. •
D does not tell us how many terrorist attacks take place and how they use social media, and whether accessing personal data on social media would prevent them.
Question 24 -
B
•
A is a valid reason but does not mention anything about illegal activity.
•
C does not relate to the illegal activity aspect
•
D is an illegal offence but does not relate to smuggling
Question 25 -
D
•
A does not relate to reducing crime.
•
B also does not relate to reducing crime.
•
C does not address the issue of the death penalty.
✓ D is valid as murder is a crime.
Question 26 •
B
A does not relate to animal cruelty.
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•
C is a valid point, but does not take away from the fact that there are zoos with animal cruelty.
•
D does not relate to animal cruelty.
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Question 1 - C
A. No. It does not follow because there could have been non-neuroscientist Nobel prize winners that were under 25. B. No. It does not follow as we only know about the last 5 years. C. Yes. It does follow as this is a paraphrase of the statement information. D. No. It does not follow as there could have been Nobel prize winners above 25 that were not neuroscientists. E. No. It does not follow as it is about neurologists, not neuroscientists. This is a subtle Passage Adjustment.
Question 2 - B and D
A. No. It does not follow as we do not know that all viruses are gram negative. B. Yes. This follows as the statement gives Epstein-Barr virus as an example of a gramnegative virus. C. No. Even though some gram-negative viruses do this, we do not know that the majority of them do. D. Yes. This does follow as the statement says that some gram-negative viruses cause disease. E. No. This does not follow as we know that some gram-negative viruses have this ability, but we don’t know if this applies to all gram-negative viruses. If the statement said ‘gram-negative viruses can interfere with the cell’s DNA’ this would be true, but instead this statement is saying that any gram-negative virus has the ability to interfere with cell DNA.
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Question 3 - B
You want to develop a list here, from fastest to slowest (top to bottom), step by step… Asafa is slower than Usain… Usain Asafa Benjamin is slower than Swarley… Usain Asafa
and
Swarley Benjamin
Gayle is faster than Swarley but slower than Asafa… Usain Asafa Gayle Swarley Benjamin Swarley is slower than Asafa and Usain… Usain Asafa Gayle Swarley Benjamin This means that the answer is B
Question 4 - B and C
A. No. This does not follow as he could also be from Brighton. B. Yes. This does follow as no citizen in Bradford has pets.
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C. Yes. This does follow as as he cannot be from Doncaster, where everyone has pets, or Bradford, where no one has pets. D. No. The statement does not say that Matthew is from a city in the DAHT, so it does not have to be Bradford. E. No. This does not follow as we do not know the number of pets per household or the total population.
Question 5 - C and E
A. No. This would apply for Alterif school, but the question talks generically about Year 11 pupils.
B. No. We know that all of them passed their other GCSEs, but we do not know if any actually passed German. C. Yes. This is plausible, as the statement is very mild as it says ‘it is possible’. D. No. Even though this seems likely due to the tone of the passage, it is not necessarily true. E. Yes. All German students passed their other GCSEs, so Harry must have passed French and Spanish.
Question 6 - 2 and 3
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1. False - we only know that some of the tribe are villagers. 2. True - some of the tribe are villagers, and all villagers are hungry, so some of the tribe must be hungry 3. True - all villagers are hungry, so this statement is satisfied. 4. False - some of the tribe are hungry (the ones that are villagers), but we do not know that all are hungry.
Question 7 - 4
1. False - we cannot infer this from the information. 2. False - again we cannot infer this from the information. 3. False - some ice cream are desserts, not all. 4. True - some ice cream is dessert, and all dessert is sweet, so some ice cream is sweet.
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Question 8 - C We need to build the Venn Diagram step by step:
All elephants are animals…
No elephants are chickens, yet some animals are chickens…
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All sharks are chickens…
C is therefore our answer.
Question 9 - C The Fill in Method works best for this question. Step 1: Set up the table Name
Original Weight
End Weight
Weight Change
62
67
+5
66
56
-10
72
63
-9
74
59
-15
76
66
-10
Step 2: Go through each piece of information step by step, updating the table:
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Answers and Explanations Mock Test 1 Samiha and Carlo lost the same amount of weight… They must both have lost 10kg as these are the only two equal weight changes. Name Samiha / Carlo
Samiha / Carlo
Original Weight
End Weight
Weight Change
62
67
+5
66
56
-10
72
63
-9
74
59
-15
76
66
-10
One out of Jack and Julian gained weight… Jack or Julian must have gained 5kg, as there is only one person with weight gain. Name
Original Weight
End Weight
Weight Change
Jack / Julian
62
67
+5
Samiha / Carlo
66
56
-10
72
63
-9
74
59
-15
76
66
-10
Samiha / Carlo
Jack started off with the second highest weight… Jack musth have started off with 74kg, as this is second highest. Therefore we also know that it was Julian who gained 5kg as it cannot have been Jack (and from the previous step we know that it was one of them). We can also fill in Marco’s position because by default he must occupy the empty spot. Name
Original Weight
End Weight
Weight Change
Julian
62
67
+5
Samiha / Carlo
66
56
-10
Marco
72
63
-9
Jack
74
59
-15
Samiha / Carlo
76
66
-10
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Marco ended up with a higher weight than Samiha… We know that Samiha either ended up with 56kg or 66kg, with Carlo being the other. Marco ended up with 63kg, so Samiha must have ended up with 56kg and Carlo 63kg. Name
Original Weight
End Weight
Weight Change
Julian
62
67
+5
Samiha
66
56
-10
Marco
72
63
-9
Jack
74
59
-15
Carlo
76
66
-10
Step 3: Eliminate and select the final answer: A. False - Samiha began with 66kg B. False - Jack began with 74kg C. True - both are correct. D. False - Julian gained weight. E. False - the sum of Julian’s (+5) and Carlo’s (-10) change is -5. Jack’s change is -15.
