Logical Reasoning and Data Interpretation for CAT PDF

3 Fully-solved practice exercises Sixth Edition...

3 Fully-solved practice exercises Sixth Edition 3 Previous years’ papers for CAT, XAT, IIFT Logical Reasoning and 3 Boost your scores with differentiated challenge levels Data Interpretation 3 Understand concepts – Apply strategies – Get your score for CAT Data Interpretation for CAT Logical Reasoning and Nishit K. Sinha This revised edition renews our commitment to provide you strong and relevant concept building and application methodology. This will help to make your preparation upgraded, Sixth Edition focused and targeted. It also has fresh worked-out examples as per the latest pattern for improved practice. You can now work on problems at all the three levels—foundation, moderate and advanced and can evaluate preparedness with the help of benchmarking tests. Logical The book also helps you prepare for other examinations such as the XAT, SNAP, IIFT, IRMA, MAT, NMAT, etc., with the help of model papers and mock tests. HIGHLIGHTS Reasoning and Data Interpretation Cover image: mw2st.shutterstock.com z Understand framework and concept building in Logical Reasoning z Learn how to apply concepts to problems successfully everytime! z Improve your scores with customized three-tiered challenge levels z 360° practice with latest and previous papers of CAT, XAT, SNAP, and IIFT for CAT ALSO USEFUL FOR OTHER MBA ENTRANCE EXAMINATIONS in.pearson.com Sixth ISBN 978-93-868-7351-4 Edition Nishit K. Sinha 9 789386 873514 Sinha Size: 203x254 mm Spine: 28 mm ISBN: 9789386873514 Territory line mQuest  About Pearson Pearson is the world’s learning company, with presence across 70 countries worldwide. Our unique insights and world-class expertise comes from a long history of working closely with renowned teachers, authors and thought leaders, as a result of which, we have emerged as the preferred choice for millions of teachers and learners across the world. We believe learning opens up opportunities, creates fulfilling careers and hence better lives. We hence collaborate with the best of minds to deliver you class-leading products, spread across the Higher Education and K12 spectrum. Superior learning experience and improved outcomes are at the heart of everything we do. This product is the result of one such effort. Your feedback plays a critical role in the evolution of our products and you can contact us at [email protected]. We look forward to it. This page is intentionally left blank Logical Reasoning and Data Interpretation for CAT Sixth Edition Nishit K. Sinha Copyright © 2019 Pearson India Education Services Pvt. Ltd Published by Pearson India Education Services Pvt. Ltd, CIN: U72200TN2005PTC057128. No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent. This eBook may or may not include all assets that were part of the print version. The publisher reserves the right to remove any material in this eBook at any time. ISBN 978-93-868-7351-4 eISBN: Head Office: 15th Floor, Tower-B, World Trade Tower, Plot No. 1, Block-C, Sector-16, Noida 201 301,Uttar Pradesh, India. Registered Office: 4th Floor, Software Block, Elnet Software City, TS-140, Block 2 & 9, Rajiv Gandhi Salai, Taramani, Chennai 600 113, Tamil Nadu, India. Fax: 080-30461003, Phone: 080-30461060 www.in.pearson.com, Email: [email protected]  To Papa and Ma Kumar Kalyan Prasad Sinha and Sanjila Sinha This page is intentionally left blank  Contents Preface to the Sixth Edition ix Chapter 22 Advanced Exercises 2.155 Prefacexi Chapter 23 Mastering Data Interpretation 2.184 About the Author xiii Acknowledgementsxiv CAT Demystified xv Part 3: Benchmarking Tests How to Use This Book xxi Benchmarking Test 1 3.3 Benchmarking Test 2 3.12 Part 1: Logical Reasoning Benchmarking Test 3 3.20 Benchmarking Test 4 3.28 Section 1: U  nderstanding Logical Reasoning Part 4: Previous years’ papers Chapter 1 Introduction to Logical Reasoning 1.3 Chapter 2 Developing the Skills 1.10 CAT 2017—SLOT I 4.3 Chapter 3 Logical Links 1.27 CAT 2017—SLOT II 4.22 Chapter 4 Sequencing and Arrangement 1.35 XAT 2017  4.45 Chapter 5 Series 1.51 XAT 2016  4.51 Chapter 6 Team Selection 1.58 IIFT 2016 4.58 Chapter 7 Blood Relation 1.72 CAT 2008 4.71 Chapter 8 Directions Decision Making 1.79 CAT 2007 4.81 Chapter 9 Syllogism 1.89 CAT 2006 4.91 Chapter 10 Input–Output 1.101 CAT 2005 4.99 Chapter 11 Cubes 1.108 CAT 2004 4.110 Chapter 12 Boolean Logic 1.117 CAT 2003 (Retest) 4.121 CAT 2002 4.136 Section 2: Practising Logical Reasoning Chapter 13 Foundation Exercises 1.127 Part 5: MODEL PAPERS (BASED ON Chapter 14 Moderate Exercises 1.157 OTHER MBA ENTRANCES) Chapter 15 Advanced Exercises 1.183 Chapter 16 Mastering Logical Reasoning 1.204 Model SNAP Paper 5.3 Model XAT Paper 5.11 Part 2: Data Interpretation Model IIFT Paper 5.27 Section 1: U  nderstanding Data Part 6: Testing Your Mettle Interpretation Section 1: Practice Set Chapter 17 Introduction to Data Interpretation 2.3 Chapter 18 Developing the Skills 2.33 Practice Exercise Based on Recent CAT Pattern 6.3 Chapter 19 Data Sufficiency 2.49 Section 2: Mock Tests Section 2: Practising Data Interpretation Mock Test 1 6.43 Chapter 20 Foundation Exercises 2.67 Mock Test 2 6.55 Chapter 21 Moderate Exercises 2.105 Mock Test 3 6.63 This page is intentionally left blank  Preface to the Sixth Edition Logical Reasoning and Data Interpretation for CAT was envisaged to provide a complete preparation resource for every management aspirant, irrespective of training levels and preparation styles. Since its first edition, the book has remained the preferred choice of students due to the superior quality of its content, the user-friendly pedagogy, and the proven methodologies and approaches. In our continued endeavor to raise the standard further and to ensure an upgraded and improved experience, we present the sixth edition. Highlights QQ An exclusive section containing 100 LRDI questions QQ Solutions to all questions QQ Explanations and answers to CAT 2017 LRDI paper (based on memory) QQ Previous years questions for XAT and IIFT QQ Embedded console with test papers on the Pearson website I am sure this book will continue being the first choice among test takers.  Nishit K. Sinha This page is intentionally left blank  Preface Among the many resources in the market for CAT and other B school entrance examinations, there are none that place adequate emphasis for concept building in LRDI. This book fills this gap by bringing together concept building, application methodology, as well as question practice. Special care has been taken in this book to ensure that even a person who does not have a formal experience of LR or DI will find him/herself in a comfortable position with a little bit of effort. Besides, this book puts as proportionate an emphasis on LR and DI as put by the CAT in the recent years. This unique book is useful for all kinds of students—those who are good at solving LR and/or DI questions as well as those who are not so. There are plenty of worked-out examples to enable the students to understand the techniques before moving on to the practice problems. Apart from this, once the practice questions at all the three levels—Foundation, Moderate and Advanced—have been tried, this book puts forth a mechanism to help the student in evaluating him/herself in a controlled, simulated environment in the form of Benchmarking Tests. And finally some more tests are there to evaluate oneself in the format of review tests. The table below will give a fair idea of the proficiencies and approaches for different students for LRDI. Student’s Type/ response Novices Apprentices Practitioners Experts Interpretation Do not under- Do not understand all the Understand all the con- Can solve the problems stand the basic concepts underlying the cepts and attempt most of correctly. concepts problems. So, unable to the main problems. attempt all the questions. Approach Do not know the Unable to pick the cor- Know and pick the Can use more than one methods to