© 2006 APTMetrics, Inc. McKinsey Problem Solving Test Practice Test A 1 Instructions Practice Test Overview and Instructions This practice test has been developed to provide a sample of the actual McKinsey Problem Solving Test used for selection purposes. This test assesses your ability to solve business problems using deductive, inductive, and quantitative reasoning. This practice test contains a total of 26 questions. The actual test contains 26 questions and you will be given 60 minutes to answer as many questions as possible. You will be presented with three scenarios based on actual McKinsey client cases. Information related to each scenario will be shown in text, tables, and exhibits. This information is presented in shaded areas and is distributed in sections throughout the scenario. The questions ask you to find the most appropriate answer to the problem as described using only the information presented. You should select one and only one answer to any question. While completing this practice test, do not use any electronic devices (e.g., calculator, computer) when performing calculations to answer the questions. Electronic devices will not be permitted to be used during the actual test administration. Also during the actual test administration, you may use all blank space in the test booklet as scratch paper to assist you in performing any calculations and recording any notes. No scratch paper will be allowed. Booklets will be destroyed after you complete the test and will not be used in any way to determine your test scores. Your final test score will be based on the number of questions you answer correctly. The practice scenarios begin on the next page of this booklet. Only consider information contained within the scenario when determining your answer. Considering all information presented within the scenario is critical to answering questions correctly. After you have completed the test, score your answers using the answer key located at the end of this booklet. Add the number of correct answers to determine your final total score. McKinsey Problem Solving Test 2 Kosher Franks Kosher Franks Kosher Franks is a company that sells hot dogs and other packaged meat products, such as salami and lunch meats, in the United States. Kosher Franks’ products are primarily sold through grocery stores. While not a very large company, it has strong brand recognition in the packaged meat market and a reputation for high quality products. Kosher Franks’ customers are large grocery store chains or grocery distributors, who sell to smaller chains or independent grocery stores across the US. The prices, which Kosher Franks presents to these chains or distributors, are negotiated individually and depend on many factors. Some of these factors include the volume to be purchased, whether the customer is a new customer or an existing one, and any promotional or marketing arrangements that have been agreed upon with the customer. The stores then sell the products to consumers at a higher price in order to make a profit. Table 1 shows Kosher Franks’ data on this year’s sales revenue and the average annual revenue growth over the last 5 years. The data in Table 1 is broken down by major product category. Table 1: Recent Revenue and Revenue Growth Data for Kosher Franks Revenue this year Average annual revenue growth over last 5 years All beef hot dogs $366.7m 4.2% Other packaged meat $65.3m 1.5% Sliced meat $55.3m 1.2% Other products (e.g., pickles, sauces) $15.1m -7.0% Kosher Franks manufactures all of its own products and invests significantly more resources than its competitors to ensure superior quality. This is especially valuable to them because this type of product has a poor overall reputation for quality in the Problem-Solving Strategies Problem-Solving Strategies Bởi: OpenStaxCollege Success in problem solving is obviously necessary to understand and apply physical principles, not to mention the more immediate need of passing exams The basics of problem solving, presented earlier in this text, are followed here, but specific strategies useful in applying Newton’s laws of motion are emphasized These techniques also reinforce concepts that are useful in many other areas of physics Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop Problem-Solving Strategy for Newton’s Laws of Motion Step As usual, it is first necessary to identify the physical principles involved Once it is determined that Newton’s laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation Such a sketch is shown in [link](a) Then, as in [link](b), use arrows to represent all forces, label them carefully, and make their lengths and directions correspond to the forces they represent (whenever sufficient information exists) 1/9 F T w Problem-Solving Strategies (a) A sketch of Tarzan hanging from a vine (b) Arrows are used to represent all forces is the tension in the vine above Tarzan, T is the force he exerts on the vine, and is his weight All other forces, such as the nudge of a breeze, are assumed negligible (c) Suppose we are given the ape man’s mass and asked to find the tension in the vine We then define the system of interest as shown and draw a free-body diagram T is no longer shown, because it is not a force acting on the system of interest; rather, T acts on the outside world (d) Showing only the arrows, the head-to-tail method of addition is used It is apparent that = − , if Tarzan is stationary Step Identify what needs to be determined and what is known or can be inferred from the problem as stated That is, make a list of knowns and unknowns Then carefully determine the system of interest This decision is a crucial step, since Newton’s second law involves only external forces Once the system of interest has been identified, it becomes possible to determine which forces are external and which are internal, a necessary step to employ Newton’s second law (See [link](c).) Newton’s third law may be used to identify whether forces are exerted between components of a system (internal) or between the system and something outside (external) As illustrated earlier in this chapter, the system of interest depends on what question we need to answer This choice becomes easier with practice, eventually developing into an almost unconscious process Skill in clearly defining systems will be beneficial in later chapters as well A diagram showing the system of interest and all of the external forces is called a free-body diagram Only forces are shown on free-body diagrams, not acceleration or velocity We