Question 10 - C • A does not address the budget restriction issue, as it doesn’t suggest why benefitting the local economies will help the budget restriction issue. • B does not tell us anything about the Paris agreement or budget restriction. • D addresses the issue of budget restriction, but is based on an assumption that it will lead to more spending in healthcare which may not necessarily occur.
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• This leaves C, which is the correct answer because it explains two ways in which the Paris agreement actually reduces budget restriction problems in both the private (NGOs) and public sectors.
Question 11 - B • A is addressing the issue of future debt for students, rather than the problem of people not being able to access university due to financial problems now. • B is correct because it addresses the issue of current financial problems hindering someone’s ability to pay for university. • C does not acknowledge the argument about accessibility of education. • D ignores the word homegrown.
Question 12 - A • C and D do not address how this will help or affect small businesses. Remember, even if the statement makes sense in a debate, it needs to address all issues of the topic. • B does consider how a cap will affect small businesses, but the logic of the statement does not make sense. It does not explain why having the same turnover will not support small business, but beyond that the logic that all businesses will have the same turnover is flawed as it is a maximum cap that many businesses may not reach. • A is the correct answer because it explains why a cap will help equalise the levels of investment small and big firms have.
Question 13 - C and E a) No. There is no information on whether Sam wants a chicken burger. b) No. They may order something else apart from a burger of fries, such as a milkshake. c) Yes. Everyone in the car wants fries except for Sam. ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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d) No. Again, Sam could want something else than fries or a chicken burger, such as a milkshake. e) Yes. As more than one person wants a chicken burger, and only one person (Sam) doesn’t want fries.
Question 14 - C For these type of questions you need to consider how many overlapping regions there are as well as how many separate sections there are. We know that there is one main title, and under that title there are two subtitles. Within each of the two subtitles there are two sets as well. There are likely to be 7 regions in total. •
A is incorrect because it only has 6 regions, ignoring the fact that all the other categories come inside animals.
•
B is incorrect because it only has 5 regions, and in general does not represent the information accurately.
•
C is correct because it has 7 regions, and fixes the issue we had with A by having an all encompassing circle to represent animals.
Question 15 - A Step 1: Write down the probabilities involved
Let’s first write down the probabilities involved: 3 types of ribbon 3 types of balls
-
1/3 chance of getting R, B or G 1/3 chance of getting R, B or G
Step 2: Work out all possible combinations to get two repeat colours
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Then we should look at the combinations that can occur for Jack to have picked the ‘same colour and ribbon twice in a row’. Let b denote bag and r denote ribbon. RbRr | BbBr
RbRr | GbGr BbBr | RbRr BbBr | GbGr GbGr | RbRr GbGr | BbBr This means that there are 6 possible occasions where this could occur.
Step 3: Work out the probability of one of these combinations happening. Let us work out the probability of one of those occurring - Red Ball and Red Ribbon followed by Blue Ball and Blue Ribbon. P(Rb) = 1/3 P(Rr) = 1/3 P(RbRr) = 1/3 x 1/3 = 1/9 P(Bb) = 1/2 P(Br) = 1/3 P(BbBr) = 1/2 x 1/3 = 1/6
(there are now two balls remember) (unlike the balls, the ribbons are replaced)
P(RbRr | BbBr) = 1/9 x 1/6 = 1/54
Step 4: Work out the probability of all six of these combinations happening and hence the final answer. The probability of all six combinations above is equal. So we can work out the overall probability by multiplying by 6: 1/54 x 6 = 6/54 = 3/27 = 1/9 The answer is therefore 1/9.
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Question 16 - A
The probability of getting heads on any coin toss is 0.5. Lets work out the number of days with: • 0 heads. On 100 days out of 200, he is likely to get tails in his first toss and finish for the day. • At least 1 head. On 100 days out of 200, he is likely to get heads in his first toss and toss again. At least 2 heads. On 50 days out of these 100 he is likely to get heads the second time, and toss again. At least 3 heads. On 25 days out of these 50 he is likely to get heads the third time, and toss again. Only 3 heads. On 12.5 days out of these he is likely to get tails the fourth time, and stop for the day. As you cannot have half days for this question, the answer must be A = 12 days
Question 17 - B
Step 1: Work out how many numbers end in 0 in the range.