solve rect method; mostly rely correct method; have a strategy to solve the the problems on luck to get the right sound strategy and solve problem for a good answer. the problems with skill, number of questions. not luck. Accuracy level Unable to get Mostly get the correct Correct answers with Excellent level of accu- correct answers answer, with few errors. hardly any mistakes. Use racy as well as speed. most of the time appropriate units. This book is designed to take care of students at all these four levels by giving them a customized preparation through the questions at different difficulty levels. This focus on providing customized content is at the heart of our drive to help every user be prepared for the LRDI in CAT. Structure of the Book This book is divided into four parts: QQ Part 1 facilitates framework and concept building in Logical Reasoning. QQ Part 2 guides the student in concepts building and development of the skills to apply these in Data Interpretation. xii Preface QQ Part 3 consists of test papers with varying levels of difficulty and QQ Part 4 contains six previous years’ CAT papers with solutions. Each part has three different levels of problems: Foundation, Moderate and Advanced. These levels are hierarchical and sequential. Students are expected to progress through them in the same order. Movement from one level to another is largely a function of sufficient experience with the specific content. A student is unlikely to perform well at a particular level without the experience of the preceding level. Time spent at one level will help the student in imbibing and assimilating the methods and approach to solve problems, which in turn will make it easier for the student to tackle problems at the next, higher stage. In other words, hard work put at one level will allow an intuitive functioning later. If one level is not mastered before moving on to the next, though good students would appear to perform well at that higher level and may get the right answers, it would be without any sound reasoning for most of the times. Benchmarking tests are also given at the end with comparative scores and then finally review tests to track your progress. Although I have tried to be meticulous in preparing this text, some errors may have crept in. I invite each one of you to be a co-author of this book for the subsequent editions by making contribution in enhancing the value of this book with your suggestions and by bringing to our notice the errors, if any, so that they can be corrected in future. I can be reached at [email protected] Nishit K. Sinha  About the Author Nishit K. Sinha, an IIM Lucknow alumnus, has been training students for the CAT and other B-school entrance examinations for more than a decade. During this period, he has successfully trained more than 10,000 students of varying backgrounds to clear various MBA entrance examinations. To best analyze the pattern of all the major B-school entrance tests, as well as to remain up to date himself on the examination pattern, he appears for important examinations, such as the CAT and XAT every year. He is Founder–Partner at his test prep organization dueNorth Academics LLP, based at Dehradun.  Acknowledgements This book bears the imprint of many people—my colleagues, my students and my teachers who have had a significant impact on my thought process and have generously extended help whenever I needed. With immense pride and humility, I acknowledge that the decade long journey of this book (1st edition came out almost a decade back) has been made possible because of the constructive feedback of the users’ of this book, ideas generated through brainstorming with my friends in the coaching industry, Pearson’s market intelligence reports and my own understanding of the entrance exams. My special thanks to my brothers Ravi Shankar Prasad, Sharat Chandra Mayank, Amit Kumar and Vinit Kumar. I would like to thank Sharel Simon and Vipin Kumar for giving the book the final shape. Thanks to Vikas Sharma and H. Nagaraja for ensuring that I get the timely and accurate feedback of the users. Thanks is going to be a small word for my wife, who took care of family and home, giving me enough time to complete this project. Love to my young son who has started helping me with the errands. Sudhir, my man-Friday, who took care of small necessities, your contribution is noteworthy. I may have forgotten some names here. I wish to express my gratitude towards all who have contributed in the making of this book.  Nishit Sinha  CAT Demystified CAT stands for Common Admission Test. It is a test conducted by IIMs for admission into several programs offered by them. Besides IIMs, there are a good number of colleges which accept CAT score in their 1st round of selection process. As of now, there are 20 IIMs offering PGP at following locations: Ahmedabad, Bangalore, Calcutta, Lucknow, Indore, Kozhikode, Shillong, Ranchi, Rohtak, Raipur, Udaipur, Tiruchirappalli, Kashipur, Nagpur, Visakhapatnam, Jammu, Sambalpur, Sirmaur, Bodhgaya, Amritsar. History of CAT In its history of almost four decades, CAT has changed its colours many a times in terms of number of questions, sections asked and orientation of the questions. Here we will discuss the examination pattern of the CAT from 2000 onwards. Number of sections Total number of questions Total Marks Time allowed CAT 2000 3 165 N.A. 120 minutes CAT 2001 3 165 N.A. 120 minutes CAT 2002 3 150 N.A. 120 minutes CAT 2003 3 150 N.A. 120 minutes CAT 2004 3 123 150 120 minutes CAT 2005 3 90 150 120 minutes CAT 2006 3 75 300 150 minutes CAT 2007 3 75 300 150 minutes CAT 2008 3 90 360 150 minutes CAT 2009 3 60 450 (scaled score) 135 minutes CAT 2010 3 60 450 (scaled score) 135 minutes CAT 2011 2 60 450 (scaled score) 140 minutes CAT 2012 2 60 450 (scaled score) 140 minutes CAT 2013 2 60 450 (scaled score) 140 minutes CAT 2014 2 100 300 170 minutes CAT 2015 3 100 300 180 minutes CAT 2016 3 100 300 180 minutes CAT 2017 3 100 300 180 minutes xvi CAT Demystified Chart 1: Time Allotted Per Question CAT 2011 had two sections: (a) Quantitative Ability & Data Interpretation (b) Verbal Ability & Logical Reasoning with 30 questions in each section. CAT 2011 also had sectional time limit of 70 minutes for each section. Before CAT 2004, CAT did not mention that how many marks one question stands for? Marks carried per questions was announced for the first time in CAT 2004. Quite obvious from the above table that time allotted to per question has risen sharply from CAT 2000 to CAT 2014 taking a small dip further. One possible conclusion drawn from here is that CAT is focussing more upon accuracy than speed, and secondly it expects students to gain a certain level of competence across all the areas in a particular section. With number of questions going down and time going up, students didn’t have much of the choices of questions to choose from. Further, introduction of sectional timers has forced students to attempt questions in that particular section only. Time allotted per question (in minutes) 2.5 2.33 2.33 2.33 2.25 2.25 2 2 2 1.8 1.8 1.8 1.66 1.7 1.5 1.33 1 0.97 0.8 0.8 0.72 0.72 0.5 0 CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Chart 2: Sectional Breakups and Getting IIM Call One thing that has remained constant during this period of CAT 2000 - CAT 2010 is the number of sections and the way these sections have been grouped – Quantitative Aptitude (QA), Logical Reasoning and Data Interpretation (LR / DI), and English Usage / Reading Comprehension (EU / RC). Though CAT 2011 changed it all: Year QA LR DI EU RC Total no. of questions CAT 2000 55 55 55 165 CAT 2001 50 50 50 150 CAT 2002 50 50 50 150 CAT 2003 50 50 50 150 CAT 2004 35 38 50 123  CAT Demystified xvii CAT 2005 30 30 30 90 CAT 2006 25 25 25 75 CAT 2007 25 25 25 75 CAT 2008 25 25 40 90 CAT 2009 20 20 20 60 CAT 2010 20 20 20 60 CAT 2011 30 (QA + DI) 30 (Verbal + LR) 60 CAT 2012 30 30 60 CAT 2013 30 30 60 CAT 2014 50 50 100 CAT 2015 34 32 34 100 CAT 2016 34 32 34 100 CAT 