have drawn several of these in worked examples [link](c) shows a freebody diagram for the system of interest Note that no internal forces are shown in a freebody diagram 2/9 Problem-Solving Strategies Step Once a free-body diagram is drawn, Newton’s second law can be applied to solve the problem This is done in [link](d) for a particular situation In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples If the problem is one-dimensional—that is, if all forces are parallel—then they add like scalars If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems This is done by projecting the force vectors onto a set of axes chosen for convenience As seen in previous examples, the choice of axes can simplify the problem For example, when an incline is involved, a set of axes with one axis parallel to the incline and one perpendicular to it is most convenient It is almost always convenient to make one axis parallel to the direction of motion, if this is known Applying Newton’s Second Law Before you write net force equations, it is critical to determine whether the system is accelerating in a particular direction If the acceleration is zero in a particular direction, then the net force is zero in that direction Similarly, if the acceleration is nonzero in a particular direction, then the net force is described by the equation: Fnet = ma For example, if the system is accelerating in the horizontal direction, but it is not accelerating in the vertical direction, then you will have the following conclusions: Fnet x = ma, Fnet y = You will need this information in order to determine unknown forces acting in a system Step As always, check the solution to see whether it is reasonable In some cases, this is obvious For example, it is reasonable to find that friction causes an object to slide down ... © 2006 APTMetrics, Inc. McKinsey Problem Solving Test Practice Test B 1 Instructions Practice Test Overview and Instructions This practice test has been developed to provide a sample of the actual McKinsey Problem Solving Test used for selection purposes. This test assesses your ability to solve business problems using deductive, inductive, and quantitative reasoning. This practice test contains a total of 26 questions. The actual test contains 26 questions and you will be given 60 minutes to answer as many questions as possible. You will be presented with three scenarios based on actual McKinsey client cases. Information related to each scenario will be shown in text, tables, and exhibits. This information is presented in shaded areas and is distributed in sections throughout the scenario. The questions ask you to find the most appropriate answer to the problem as described using only the information presented. You should select one and only one answer to any question. While completing this practice test, do not use any electronic devices (e.g., calculator, computer) when performing calculations to answer the questions. Electronic devices will not be permitted to be used during the actual test administration. Also during the actual test administration, you may use all blank space in the test booklet as scratch paper to assist you in performing any calculations and recording any notes. No scratch paper will be allowed. Booklets will be destroyed after you complete the test and will not be used in any way to determine your test scores. Your final test score will be based on the number of questions you answer correctly. The practice scenarios begin on the next page of this booklet. Only consider information contained within the scenario when determining your answer. Considering all information presented within the scenario is critical to answering questions correctly. After you have completed the test, score your answers using the answer key located at the end of this booklet. Add the number of correct answers to determine your final total score. McKinsey Problem Solving Test 2 Freddie’s Shrimp Shack Freddie’s Shrimp Shack Freddie’s Shrimp Shack (Freddie’s) is a chain of approximately 100 seafood restaurants located along the Gulf Coast of the United States. Freddie’s has a reputation for serving high quality seafood at a reasonable price. Although Freddie’s serves a wide variety of seafood, the most popular food sold is shrimp. Two types of shrimp are available on the Gulf Coast: Aquaculture Shrimp: These shrimp are raised on farms at any time of the year. They are usually imported into the United States by large seafood wholesalers and distributors. Wild Shrimp: These shrimp are caught in the wild in the Gulf of Mexico in the summer and autumn months. Hundreds of small, family-owned boats catch the shrimp and sell them at dock shrimp processors. There are dozens of these shrimp processors scattered along the Gulf Coast. Boat owners will take the shrimp to the nearest processor who is paying the highest price. The processors then grade, de-head, and freeze the shrimp. In some cases, they also peel and de-vein the shrimp. There are two standard forms that these shrimp are sold in: headless, shell-on shrimp and peeled and de-veined (P&D) shrimp. Freddie’s buys only headless, shell-on, wild shrimp because of their perceived higher quality. It is now October and Freddie’s overall profitability has been falling since immediately before the summer season. The CEO has asked McKinsey to help her understand the reasons behind this trend that started in May. She states that the recent fall in profitability has been totally unexpected and she would like McKinsey to look into it. She also notes that it seems like too much of a © 2006 APTMetrics, Inc. McKinsey Problem Solving Test Practice Test C 1 Instructions Practice Test Overview and Instructions This practice test has been developed to provide a sample of the actual McKinsey Problem Solving Test used for selection purposes. This test assesses your ability to solve business problems using deductive, inductive, and quantitative reasoning. This practice test contains a total of 26 questions. The actual test contains 26 questions and you will be given 60 minutes to answer as many questions as possible. You will be presented with three scenarios based on actual McKinsey client cases. Information related to each scenario will be shown in text, tables, and exhibits. This information is presented in shaded areas and is distributed in sections throughout the scenario. The questions ask you to find the most appropriate answer to the problem as described using only the information presented. You should select one and only one answer to any