So, first of all we know that Lai’s number and Timothy’s number are mutually exclusive events. This means that the number Lai chooses does not affect which number Timothy chooses. The numbers ending in 0 from 1-100 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. There are 10 numbers in total ending in 0. We need to work out the probability that they will both guess one of these 10 numbers.
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Answers and Explanations Mock Test 1 Step 2: Write down the probability of choosing one of these numbers. The probability of choosing any of these numbers is 1/100 for each player.
Step 3: Write down the combinations that could occur to satisfy the question. For them to both choose the same number which ends in zero, they need to have one of the following combinations. The sum of the probabilities is 10 / 10,000 = 1 / 1,000 Medic Mind Tip: It is not time efficient to draw out this whole table as shown above. We have only presented it in full for clarity, but in the exam you should look to save time wherever possible by avoiding writing down too much in tables.
Question 18 - B P (scoring over 100 in total at least once) = 1 - P (scoring over 100 zero times) The probability of Charles scoring below 100 on any given round is 0.6. Hence the probability of Charles scoring below 100 three times is 0.6 x 0.6 x 0.6 = 0.216 P (scoring over 100 in total at least once) = 1 - 0.216 = 0.784
Question 19 - B To tackle this question draw a diagram and work through each statement: Bella and Iresh were sitting on the ends of the row… Bella
Iresh
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Answers and Explanations Mock Test 1 Bella was not being examined for Art. The pupil examined for Art was sitting next to Sheena… Bella
Sheena / Arthur
Sheena / Arthur
Iresh
Sheena can only be at B2 if B3 is studying Art (as Bella doesn’t study Art).
The pupil sitting on seat B3 was being examined for Chemistry… This confirms that Sheena is sitting at B3, studying Chemistry. If she was at B2, she would be next to Bella (not doing Art) and Arthur (studying Chemistry), which cannot work as she sits next to an Art student. Bella
Arthur
Sheena (Chemistry)
Iresh
The answer is therefore B.
Question 20 - A
Fill in the Venn Diagram step by step, starting with the information involving the most number of categories.
1 bag has just Brownies and Strawberries. 1 bag has just Marshmallows, Smarties and Brownies.
1
1
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Answers and Explanations Mock Test 1 13 0 0
1
No bags have just Strawberries and Smarties. No bags have just Brownies and Smarties. No bags have just Marshmallows and Brownies. No bags have Strawberries, Brownies and Smarties.
4
3
1 0
2
4 bags have just Brownies. 2 bags have just Strawberries. 3 bags have just Smarties. 13 bags have just Marshmallows.
0 0
1
1 0
13 0
31 bags include Marshmallows. 25 bags include Smarties.
17
0
1
3
4
4 1
0
2 The answer is therefore A.
Medic Mind Tip: This question is quite different to other Venn Diagram questions in the sense that there is less calculating and more manual input of numbers into the correct places in the Venn. However, it takes time to manoeuvre and input the correct numbers, and the various shapes make it all the more challenging. Remember to start with the information involving the most categories.
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Answers and Explanations Mock Test 1 Medic Mind Tip: This is the type of question which might take 2-3 minutes to do, so if you are running short of time you might want to Flag it and move on.
Question 21 - D They have presented us with a great deal of information. The best thing to do here would be to covert the information into a form that is understandable - a Venn diagram. Let’s fill in the information one by one. It is best to start with information that tells us about more than one category so let’s start from the bottom.
No repeat customers came on both Wednesday and Sunday, and no customers came on all three days…
13 repeat customers on just Friday and Sunday…
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Answers and Explanations Mock Test 1 12 repeat customers on just Wednesday and Friday…
Now we’re left with the rest of the statements that only tell us about each day individually.
13 customers came on at least Wednesday. 20 customers came on at least Sunday…
We need to put 1 in the ‘Wednesday only’ section because we already have 12 who came on Wednesday and Friday overlap on two days and 13 -12 = 1. We need to put 7 in the ‘Sunday only’ section as we already have 13 and 20 -13 = 7
If we add up all the numbers that are present in the Venn diagram, we have 33 customers. We know 50 customers came Since we have all the other information in the Venn diagram apart from customers who came ‘Friday only’, we can minus 50 – 33 = 17.
Question 22 - D As with previous Venn Diagram questions, work through step by step to fill in the Venn. The answer is 9 - D.
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Question 23 - A
4 is the correct number where the three shapes of strawberry, chocolate chips, and smarties overlap.