2017 34 32 34 100 2-sections pattern continued till CAT 2014. From CAT 2015, total number of sections were three. CAT 2015 brought some questions in non-MCQ format –fill in the blanks questions, where an aspirant is required to type the answer. These questions had no negative marking. Chart 3: Marks required to get atleast one IIM Call Past CAT trends show that a student is required to get around 70% of the marks to get atleast one IIM call (with clearing the sectional cut-off). Following table and bar chart gives us some clarity regarding the same: Year Total marks or questions Marks /Qs required to get atleast one IIM call CAT 2000 165 75 CAT 2001 150 70 CAT 2002 150 72 CAT 2003 150 56 CAT 2004 123 54 CAT 2005 150 48 CAT 2006 300 115 CAT 2007 300 118 CAT 2008 360 120 xviii CAT Demystified CAT 2009 60 42 CAT 2010 60 40 CAT 2011 60 35 CAT 2012 60 35 CAT 2013 60 35 CAT 2014 300 180 CAT 2015 300 156 CAT 2016 300 158 CAT 2017 300 155 Chart 4: Percentage obtained for IIM Call Following line chart gives questions solved or marks required as a percentage of total marks or total questions (as applicable): % marks or Questions done to get one IIM call 80.0 70.0 70.0 66.7 60.0 58.3 58.3 58.3 60.0 50.0 52.0 52.751.7 48.0 45.5 46.7 43.9 40.0 38.3 39.3 37.3 32.0 33.3 30.0 20.0 10.0 0.0 CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Note: Above calculation is based upon the data collected from the students who got IIM calls in that particular year. So, to get atleast one IIM call in CAT 2008, a student was required to get 33.33% Marks out of total with clearing the cut-off across the sections. Though in the online format of CAT (since 2009), percentage questions to be done to get atleast one IIM call has gone up. Post 2011, % marks required to get atleast one IIM call has hovered in between 50%–60%.  CAT Demystified xix Chart 5: No. of Questions and Time Per Question If we convert the requirement of marks to be obtained from the above line chart into questions to be done, we get the following table: Year No. of questions to be solved Time allotted Time invested per qn. CAT 2000 85 120 minutes 1.4 CAT 2001 80 120 minutes 1.5 CAT 2002 81 120 minutes 1.5 CAT 2003 60 120 minutes 2.0 CAT 2004 42 120 minutes 2.9 CAT 2005 38 120 minutes 3.2 CAT 2006 33 150 minutes 4.5 CAT 2007 33 150 minutes 4.5 CAT 2008 34 150 minutes 4.4 CAT 2009 42 135 minutes 3.2 CAT 2010 40 135 minutes 3.3 CAT 2011 35 135 minutes 3.8 CAT 2012 35 135 minutes 3.8 CAT 2013 35 135 minutes 3.8 CAT 2014 60 170 minutes 2.83 CAT 2015 52 180 minutes 3.46 CAT 2016 53 180 minutes 3.39 CAT 2017 52 180 minutes 3.46 Chart 6: Time Allotted vs Time that can be Invested Per Question For CAT 2000 to CAT 2008, at 90% accuracy with 1/4th negative marking, these are the approximate number of questions to be done. For CAT 2009 to CAT 2011, net of these many questions to be done. To summarize this whole discussion till now, we will compare chart 2 with chart 6 and present them in a unified line chart given below. xx CAT Demystified Time allotted vs Time that can be invested per Qn(in minutes) 5 4.5 4.5 4.5 4.4 4 3.8 3.8 3.8 3.5 3.46 3.393.46 3.2 3.2 3.3 3 2.9 2.83 2.5 2.26 2.26 2.33 2.33 2.33 2 2 2 2 1.67 1.7 1.8 1.8 1.8 1.5 1.4 1.5 1.5 1.33 1 0.98 0.73 0.73 0.8 0.8 0.5 0 CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Time allotted per Qn. Time that can be invested per Qn. This line brings to us an important information—For CAT 2006, CAT 2007 or CAT 2008, Even if a student has taken approximately 4.5 minutes to solve a question correctly, s/he has got enough marks to get atleast one IIM call (provided s/ he clears the sectional cut-off too). For the last three CAT papers (2015 – 2017), even if a student has taken 3.4 minutes to solve a question correctly, s/he would get sufficient marks to get atleast one IIM Call. It also points out towards other side of story that a student can get calls from IIM by solving nearly half of the total questions, skipping entire half of the questions.  How to Use This Book There are few important guidelines mentioned below that we must keep in our mind while going through any book, be it a text book or a reference book or a book on LR/DI or QA of CAT: 1. Passive reader Vs Active learner A passive reader is a person who goes through any content in real time frame without putting any efforts to induce the learning, assuming that there will be a tomorrow when he would come back to the same content and learn the things given. We know that either tomorrow never comes or it comes so late that everything is almost over. An active learner is a person who keeps a piece of paper and a pencil/pen with him so that he can integrate the various activities like reading–learning–practicing at the same time. At the end of the process, this person realizes that she/he has a better understanding than the passive reader. 2. Mechanical process Vs Logical process Mechanical process is the assembly line production system—put the input into the controlled system and we will receive the output. But unfortunately in CAT, now a days, neither the input (the fundas to be used) nor the output (process to arrive at the end) is given. The logical process of solving the question not only involves the mechanical process of solving the question as the 1st step of learning, but also uses visualization of the problem scenario as the 2nd step of mental development. In this process, we slowly move towards a stage where a good number of problems can be done through mental mapping only, without using pen or paper. In the past also, CAT used to be logical, but in the recent years, the need of being strong in visualization has become more. Now, I treat the above written points as a choice—whether you want to be in the 1st category (Passive reader + Mechanical Process) or in the 2nd category (Active Learner + Logical Process). The choice made here will have a very serious implication on our capacity building and ability to use the same in cracking CAT. How to go ahead with this book? When you start going through this book, I would request you to have above-mentioned points in your mind. Let us see this in steps: Step 1 Go through learning objectives and as you go through each and every word of the learning objectives, you should have the end result of getting into the IIMs in your mind. This will also help you in understanding all that is to be achieved in the chapter. Step 2 I have given absolute freedom to the individuals to start with either Part 1 or Part 2 of the book, but definitely not the rest of the parts. Start with the concept first and before proceeding towards the next concept, solve all the worked out examples related to that concept and move ahead only when you have internalized the same. Sometime, this might appear to be xxii How to Use This Book drudgery, but see that you do it. Also, make sure you don’t succumb to temptations like finishing the topic as fast as possible. Step 3 Once you have got the confidence over whatever you have done previously, do the foundation exercise. It is a precursor to the actual CAT problems. Solve it without any time-constraint. This level tests mostly your comprehension of the concept and a bit of application. Most of the questions in this exercise will check only your understanding of the concept, and not the application of it. Ideally you should not give more than 2 minutes to any question in foundation exercise. If you get less than 75% questions correct, revise the concepts for which you got the answers wrong. One more suggestion—try to solve one exercise in one sitting, whatever time it takes. If you get the answers right, its good and if you don’t get the answers correct, attempt the same questions once again in next sitting (preferably the next day). Solving these will QQ help to gain thorough understanding of the concepts QQ provide interaction with the problems that are being asked at basic level QQ Lead to confidence building Step 4 Welcome to the moderate exercise. Questions at this level matches with CAT