Question 24 - A Go through each piece of information to knock out answer options. A group of 20 friends are asking each other what countries they’ve visited in their life… B does not add up to 20. 11 have visited France, 11 have visited Germany and 14 have visited Spain… C does not have a circle which adds up to 11. 6 have visited Spain and Germany and of these 3 have visited France as well… D does not have 3 in the centre. This leaves us with A, the correct answer.
Question 25 - D The trapezoid is not allocated to Maths. The Maths classroom is as far way from Biology as possible, because of the lack of timetable clashes…
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Maths cannot be the trapezoid. To maximise the distance between Maths abd Biology we need to pick the plus and heart for these two subjects.
Maths is equidistant from Chemistry and Physics… Maths must be the plus as it has to be equidistant from Chemistry (arc) and Physics (circle or trapezoid).
Physics is closer to Biology than Chemistry… Physics has to be the circle, as the trapezoid is closer to Chemistry than Biology. German by elimination is the trapezoid. This means that the circle is Physics, D.
Question 26 - D •
A only tells us about the methodology and does not specify where these customers were from. They could be general Rurre customers, rather than specific to Las Pampas.
•
B does not justify the claim, it just shows the mathematical logic for a fraction being converted to a decimal.
•
C does not make sense, as the customers are recommending the Las Pampas tour by Rurre, not by any other company.
•
D is the correct answer, as it spots the flaw in the argument. 8 in 10 customers who did a review said they would recommend the tour. However, there could have been over 1000 customers with only 10 giving reviews. The 80% statement on the website is a generalisation extending from the small sample to the whole customer base.
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Question 27 - A There are 18 students in Year 12. Therefore there are 12 students in Year 11. There are 13 boys and 5 girls in Year 12. In total there are 6 more boys than girls. Number of girls = G ①
B=G+6
②
B + G = 30
Number of boys = B
G + 6 + G = 30 2G = 24
G = 12
B = 18
There are 13 boys in Year 12, so there must be 5 Boys in Year 11 and 7 Girls. Answer is A.
Question 28 - D We can use the Fill In Method for this question. Let’s fill in the information one by one. The information which tells us clearly what a person’s stall or cost is, is best to use. Step 1: Let’s start with stalls. Beth chose to took part on the Merry Go Round… Naomi didn’t go on the Go-Karts… Liam did not go on the Teacup Ride… Name
Stalls
Liam
N (Teacup)
Naomi
N (Go Kart)
Beth
Merry Go Round
Cost
Georgee
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This doesn’t really give an indication of what the most expensive stall is. In Decision Making questions they will present you with a lot of information, and much of it may be unnecessary, but you can rarely know this unless you write the information down in a format which is more understandable like above. In this scenario the stalls were a distractor. Step 2: Now let’s look at the costs. Liam did not spend the most money, but he did spend £2 more than than Beth… We know that Liam spent more £2 more than Beth. This must mean that their spends must be £8 and £6, or £5 ad £3. Liam did not spend the most money, so it must be the latter. . Name
Stalls
Cost
Liam
N (Teacup)
£5
Naomi
N (Go Kart)
Beth
Merry Go Round
£3
Georgee
Naomi didn’t go on the Go-Karts but her stall costs less than Georgee’s… We’re left with the fact that two items cost £6 and £8. We know Naomi’s stall cost less than Georgee’s, so Georgee’s spend was the most expensive - £8. Name
Stalls
Cost
Liam
N (Teacup)
£5
Naomi
N (Go Kart)
£6
Beth
Merry Go Round
£3
Georgee
£8
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Question 29 - A Cucumber = C
Beetroot = B
Halloumi = H
Let’s take the four fillings as x and y. At first, these were the possible combination of fillings Sam could have: C, B, CB
=
3 combinations
Now we have H (Halloumi). These are the possible combinations with Halloumi: C, B, CB
(ones from before)
H, CH, BH
(new combinations)
This means there are now 6 combinations, in addition to the original 3. The correct statement is therefore A.
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Question 1 - B and E Looking at Medic Mind’s Guide to Syllogisms, this is an example of Pattern 9. We can draw a Venn diagram to represent this information and help us answer the question much more quickly.
Petrol Stations
Ice Cream Vans
Shops
A. No. Looking at the Venn diagram, they are two separate circles and so there is no known relationship between them. B. Yes. All petrol stations are shops, so it is correct to say some are shops. C. No. Just like for A, looking at the Venn diagram, they are two separate circles and so there is no known relationship between them. D. No. If all ice cream vans are shops, then there cannot be any ice cream vans that are not shops. E. Yes. There is no known relationship between petrol stations and ice cream vans, but there could be a relationship if we were given further information. The wording is very broad, and not extreme at all - it is just asking if there is a possibility, which there is. We cannot definitely say that there is no relationship, but there is no known relationship based on the information we have.
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Question 2 - A, C, D and E This is an example of Pattern 11 of Medic Mind’s Guide to Syllogisms.
Rivers
Meanders
Ox-bow lakes
A. Yes. We know that all rivers are meanders, therefore some meanders are rivers. B. No. We know that no meanders are rivers, and this also means no rivers are ox-bow lakes by the same logic, as all rivers are meanders. C. Yes. We know that no meanders are ox-bow lakes, and all rivers are meanders. By this logic, all rivers are not ox-bow lakes. D. Yes. No meander is an ox-bow lake. E. Yes. Yes, we know this as no ox-bow lake is a meander, and all rivers are meanders.
Question 3 - A, C, D and E This is an example of Pattern 8 of Medic Mind’s Guide to Syllogisms
Towers
Buildings
Landmarks
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Answers and Explanations Mock Test 2 A. No. You may think that since all buildings are towers, then it is fair to say some buildings are landmarks. However, looking at the Venn diagram you can clearly see that there could be towers that are not necessarily buildings but do overlap with landmarks. We cannot therefore deduce for sure that some buildings are landmarks. B. No. All buildings are towers, but we do not know if all towers are buildings. C. Yes. We know that some towers are landmarks, so therefore some landmarks are towers. D. Yes. This is in true. If all buildings are towers, some towers will be buildings.
Question 4 - D •
A is a valid reason but does not have any mention of the cultural understanding of other countries.
•
B makes an assumption that people will come back and be better people, however there is no evidence to support this assumption. Also there is no reference to cultural understanding.
•
C also does not relate to cultural understanding.
•
D supports the argument against, and addresses the cultural understanding issue. It is therefore the correct answer.
Question 5 - A • Remember, the easiest way to answer these questions is to rule out the ones that do not answer the statement fully. D does not relate to an increase in applicants. • Next, look at statements which have assumptions based on a lack of evidence. B and C are two examples of these. We do not know for sure that there will be more doctors as there could still be the same number of places at medical school. We do not know that there will be incompetent doctors if a greater number of people are applying either.
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Answers and Explanations Mock Test 2 • The answer is A. This statement addresses the financial barrier for applicants, and it addresses both aspects of the debate - tuition fees (finance) and application numbers.
Question 6 - B • B is a fact based on evidence, and is related to healthy eating so is therefore the correct answer. The statement addresses both aspects of the debate - free school meals and healthy eating. • A and C do not relate to healthy eating. • D is an assumption based on a lack of evidence. When you see futuristic statements making drast predictions, be careful.
Question 7 - B Step 1: Work out probability of Salah scoring 15 Salah can score 5 or 1 in each round. To score 15 in three rounds, he has to score 5 in every round. P (Salah scoring 15) = P (Salah scoring 5 in one round) 3 P (Salah scoring 15) = 1/3 x 1/3 x 1/3 = 1/27 Step 2: Work out the probability of Tom scoring 40 or over Tom can score 8 or 0 in each round. To score 30 in six rounds, Tom has to score 8 points either five or six times. Four times (32) would not be enough. P (Tom scoring 8 five times) The 6 different ways this can happen: YYYYYN YYYYNY YYYNYY
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Answers and Explanations Mock Test 2 YYNYYY YNYYYY NYYYYY P (YYYYYN) = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/64 P (Tom scoring 8 five times) = 6 x 1/64 = 6/64
P (Tom scoring 8 six times) P (YYYYYY) = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/64
P (Tom scoring 40+) = P (Tom scoring 8 five times) + P (Tom scoring 8 six times) P (Tom scoring 40+) = 6/64 + 1/64 = 7/64
Step 3: Work out the answer The probability of Tom scoring 40 or over is greater than the probability of Salah scoring 15. The answer is B.
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Question 8 - A We need to list the different combinations which will give us a cumulative score of 16 or more. • • • •
3 six 2 six + 1 five 1 six + 2 five 2 six + 1 four
3 six
2 six + 1 five
Roll 1
Roll 2
Roll 3
6
6
6
6
6
5
6
5
6
5
6
6
Continued…
We do not need to write out everything for the last two combinations of 1 six / 2 five and 2 six / 1 four, as they will have the same probability as 2 six / 1 five. The probability of getting any combination is 1/6 x 1/6 x 1/6 = 1/216 • The probability of getting 3 sixes is 1/216 as there is 1 combination. • The probability of getting 2 sixes and 1 five is 3/216 as there are 3 combinations. • The probability of getting 1 six and 2 fives is 3/216 as there are 3 combinations. • The probability of getting 2 sixes and 1 four is 3/216 as there are 3 combinations. The total probability of getting 16 or more = (1 + 3 + 3 + 3) / 216 = 10 / 216 The answer is therefore A.