level and sometimes, above that level as well. This level tests your ability to apply a particular concept and also combination of concepts in single problem. If you are not able to solve a particular question, do not go for the solution until you have attempted the question at least thrice. Solving these will— QQ hone the Ability to identify easy and difficult questions QQ develop Mental imaging and visualization of the problems QQ Help in creating a neural-network inside the mind to think about the different processes to solve the problems QQ Establish a logical connection between concepts and their application. Step 5 Don’t go for advanced level right now. Relax and don’t solve any question of LR/DI for one day. Then the next day, take the benchmarking test. Your performance in this test will help you to assess yourself. Ideally, you should aim for anything above 85 percentile. Step 6 Once the whole book is covered with all the moderate exercises and bench marking tests, go for the revision of the topics. From here on, you can jump on to the advanced level of questions. Most of the questions which you will get here are above CAT level. The idea is to prepare you at a level which is above CAT. If you excel at this level, CAT will be a cakewalk for you. Go for Practice Questions based upon recent CAT pattern now. Attempt the questions, try to solve, if you cannot solve, try once again. Give a second chance and solve them. Now if you cannot solve the problems, go for hints and solutions. Step 7 Go to the Part 3 - Benchmarking test and target anything above 98 percentile. If you get it consistently in all the tests you are prepared for CAT. And if not, repeat the process from Step 4. If in any one of these tests, you get less than 85 percentile, repeat the process from Step 3. All the best for life! Nishit K. Sinha Mail me at—[email protected] PART 1 LOGICAL REASONING SECTION 1 UNDERSTANDING LOGICAL REASONING This page is intentionally left blank Chapter 1 Introduction to Logical Reasoning lEARNING Objectives In this chapter, you will learn:  Logic as tool for inference  The strength of logical argument  Logic and decision making  Applying logic Human life is full of situations where one is called to proofs or stronger reasoning in favour of south, then it is make a decision. This also includes making significant more logical to say that the sun rises from south than to choices about what to believe and what not to. Although say that it rises from east. everyone prefers to believe what is true, we often An important application of the logic is in disagree with each other about a particular issue due the area of law and the judicial system—an area to the subjective nature of our judgements. We often where proceedings are heavily dependent on logical find individuals or groups locked in conflict because processes—of any civilized society. The following our reactions to situations are guided by our impulses. example tells a lot about the logic and its constituents: Humankind has developed a mechanism through which While pronouncing his verdict in one of the we are able to move beyond our individualistic and most senstational murder cases in India, the judge said, idiosyncratic notions and establish indisputable facts. “Though I know that this is the man who committed the This mechanism is called Logical Reasoning and Logic crime, I acquit him, giving him the benefit of doubt.” has come to play a very important role in ascertaining What is the judge saying? what is more credible or whose reasoning is sounder. Even though he knows that the defendant is indeed It is imperative to understand that Logic is not the culprit, the fact has not been proven, that is, it cannot mainly concerned about finding the ‘Truth.’ Logic’s be logically deduced on the basis of arguments and prime interest lies in f inding that, which can be evidence; consequently the accused has to be acquitted. established as a fact using several strands of reasoning Despite the above example some authoritativeness supported by sophisticated arguments. It may seem like a can indeed be attached to the way of logical reasoning. big coincidence that the event or situation that is correct No matter how sceptical we are about the points from will have more substantial proofs or arguments in its where we begin to reason, if we follow the rules of logic favour, rather than the even or situation that is not so we will reach an acceptable conclusion. It is almost For example, if we are discussing about the always possible to distinguish between correct from direction from which the sun rises, we will always have incorrect reasoning independent of our agreements or more proofs or stronger arguments in favour of east disagreements regarding substantive matters. Logic rather than west. However, if somehow we get more is the discipline that studies the distinction—both by 1.4 Logical Reasoning  determining the conditions under which the truth of 7. Proof—A formal series of statements given showing certain beliefs leads naturally to the truth of some other that if something is a fact, then something else belief, and by drawing attention to the ways in which we necessarily follows from it. may be led to believe something without the respect for 8. Paradox—A self contradiction (As in the statement— its truth. This provides no guarantee that we will always ‘I always lie’ is a paradox.) arrive at the truth, because the beliefs or assumptions 9. Postulate—A declaration of something self evident. with which we begin are sometimes erroneous. But 10. Proposition—A statement that affirms or denies following the principles of correct reasoning does ensure something and is either true or false. that no additional mistake creeps in during the course of 11. Negation—A proposition that is true if and only if our progress. another proposition is false. Hence, Logic can be seen as a tool using which 12. Axiom—A proposition that is always true and we find out the strength of reasoning or the various does not require proofs or disproofs to be true. arguments put forward in favour of or against something. 13. Tautology—A statement that is always necessarily This is reflected in the origin of the word ‘logic’. It takes true (As in the statement—‘He is honest or he is not its roots from the Greek work logos which means reason honest.) or principle. Taking a broad view, we can see several 14. Contradiction—Opposite of consistency. dimensions, or usages of the term logic. Some of these 15. Logical relation—A relation between propositions. are given below: 16. Inductive Reasoning—Proceedings from particular facts to a general conclusion. 1. A system of reasoning: Aristotle’s logic. 17. Deductive reasoning—Proceedings from general 2. A mode of reasoning: By that logic, we should sell facts to a particular conclusion. the company tomorrow. 3. The formal, guiding principles of a discipline, school, or science. 4. The relationship between elements and between Reasoning Questions and Puzzles an element and the whole in a set of objects, individuals, principles, or events: There’s a certain Puzzle 1 logic to the motion of rush-hour traffic. Put the digits from 1 to 9 into the given circles so that 5. In the field of Computer Science the term, logic, the sum of the numbers in each straight line is the same. may mean any of the following: a. The non-arithmetic operations performed by a computer, such as sorting, comparing, and matching, that involve yes-no decisions. b. Computer circuitry. c. Graphic representation of computer circuitry. Terms related to Logic: 1. Consistency—An attribute of a logical system that is so constituted that none of the propositions deducible from the axioms contradict one another. 