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Question 9a - D For Amaru to pick Chile, it has to be avoided by the first two picks of the draw. • The probability of not picking Chile in the first round is 6/7. • The probability of then not picking Chile in the second round is 5/6. • The probability of then picking Chile in the third round is 1/5. All of these three events need to happen for Amaru to pick out Chile. P (Amaru picking Chile) = 6/7 x 5/6 x 1/5 = 30/210 = 1/7 = D
Question 9b - C For this to happen we need two South American teams drawn in the first two picks, and a European team in the third pick. The table below shows all the combinations possible: Team 1
Team 2
Team 3
Brazil
Argentina
European
Argentina
Brazil
European
Brazil
Chile
European
Chile
Brazil
European
Chile
Argentina
European
Argentina
Chile
European
The probability of any given combination is 1/7 x 1/6 x 4/5 = 4 / 210 = 2 / 105 There are 6 combinations, so the probability of Amary picking the first European time is 6 x 2 / 105 = 12 / 105. Medic Mind Tip: Above we have gone through the longer method to show clearly the different combinations. However, you know the probability of picking a South American team first is 3/7, and then second is 2/6, and then picking a European team third is 4/5. So multiplying these will give you 12 / 105 much faster! ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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Question 10 - D This is an example of Pattern 12 of Medic Mind’s Guide to Syllogisms. • • • •
A is not showing that no windows are satellites. B is showing that some windows are satellites, which is false. C is showing that no chairs are satellites. D is the correct answer. It shows that all windows are chairs, but no windows are satellites.
Question 11 - C Probability of Event Probability of Event
= =
Probability of rolling 6 1/6
x Probability of flipping a head x 1/2 = 1/12
There are 7 days x 6 weeks = 42 repeats of the event. Expected Frequency Expected Frequency
= =
Probability 1/12
x x
Number of Repeats 42
=
3.5 days
You can’t have 3 and a half times, so the answer will be 3 = C.
Question 12 - D P (She pops the red balloon) = P (She pops the red first) + P (She pops the red second) In the previous question we mentioned that we took the long route in the explanation by breaking down all the possible combinations. Here we are going to go straight for the short route, as hopefully you are comfortable with probabilistic reasoning questions by now. P (She pops the red first) = 1/3 P (She pops the red second) = 2/3 x 1/2 = 2/6 For the second calculation, we multiply the probability she pops a non-red first (2/3) by the probability she pops the red next (1/2) out of the two balloons remaining. P (She pops the red balloon) = 1/3 + 2/6 = 4/6 = 2/3
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Question 13 - C Looking at the question, we need to look for areas of overlap. The easiest ones to rule out are the ones that involve the fewest categories. Let’s start with A. Scuba diving is a pentagon, and there is an area in the pentagon that is not overlapping with other regions. We can therefore rule A out, as scuba diving is available as a sole activity. Next look at the answers with two categories. B and C fit this description. We need to look for an overlap of a pentagon and diamond for B, and we see that so B can be ruled out. We need to look for an overlap of a diamond and an arrowhead for C - these two do not overlap, therefore C is the correct answer.
Question 14
- B
• A is not a valid reason for the UK to also have military service. Just because one country is doing it, it does not mean it is successful. The statement also does not address how it will affect future careers. • B is the correct answer as it gives examples of how the military service could help someone gain skills. • C is a good reason, but it does not focus on how it will affect 18 year olds careers, but instead focuses on how it will influence the economy. • D is an assumption based on a lack of evidence.
Question 15
- C
As we learnt in Tutorial 4: Venn Diagrams, when you get this type of Implicit Text to Venn question, they will not explicitly tell you to draw a Venn Diagram. However, you have to draw one to answer the question. As always, we start with the information involving the most categories. 3 people had all orange juice, lemonade, banana smoothie…
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Orange
Lemonade
3
Banana Smoothie
18 people had banana smoothie and orange juice… 50 people had banana smoothie…
Orange
Lemonade
15
3
24
Banana Smoothie
The overlap between Orange and Banana smoothies includes 15 + 3 = 18. The overlap between Lemonade and Banana smoothies includes 24 + 3 = 27.
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Answers and Explanations Mock Test 2 50 people had banana smoothie… 20 people had orange juice as their only drink… 4 people had lemonade as their only drink…
Orange
Lemonade
20 15
3 24 8
Banana Smoothie
The Banana smoothie circle in total contains 50 people. We did 50 - 15 - 3 - 24 = 8 to get the value for the ‘Banana only’ region. The Orange circle has 20 people in the ‘Orange only’ region. The Lemonade circle has 4 people in the ‘Lemonade only’ region.
47 people had orange juice… 40 people had lemonade…
Orange
Lemonade
20
x 15
3 24 8
Banana Smoothie
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Answers and Explanations Mock Test 2 We came to this information last because before this point we had two or more unknown regions for both Orange and Lemonade, so we needed to fill regions up before using this data. Orange Juice
20 + 15 + 3 + x = 47
x=9
You could have also used the lemonade value of 40 to do a similar calculation. Therefore the total number of people who had both orange juice and lemonade is 3 + 9 = 1
Question 16
- A
This is an example of a Text to Venn question, the first type of question we learnt in the Venn Diagrams tutorial. 1. Whenever you get a Text to Venn question such as this, a good thing to check would be that the Venn adds up to the total mentioned in the question text. There were 34 participants… When counting up the numbers for each Venn diagram we find: A - 34 B - 34 C - 35 D - 34 This means we can rule out C 2. Now, as always first use the information that tells us about the most categories.