2. Completeness—This is an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the system. Puzzle 2 3. Corollary—An inference that follows directly from Our local town hall has a clock which strikes on the hour the proof of the another proposition. and also strikes just once on the half hour. While I was 4. Non sequitur—A conclusion that does not follow awake the other night, I heard the clock strike once, but from the premises. I could not tell what time it was. Half an hour later it 5. Subject—The first term of a proposition struck once again, but I still could not tell what time it 6. Predicate—What is predicted about the subject of a was. Finally, half an hour later it struck once again and I proposition. knew what the time was. What time was it?  Introduction to Logical Reasoning 1.5 Puzzle 3 Puzzle 7 You are running in a marathon and you overtake the Abhishek said that he was born on 29 February 1900. person in second place, what position are you now in? What birthday will he celebrate in the year 2000? Puzzle 4 Puzzle 8 Tree-Tent is a logical game (similar to minesweeper) in During a recent police investigation, IG Khan was inter- which the aim is to identify all tents in the grid. Each tree rogating five criminals—A, B, C, D and E—to try and identify is exactly connected to only one tent. A tent can be found who is the culprit. Below is a summary of their statements: in a horizontally or vertically adjacent square of a tree. The tents are never placed adjacent to each other, neither vertical, A:   it wasn’t E horizontal, nor diagonal. The numbers outside the grid give       it was B the total number of tents in the corresponding row or column. B:   it wasn’t C A tree might be next to two tents, but is only connected to       it wasn’t E one, and vice versa. Find all the tents. C: it was E       it wasn’t A 1 D:   it was C       it was B ♠ ♠ 1 E:   it was D         it wasn’t A ♠ ♠ 1 It was well known that each suspect told exactly 1 one lie. Can you determine who the criminal is? ♠ 1 Puzzle 9 ♠ 2 At the local school, I was chatting to my sister’s friends ♠ 1 and noticed a number of things. Jessica has mousey coloured hair and the girl with black hair was wearing ♠ ♠ ♠ 2 a green dress. Lucy is not blonde and Lauren does not have brown hair, Chloe was wearing a blue dress. The 1 1 3 1 1 1 1 1 blonde girl was not wearing red and Lauren was not wearing green. I can’t remember which girl was wearing a yellow dress. Can you determine the colours of the Puzzle 5 girl’s dresses and their hair? Find the highest total—you can only move up or right— using the mathematical signs coming on the way. Puzzle 10 + 4 – 2 + 2 Draw a continuous line that travels in order from 1 to 6. 2 + 2 – 2 + You can only move horizontally and vertically, the line – 1 + 2 – 4 must not cross itself and every square is visited. 2 – 1 + 1 – 3 + 1 – 2 + 3 4 1 3 + 3 – 4 + 6 5 Puzzle 6 2 In the above question, if we can move up and left only, then what is the maximum sum that we can get? 1.6 Logical Reasoning  Puzzle 11 14. The answer to question 15 is (a) B (b) C A bank customer had `100 in his account. He then made (c) A 6 withdrawals, totalling `100. He kept a record of these withdrawals, and the balance remaining in the account, 15. The first question with (B) as the correct answer is as follows: (a) Q3 (b) Q1 (c) Q2 Withdrawls (`) Balance left (`) 16. The only option not used so far is 50 50 (a) A (b) B (c) C 25 25 10 15 Puzzle 17 8 7 If yesterday was Saturday’s tomorrow and tomorrow was Wednesday’s yesterday, what day would it be today? 5 2 2 0 Puzzle 18 to 20 100 99 Directions for questions 18 to 20: Read the passage When he added up the columns as above, he given below and solve the questions based on it. assumed that he must owe `1 to the bank. Was he right? In a shooting competition, a person is allowed to shoot at four targets successively, followed by the next shooter. When all the shooters have finished one such round, the Puzzle 12 process is repeated. If a target is hit, the shooter gets Can you draw exactly 4 straight lines that pass through 2 points and if he misses the target, the other shooters are ALL 9 spots, without removing your pen from the paper? awarded one point each. The first shooter to get 60 points wins the shooting competition. In a contest among three persons—Akhil, Bharat and Chand, their score at the end is as follows: Akhil = 60, Bharat = 53 and Chand = 43. Out of a total of 78 shots being fired, only 43 hit the target. 18. Who was the first to shoot? (a) Akhil (b) Bharat (c) Chand Puzzle 13 (d) Cannot be determined 19. Who was the second to shoot? In a football syndicate, the winnings amounted to (a) Akhil `7657. There were more than 30 people in the syndicate (b) Bharat but less than 100. Each won exactly the same number of (c) Chand rupees and no paise were involved. How much did each (d) Cannot be determined win? 20. Who was the third to shoot? (a) Akhil Puzzle 14 to 16 (b) Bharat Here is a snippet of curious multiple-choice entrance (c) Chand exam. (d) Cannot be determined  Introduction to Logical Reasoning 1.7 Hints and Explanations 6. 14 1. + 4 – 2 + 2 6 7 1 2 + 2 – 2 + – 1 + 2 – 4 2 8 4 3 2 – 1 + 1 – + 1 – 2 + 3 3 + 3 – 4 + 5 9 7. Abhishek was lying, 1900 was not a leap year. 2. 1.30 in the morning. The initial single strike was at 12.30. 8. C committed the terrible crime. The way to solve this puzzle is to look at each clue. We know that 3. If you think that you are now in first place, then think exactly one of each person’s statements is true. again! If you overtake the person in second place, Looking at A statements, let’s check to see ‘it was you are now in second place yourself. B is true? If ‘it was B is true, then we know the other statement is false, hence it was E. This is a 4. contradiction. Hence, we now know it wasn’t B, nor E (as ‘it wasn’t E must be the true statement). Looking ▲ at C statement, we can similarly determine that it wasn’t A either. E statement gives us that it wasn’t D, ♠ ▲♠ which leaves only C as the culprit. ▲♠ ♠ 9. ▲ Name Dress colour Hair colour ▲♠ Jessica Red Mousey ▲ ▲♠ Lauren Yellow Blonde ♠ ▲ Lucy Green Black Chloe Blue Brown ▲♠ ▲♠ ♠ 5. 10 10. + 4 – 2 + 2 3 2 + 2 – 2 + 4 1 – 1 + 2 – 4 2 – 1 + 1 – 6 5 + 1 – 2 + 3 2 3 + 3 – 4 + 1.8 Logical Reasoning  11. There is no reason what ever why the customer’s Total number of shots fired by the 2nd person original deposit of `100 should equal the total of = 26 the balances left after each withdrawal. The total of Total number of shots fired by the 3rd person withdrawals in the left-hand column must always = 24 equal `100, but it is purely a coincidence that the total of the right-hand column is close to `100. Problem–Besides the problems given in the question set, let us raise some more pertinent points regarding 12. this set: i. Since Akhil was the first on to get 60 points, can we assume that Akhil was the first one to shoot? If yes, then why and if no, then why? ii. Since Bharat was the second ranker, can we assume that Bharat was the second one to shoot? If yes, then why and if no, then why? FLAW DETECTOR—While operating on the surface only gives us an idea that Akhil was the first one to shoot because he got 60 points first, it also gives us the reason why we get this conclusion– 13. 31 Each one won `247. because we were operating on surface only. 14 to16 Understand the points scheme—A person can get points without hitting any target or even without firing shots. As 14. (c) it is given that two points are awarded for a hit and one 15. (a) point is awarded to the opponents in case of a miss. It 16. (b) might be a possibility that Akhil would have got 59 points or 58 points or so in his round, and then other shooters go 17. Monday to shoot, they miss and in turn Akhil gets the point, and thus he gets 60 points. 