11 people use all three… Looking at all four options, all have 3 in the middle except B. This means we can rule out B
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3. Next we look at information that tells us about 2 categories 6 people use two forms of transport… Unfortunately, this does not help us as A and D both have a 6 in between two circles! 4. 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 people that use bus only as Tube only... This means that at the centre of each circle there should be two numbers that are the same. A - Yes D - No This rules out D This means the answer is A.
Question 17
- C
For this type of question we cannot do much from just the Venn, apart from set up the formula: 13 + 2X + 2Y + 11 + 24 = 60
so…
2X + 2Y = 12
It is better to now go through each statement: A. Let us investigate: The number of people with 2 options is 2X + 11. The number of people with 1 option is 27 + 2Y Using the equation above (2X + 2Y = 12), we can substitute 2X with 12 - 2Y: The number of people with 2 options is 23 - 2Y ••••••••••••••••••••••••••••••••••••••••••••••••• UKCAT
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The number of people with 1 option is 27 + 2Y Therefore the number of people with 1 option is greater.
B. This is false, as there are no people with all four options because there is no overlapping region covering all four sets. We can calculate it - it is zero!
C. Let us investigate: The number of people with fries The number of people with apple pie
= =
X + Y + 11 X+Y
By inspection we can see that 11 more people had fries than apple pie.
D. For completion sake, let us investigate: The number of people with pizza = The number of people with watermelon =
X + 13 X + 35
By inspection we can see that 22 more people had watermelon than pizza.
Question 18
- C
This is a Euler diagram question. These are different to Venn diagrams, because they represent real-life relationships between categories. Here we are given information about Geography, and are told that one of the four diagrams represents the information. We know that England, Scotland and Wales are three different countries. They all come under Great Britain and Great Britain comes under the United Kingdom (along with Northern Ireland). We are therefore looking for one circle enclosed in another circle which contains three smaller circles. The answer is therefore C.
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Question 19
- C
A. No. There could have been some under 30 years older that were right handed, it was just that none of the winners fit the category of being left-handed and older than 30 years old. B. No. We do not have sufficient information to make this assumption. C. Yes. This is true - the information tells us this. D. No. We only know that none fit into the category of being left-handed and older than 30 years old. The winners could have been either right handed and over 30 years old or younger than 30 years old and left or right handed. This means that we do not know if all the champions in the past three years younger than 30 years are left handed, as we don’t know if they were all younger than 30 years.
Question 20
- D
A. No. This does not follow: Oracle of Information: 0.1 x 1376 = 137.6 Sign of the Times: 0.21 x 1148 = 241.08 B. No. This does not follow: We do not have enough information to answer this question. The reader count is for the year, but we do not know if this is concentrated in just a weeks of the year, or is spread through with many readers every day. C. No. This does not follow: We do not have enough information to answer this question, as we only know readers that are 35-44. The number could be skewed to a larger portion towards 35-39 rather than 40-44 in this cohort.
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Answers and Explanations Mock Test 2 In an extreme scenario, all the 35-44 scenario could be below 40 for the Oracle, and above 40 for Sign of Times. in this case the Oracle does not have more readers above 40, so we cannot say Yes for this statement. D. Yes. This does follow: The key word here is proportion. If it was actual number, then it would be a different story. For Sign of the Times it is 11%, for the Oracle of Information it is 8%.
Question 21
- D
D is the correct answer… Elizabeth Alex
(31 + 15) = 46 (11 + 23) = 34
Knocking out A… We do not have sufficient information to know this. Knocking out B… Bethany (47 x 5) + (4 x 10) = £275 Alex (11 x 5) + (23 x 10) + (4 x 15) = £345 Knocking out E… Alex Bethany Elizabeth
(11 + 23 + 4) = 38 (47 + 4 + 0) = 51 (31 + 15 + 5) = 51
Both Bethany and Elizabeth sold 51 tickets therefore this is false.
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Question 22
- A
The Wi-Fi router is represented by the arrow head.
Emergency exit / kitchen
Wi-Fi router Cabin crew
Toilet
Emergency exit / kitchen
The emergency exit is as far away from the kitchen as possible to help ease confusion… This helps us identify the pentagon and circle as representing the emergency exit and kitchen (in either order). The cabin-crew seat is almost equidistant from the Wi-Fi router and the toilet… If you looked at this first then the pentagon and circle could easily have also represented the Wi-Fi router and toilet, with the Cabin Crew being in the middle. However, we now have allocated these two shapes to other things. So the toilet and Wi-Fi router must be the triangle and arrow. The arrow is not allocated to the toilet… This confirms that the toilet is the triangle, and the arrow is the Wi-Fi router.