18 to 20 And otherwise also, a deep thinking tells us that game ends with second shooter (because a total of Scenario—The problem set given above involves many 78 shots are fired), so Akhil could be at best second facts–the scheme of firing shots, the way the points are shooter and not the first shooter. awarded, the number of shots fired and the number of shots hitting the target. Explanation—As we have discussed above also, this Observation—After going through the set up given question set involves many facts and hence lets make above, following points should come of the surface: some equations. i. One round of firing involves 12 shots being fired, four shots by each shooter. Hits Miss Points ii. Since 12 shots are being fired in one round, so a total of 72 shots are being fired in six such rounds. Akhil A b 2a + d + f Out of the 72 shots, 24 shots have been fired by each of them. Now, in the next six shots, 4 shots Bharat C d 2c + b + f must have been fired by the person who was the first person to shoot and rest two must have been Chand E f 2e + b + d fired by the person who was the second person to shoot. We are using six variables above, so we need to iii. So, total number of shots fired by the 1st person have six equations to solve this set. Let us make the = 28 equations—  Introduction to Logical Reasoning 1.9 Points scored by Akhil = 2a + d + f = 60  ………...(i) Alternative Solution—The more the number of Points scored by Bharat = 2c + b + f = 53 ………...(ii) variables, the more difficult the solution will be. Points scored by Chand = 2e + b + d = 43 ……......(iii) Let us reduce some variables and start directly Total hits = a + c + e = 43 ……......(iv) from the ‘hypothetical equation’ itself. Total misses = b + d + f = 35 ………...(v) Assume that the total number of hits by the first Till now we have been able to construct only five one to shoot = N, so total number of misses by him = equations. Since we have used all the given information, 28 – N. we cannot have a sixth equation directly from the So, total number of misses by the other two given set. Hence, we will introduce the ‘hypothetical shooters = 35 – (28 – N) = N + 7 equations’ now that will work as sixth equation. [Total number of shots fired by all the shooters = 78 and total hits by all the shooters = 43, so total number Assume that Akhil is the first one to start, so a + b = 28 of misses by all the shooters = 35] ………...(vi) So, the points scored by the first person to shoot = Doing (i) – (v) gives us: 2a – b = 25 ..……...(vii) 2N+N+7=3N+7 Adding (vi) and (vii), Now, if Akhil is the first one to shoot, then 3 N + 3a = 53, since we are not getting the integral value 7 = 60 1 3 N = 53 of ‘a’ from here, we would conclude that (vi)th equation Since no integral value of N is obtained from a + b = 28 is not a valid equation and so Akhil is not the here, so Akhil is not the first one to start. first one to shoot. Again, if Bharat is the second one to shoot, then Similarly, assuming Bharat to be the first one to 3 N + 7 = 53 1 3 N = 46 shoot gives us: c + d = 28 .……...(viii) We are not getting integral value of N, so Bharat Solving equation (ii) and equation (v), 2c – d = 18 is not the first one to shoot. ...(ix) Hence, Chandan is the first one to shoot. Adding equation (viii) and equation (ix), 3c = 46. Let us verify that: Again we are not getting the integral value of c from If Chandan is the first one to shoot, then 3 N + 7 = here, so Bharat is not the first one to shoot. 43 1 3 N = 36 1 N = 12 Obviously, it means Chandan is the first one to Now to find the second person to shoot, assume shoot. Let us check that also: that the total number of hits by the second shooter = M, If Chandan is the first one to shoot then, e + f = 28 ..(x) so total number of misses by him = 26 – M. Solving equation (iii) and equation (v), 2e – f = 8 ...(xi) So, total number of misses by the other two shooters = 35 – (26 – M) = M + 9 Adding equation (x) and equation (xi), 3e = 36, so, Or, the points scored by the second person to e = 12. shoot = 2 M + M + 9 = 3 M + 9 Similarly, to find out the second shooter, we will If Akhil is the second one to shoot, then 3 M + 9 = insert, one by one, an additional equation besides the 60 1 3 M = 51 1 M = 17 above given 5 equations, by assuming that Akhil is the Hence, Bharat is the second one to shoot. second one to shoot (and hence a + b = 26). If it does 18. (c) not satisfy the given conditions, then we will construct the additional equation by assuming Chandan to be the 19. (a) second shooter (and hence c + d = 26). 20. (b) Chapter 2 Developing the Skills lEARNING Objectives In this chapter, you will learn:  What constitutes Logical Reasoning?  Different types of Logical Reasoning questions  Skill set required to excel in Logical Reasoning  Approach to solve the questions Constituents of Logical Scenario Reasoning The scenario introduces a set of variables—people, places, things or events involved in an easy to under- Before we move on to solving the questions, it is very stand activity such as sitting in seats or singing songs. imperative that we understand the constituents of the Here is an example: Logical Reasoning Questions and at the same time the A postman has to deliver exactly seven letters— skill-sets required to crack them. N, O, P, Q, R, S and T on seven days of a week; not Logical reasoning questions are designed to mea- necessarily in the same order. The seven deliveries must sure the students’ ability to understand the structure of be made according to certain conditions. relationships and to draw conclusions from it. Students will be asked to make deductions from a set of state- In the above situation, there are two variable sets— ments, conditions or rules that describe the relation- the letters N, O, P, Q, R, S and T and seven different ships among various variables such as persons, places, delivery positions, which would be numbered 1 through things or events. These questions simulate the kinds of 7 for the different days of the week. detailed analyses of relationships that management stu- In the above situation, there are two variable sets- dents must perform in solving problems. Additionally, the letters N, O, P, Q, R, S and T and seven different they require the ability to reason clearly and deductively delivery positions, which would be numbered 1 through from a given set of rules or restrictions; all under a strict 7 for the different days of the week. time frame. Each logical reasoning question contains three Rules separate parts— The scenario is followed by a series of rules or conditions (i) Scenario which impose specific restrictions upon the relationships (ii) Rules and among the subjects. Rules can also be seen as a set of (iii) Question/s statements that describe the relationships between the  Developing the Skills 1.11 variables. An LR set may include as few as two or as 2. Which of the following is a complete list of the days many as ten rules or may be more. Besides, these rules on which letter O could be delivered? or conditions specify the relationship between the (a) Wednesday, Friday different variables. (b) Wednesday, Friday, Sunday Here are the rules that accompanied the above (c) Wednesday, Thursday, Friday given LR set: (d) Any day of the week except Saturday (i) Letter P and Letter O have to be delivered on 3. Which of the following cannot be true? consecutive days. (a) Letter Q is delivered on Wednesday (ii) The postman cannot deliver letter O and letter S (b) Letter Q is delivered on Friday on consecutive days. (c) Letter R is delivered on Wednesday (iii) Letter T has to be delivered on the fourth day of the (d) Letter S is delivered on Tuesday week. We will go through the solution of the questions (iv) The postman has to deliver S and N both before given above after discussing the Skills set required to delivering letter Q. excel in the Logical Reasoning section. (v) It is also given that Monday is assumed to be the first day of the week. Rules also help us in providing a proper sequence of events or arrangement of several variables involved in Skill-set required the question. We will discuss more about ‘Sequencing and Arrangement’ in Chapter 4 of this section. We have understood and observed uptill now that the LR questions test the following: Command of the details given, Questions Formal deductive abilities, The rules are followed by a series of questions about the Understanding of how rules limit and order behavior, relationships defined by the conditions. The questions and call for a deductive analysis and a right correspondence Ability to cope up with many pieces of data simulta- between the scenario and the rules. This third and final neously to solve the problems. part of any LR set, tests the students’ knowledge about In my experience of dealing with a good number the relationships between the variables, the structural of students, most of them already have these skills, the features of the given set, and the way these relationships problem lies with the fact that they probably haven’t and features change as the conditions in the set change. acquired the know-how to apply these skills to their best As in QA problems, one and only one response advantage in the rarified atmosphere of a standardized can be proven beyond any doubt to be the correct one. time-bound skills-based test. In CAT, the number of questions per set normally ranges While discussing the various skills required, we from one to six, although CAT does not follow certain will assume that a student has no prior background of pattern. solving these kinds of questions and owing to this; he/ All initial rules or conditions are applied to all she is almost at a very basic level. the questions given thereof. However, sometimes a particular question might introduce something new after suspending the parent information. Hence, students are Skill 1— Understanding the expected to consider each question separately from the Information other questions. Do not carry over information provided in any particular question to the other questions. This simply means that, “Are you able to decipher the Some of the sample questions pertaining to the different kinds of statements given?” above LR set are as follows: Let us have a look at these statements: 1. Which of the following lists an acceptable order of (i) Game B must be played on the day following the day deliveries of letters? on which game F is played. (a) NQPTOSR (b) POSTRNQ (ii) Game D must be staged on Sunday and is not to be (c) NRSTPQO (d) RSOTNPQ immediately preceded by game B. 1.12 Logical Reasoning  (iii) The population of Maharashtra is followed by the Statement (ii) – There are three cottages in a row facing population of Bihar whereas population of Orissa south and three friends A, B and C are living in these is preceded by the population of Bihar. cottages one person in each cottage. When A, B and Which of the following options is least likely to C are standing in front of their houses facing north, A be wrong? makes a statement that cottage of one of B and C is on Obviously, the above written statements are just a his right and another cottage is on his left. part of any particular LR set, but play an important role in Statement (iii) – There are three cottages in a row making a sequence of events. Besides, there can be a few numbered 1 through 3 and three friends A, B and C are questions, which by virtue of juggling with the words, can become difficult to comprehend within that time-bound living in these cottages, one person in each cottage. A test ambience. This can best be understood by looking at finds that his cottage number is less than the cottage a few examples with their proper explanations. number of one of his friends. Sometimes just for the sake of making a statement We do understand that the interpretation of all difficult to understand, the test makers start playing with the three statements is the same i.e., the order of their the words, as seen in the following example: cottages being—BAC or CAB. Statement (i) – There are three cottages in a row and At the same time, we should understand some three friends A, B and C are living in these cottages, one of the basic statements pertaining to the questions. To person in each cottage. The cottage of A is in between answer these questions, we should focus on the nature of the cottages of B and C. the right and wrong answer choices: Question reads as… Its meaning... Which one of the following statements A statement that could be true. The remaining wrong choices will be could be true? statements that cannot be definitely true. (i.e., statements that must be false) Which one of the following statements A statement that cannot be true(must be false). The remaining wrong cannot be true? choices will be the statements that can either be definitely true or at least could be true. Which one of the following statements A statement that must be true. The remaining wrong choices will be state- must be true? ments that either cannot be true or only could be true. All of the following statements could be A statement that cannot be true. The remaining wrong choices will be true EXCEPT…… statements that either could be true or are definitely true. All of the following statements must be A statement that either cannot be true or merely could be true. The re- true EXCEPT… maining wrong choices will be statements that must be true. Which one of the following statements A statement that cannot be true or could be true or false. The remaining could be false? wrong choices will be the statements that must be true. Which one of the following statements A statement that cannot be true. The remaining wrong choices will be the must be false? statements that are either definitely true or only could be true. Which of the following statements is least A statement that is true. The remaining options will be false. likely to be wrong?  Developing the Skills 1.13 Skill 2— Diagramming the Information Rather what I would suggest as a thumb rule: do not erase any work that you have done unless you have This is the most important stage of solving any LR set. made a mistake. This particular skill in itself requires the students to be aware of various factors related to the scenario and the rules, such as: Approach 2 What kind of diagram viz., table or line diagram Create a “grid” and do the work for each question in etc., is the most best suitable for the given set? the rows within the grid How many variables are there in the set and out of This approach requires you to create a grid near the main the given variables, which of the variables are most setup. The work for each question is then done within helpful in making the diagram and representing the the rows of the grid, as follows: rules and the scenario? Questions/Scenario 1 2 3 4 5 Ideally, in case of two variables, the work done or conditions in creating the setup and making inferences will be sufficient to answer the question. But the problem starts Q1 A B C surfacing when the number of variables increases to three or more. We will discuss more about the variables Q2 B A C and the way to use them to our benefit later in this chapter. Q3 D E A D Besides the given data in the LR set, sometimes the questions which supply a new piece of information After going through the above discussion, we can specific to that question alone, also tend to help us in conclude that achieving a complete diagram. And this is the reason why Drawing the grid along with the main setup requires students should do this diagramming work next to the a large amount of space, which might not be always question itself, if enough space is available. This provides available in the test paper. In contrast, doing the you several benefits: work next to the question is space-efficient. In case of LR sets with less than four variables, working By doing the work next to the problem, you increase next to the question is always efficient, as it allows you the visual connection between your diagram and the to draw the most appropriate diagram for the given LR set. scenario. If you need to come back to a question, when you return you will be able to clearly see the work done up Lastly, since the LR sets asked in the CAT are too to that point. dynamic in nature, the proper use of scratch work is an important pre-requisite. There are two approaches that are widely propagated and used to form a diagram. Let us look at Skill 3—Sequencing the the pros and cons related to the approaches: Information to get the Answer Uptill now, we have understood how the given variables Approach 1 can be arranged in a proper structure. Before moving on Do the work for each question on the main diagram to the actual problem solving of two or more variables, we This approach suggests that the work for each question have now reached a stage (theoretically) where the given should be done on the main diagram itself. In order to information is to be used to solve the LR set. The idea utilize this method, you must erase your previous work is to focus on what the question requires of you, before before beginning each question. However, erasing your starting the solving process. work has a number of negative effects too: you could Remember some of the very basic rules: accidentally erase important information that applies to Always pay special attention to the sequencing all the questions and more importantly, every time you aspect in every set. Many questions are answered erase your work you lose some of the knowledge that just by thinking, “What things are left? Where can you created about the game. (or must) they be placed and at which position?” 