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Question 23
- A and C
A. Yes. This does follow: ILTSS JFJB
50 + 40 + 70 + 60 = 20 + 20 + 50 + 100 =
220 190
B. No. This does not follow: We do not have information to make this inference. The difference in sales is not just down to quality, it could be due to price or other factors. C. Yes. This does follow: April - 70 May - 60 June - 120 July - 160 D. No. This does not follow: JFJB ILTSS
100 - 20 70 - 50
= =
80 20
Medic Mind Tip: With graphical questions you can often answer by inspection. For part A, we can see that ILTSS had higher sales in three out of four months, and it is quite clear by inspection that they had more sales. For part C, from inspection we can see that July has the highest total number of sales. For Part D, we can see from inspection that JumpingForJoyBeds has both the highest and lowest sales value in the whole table.
Question 24
- C
For this question we will use the Cross Hatch Method which we learnt in Tutorials 8 and 9. Set up the table with the four airlines and four destinations. A flight by Jetlag Airways, a flight to Bangkok, a flight to Berlin and a flight to Dehli… The other destination is Toronto…
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Answers and Explanations Mock Test 2 We know that Jetlag airways must fly to Toronto by the process of elimination. Jetlag Airways
Skyline Airways
OrangeJet
GlorianAir
✖
✖
Bangkok Berlin Dehli
✖
✔
Toronto
Skyline Airways does not fly to Delhi… The airline which flies to Bangkok is a sister airline to OrangeJet… GlorianAir is flying to Berlin…
Skyline doesn’t go to Dehli, and OrangeJet can’t go to Bangkok. Since GlorianAir is going to Berlin, we know no other airline can be. Jetlag Airways
Skyline Airways
OrangeJet
GlorianAir
✖
Bangkok Berlin
✖
✖
✖
✔
✔
✖ ✖
✖
✖
Dehli Toronto
Looking at the table now, we can tell that OrangeJet flies to Dehli and Skyline Airways flies to Bangkok. There is no need to go further as we have our answer. Jetlag Airways
Skyline Airways
Bangkok
✖
Berlin Dehli
✔
Toronto
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✔
✖
✖ ✖
✖
✖
✖
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GlorianAir
✔
✔
✖
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Question 25
- D
For this question we can use the Fill In Method which we learnt in Tutorials 8 and 9. Set up the table with the four glasses colours and four dress colours. Felicity wore black glasses… Alice wore a purple T-shirt and Sandra wore a green T-shirt… Input these into the table to get you started. Name
T-Shirt
Glasses
Felicity
Black
Alice
Purple
Sandra
Green
?
The person wearing a black T-shirt wore yellow glasses… Based on this information, there is one T-shirt colour missing which is orange. This means Felicity is wearing orange. Name
T-Shirt
Glasses
Felicity
Orange
Black
Alice
Purple
Sandra
Green
?
Black
Yellow
This shows that answer D is correct. For reference, the two glasses colours that remain are burgundy and red. We are not told any information about these two, so we can’t be certain for anything that references these two glasses colours.
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Question 26
- A, C, D
A. Yes. This does follow:
Today Anjali is satisfied. When she doesn’t go swimming she doesn’t feel satisfied. This means when she does go swimming she is satisfied, meaning Anjali went swimming today and the conclusion therefore does not follow. B. No. This does not follow: We know that Anjali is satisfied and has lunch when she naps. However, when she doesn’t nap she doesn’t have lunch, but can still be satisfied. So we cannot saw she naps on the basis of the fact that she is satisfied today. Moving on to the ‘two great meals’, we don’t know if this includes lunch (could be breakfast and dinner) so we can’t be sure she napped. C. Yes. This does follow: When Anjali doesn't go swimming she doesn’t feel satisfied, meaning when she does go swimming she does feel satisfied and the conclusion therefore does follow. You might argue that she could be content, in the middle of satisfaction and dissatisfaction. Many Decision Making UKCAT Official questions will involve some element of ambiguity, so be prepared for it and go with what you think is most likely to be correct. D. Yes. This does follow: When Anjali doesn’t swim she feels unsatisfied, and when she does swim she does feel satisfied. So she must not be swimming. E. No. This does not follow: If Anjali naps, she feels satisfied. However, if she doesn’t nap it doesn’t sat she doesn’t feel satisfied. So if, for example, she swims and doesn’t nap, she will still feel satisfied.
Medic Mind Tip: For this type of question they don’t tell you what happens is Anjali doesn’t nap but swims - is she satisfied? Therefore work on the presumption that if there is
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Answers and Explanations Mock Test 2 a clash you don’t know what she will feel. The question will normally be designed in a way to avoid a clash.
Question 28
- B
• B is a reason which is also supported by evidence. The statement addresses both aspects of the debate - laptops on aircrafts and security. • A does not address the security threat aspect of the debate. • C is an assumption based on a lack of evidence. • D does not rule out the fact that laptops on aircrafts could still be a threat. It addresses the debate more closely than A or C, but it is still not as good a fit as B is.
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