1.14 Logical Reasoning  Many a times it will happen that we don’t fully (A) Six plays and grasp a LR situation. In such cases keep asking (B) Six days as six different positions yourself questions and go through a couple of “what Now according to the given conditions, we will be ifs?” to keep the LR set going. Whenever you are in establishing the correspondence between these plays and a fix, ask yourself, “What if it goes here? What does the days on which they can happen. that mean for the other things?” Even if you don’t get any help from this, but it’s still time worth spent because it helps you to understand the LR set better. Example 2: Three variable LR set The best way to deal with any LR set is to build it There are five men working in Due North Inc. namely A, directly into a diagram from the given information. B, C, D and E. Their respective salaries are different and Sometimes, the students are expected to fill some they are married to five women namely F, G, H, I and J. of the unoccupied places on their own by assuming In this situation, there are three sets of variables— something. Then it becomes essential to segregate the given information in the LR set with your (A) Five men working in an organization. assumed information. You can do it by encircling the (B) Their respective salaries which are different. data assumed by you. (C) Their wives, which are of course different. While assuming some information on your own, Before plotting the diagram for the above set, the always keep an eye on the options provided along most important thing to remember here is the fact that we with the question. Sometimes you might get a lot of can establish direct correspondence on paper, only between help from the options as well. two variables, and so the third variable is to be kept in the Remember that the test-maker has scattered the mind. Now, to choose the two variables out of the given easy, the moderate and the difficult questions across three variables, we should keep an eye on the rules or the the entire paper in no proper order. So, solve the given conditions. The more the conditions related to a question which you find the easiest first, and not the particular variable are given, the more the chances are of it one which is Q 1. being taken as one of those two variables which are to be used in the diagram on the paper. Managing the Variables Example 3: More than three variable LR set Let me clarify at the onset, that the variables which we are talking about here are not the same as the Five men from five different states of India work in mathematical variables. Rather, what we mean to say is a factory and each of them performs a different job. that the word variable here represents all the entities, be Each man commutes to work using a different mode of it the name of a place, a person or the days; a book which transport and most work on different shifts. There are they might have been reading or practically anything three shifts—1st shift, 9 A.M.–12 Noon; 2nd shift, 12 given in the LR set. Additionally, there will be some Noon–3 P.M. and 3rd shift, 3 P.M.–6 P.M. All the people rules or conditions encompassing these variables. And working on the same shift come at the same time. as it is correctly said, “Our variables are our resources”; How many variables are there in the above LR set? similarly we should use the variables given to us in our Let us count— questions, in the same way. Understandably, a LR set can have two or more (A) 1st variable – five men variables. Let us see some examples: (B) 2nd variable – five states (C) 3rd variable – different job (D) 4th variable – mode of transport Example 1: Two variable LR set (E) 5th variable – work-shift Six plays, viz., Ram teri Ganga maili, Satya, Don, We do understand that most of the time managing Bakri.com, Andha Mughal and Angrezo Bharat aao, are fewer variables is easier than managing more variables. to be staged, one on each day starting from Monday to From here we will start with LR sets of two Saturday. variables and then move on to the LR sets of a higher In the above written statement, which can also be number of variables. the opening statement of an LR set, we see that there are One thing I would like to reiterate— Please don’t two sets of variables— just read this book; rather, sit with a pen/pencil and paper  Developing the Skills 1.15 and before going through the solution of any LR set, give Solution it a try. Scenario There are two sets of variables—1st set being five boxes How to Approach LR and 2nd set being five days Monday through Friday. As the boxes must be delivered in these five days, In this section, we will learn the method of solving LR so one box is to be delivered everyday. questions keeping in mind various do’s and don’ts. Rules Problems in Two Variables There are two sets of rules given here: Directions for questions 1 to 4: Read the following (A) Strict sequencing rule—These are the rules which passage and solve the questions based on it. give us the exact position of the variables. There are five boxes viz., T, U, W, X and Z, to be (B) Loose sequencing rule—These are the rules which delivered on five consecutive days, Monday through give us the relative positioning of one variable Friday one box per day. The following conditions are to with respect to the other variable, without giving be kept in mind while formulating the delivery schedule the exact position. of the boxes: We will discuss about Sequencing in Chapter 4 of this section. (i) Box X is not delivered on Monday Now let us interpret the rules: (ii) If box T is delivered on Monday, then box X must be Box X is not delivered on Monday—This is a delivered on Friday. strict sequencing rule. (iii) If box X is delivered on Tuesday, box U is delivered If box T is delivered on Monday, then box X must be on Monday. delivered on Friday. (iv) Box W is delivered the day following the day of the delivery of box Z. This is a loose sequencing rule which introduces further conditions related to the delivery of box T and 1. Box W could be delivered on any day except: box X. But we should be very clear about certain facts (a) Monday (b) Tuesday related to this statement: (c) Wednesday (d) Thursday (i) If box T is not delivered on Monday, then box X can 2. If box U is delivered the day after the box T is be delivered on any day (except Monday) delivered, which of the following is a complete and (ii) If box X is not delivered on Friday, then box T accurate list of the days on which box X could be cannot be delivered on Monday. delivered? (a) Tuesday, Wednesday, Thursday I f box X is delivered on Tuesday, box U is delivered (b) Wednesday, Thursday, Friday on Monday. This is again a loose sequencing rule which intro- (c) Tuesday, Wednesday, Friday duces conditions related to the delivery of box X (d) Wednesday, Friday and box U. Th