question. While completing this practice test, do not use any electronic devices (e.g., calculator, computer) when performing calculations to answer the questions. Electronic devices will not be permitted to be used during the actual test administration. Also during the actual test administration, you may use all blank space in the test booklet as scratch paper to assist you in performing any calculations and recording any notes. No scratch paper will be allowed. Booklets will be destroyed after you complete the test and will not be used in any way to determine your test scores. Your final test score will be based on the number of questions you answer correctly. The practice scenarios begin on the next page of this booklet. Only consider information contained within the scenario when determining your answer. Considering all information presented within the scenario is critical to answering questions correctly. After you have completed the test, score your answers using the answer key located at the end of this booklet. Add the number of correct answers to determine your final total score. McKinsey Problem Solving Test 2 Mail-It Mail-It Mail-It is a company that runs postal services for both personal and business customers in the country of Molvania. The postal services that Mail-It provides cover all areas from collection to delivery. The main stages of operating a postal service are as follows: Retailing postal fees: The customer pays Mail-It for the cost of sending a letter or package. For a personal customer, this service is often completed by the customer purchasing stamps at Mail-It post offices. For larger business customers, this can be completed via the automated stamping of their mail. The price of sending a letter or package depends on its destination, its weight, and the required speed of its delivery. For business customers, the price is usually cheaper because they often use automated stamping and often bring the mail to Mail-It themselves. Collection: Mail-It collects the stamped mail from designated post boxes. Customers deposit the majority of this mail into the designated post boxes. However, some business customers may take their mail directly to Mail-It’s sorting offices. Sorting and stamp cancellation: Mail-It sorts the mail according to the destination. This sorting usually happens at designated offices nationwide. Most domestic mail has an address code written by the sender which can be read and sorted automatically by machines. When mail is sent without a code or the machine cannot read the code, the sorting must be done by hand. At this stage, the stamp on the letter or package is also “cancelled” using an ink mark to ensure that the stamp cannot be re-used. Transportation and delivery: Once the mail has been sorted, it is transported to the Problem-Solving Strategies Arthur Engel Springer [...]... planes 1 The Invariance Principle We present our first Higher Problem- Solving Strategy It is extremely useful in solving certain types of difficult problems, which are easily recognizable We will teach it by solving problems which use this strategy In fact, problem solving can be learned only by solving problems But it must be supported by strategies provided by the trainer Our first strategy is the search... 2 y0 − x0 arccos(x0 /y0 ) (4) It would be pretty hopeless to solve this problem without invariants By the way, this is a hard problem by any competition standard E7 Each of the numbers a1 , , an is 1 or −1, and we have S a1 a2 a3 a4 + a2 a3 a4 a5 + · · · + an a1 a2 a3 0 Prove that 4 | n Solution This is a number theoretic problem, but it can also be solved by invariance If we replace any ai by... let us cut out two diagonally opposite corners of the board In how many ways can you cover the 62 squares of the mutilated chessboard with 31 dominoes? The problem looks even more complicated than the problem solved by Fisher, but this is not so The problem is trivial There is no way to cover the mutilated chessboard Indeed, each domino covers one black and one white square If a covering of the board... please, fill up the lattice points below or on the x-axis by chips By solitaire jumps try to get one chip to (0, 5) with all other chips cleared off (J H Conway.) The preceding problem of Kontsevich might have been suggested by this problem A solitaire jump is a horizontal or vertical jump of any chip over its neighbor to a free point with the chip jumped over removed For instance, with (x, y) and (x, y... ) ← · · · shows that, for q 1, the iteration ends up with I For q > 1, we eventually arrive at I iff we ever get q identical blocks of length 2k , i.e., we have period 2k Try to prove this The problem- solving strategy of working backwards will be treated in Chapter 14 6 All three numbers a, b, c change their parity in one step If one of the numbers has different parity from the other two, it will... intentionally left blank 2 Coloring Proofs The problems of this chapter are concerned with the partitioning of a set into a finite number of subsets The partitioning is done by coloring each element of a subset by the same color The prototypical example runs as follows In 1961, the British theoretical physicist M.E Fisher solved a famous and very tough problem He showed that an 8 × 8 chessboard can... Decide if the algorithm always stops (Most difficult problem of IMO 1986.) Solution The algorithm always stops The key to the proof is (as in Examples 4 and 8) to find an integer-valued, nonnegative function f (x1 , , x5 ) of the vertex labels whose value decreases when the given operation is performed All but one of the eleven students who solved the problem found the same function 5 (xi − xi+2 )2 ,... of one color and 32 squares of the other color The following problems are mostly ingenious impossibility proofs based on coloring or parity Some really belong to Chapter 3 or Chapter 4, but they use coloring, so I put them in this chapter A few also belong to the closely related Chapter 1 The mutilated chessboard required two colors The problems of this chapter often require more than two colors ... has period k with tail p (c) The result is nonterminating and nonperiodic: a/n 0.d1 d2 d3 In this case, the algorithm will not stop, and the sequence (1) is not periodic 5 This is a special case of problem E10 on shrinking squares Addition is done mod 2: 0 + 0 1+1 0, 1 + 0 0+1 1 Let (x1 , x2 , , xn ) be the original distribution of zeros and ones around the circle One step consists of the replacement... Is there convergence to an end state? 4 Find all periods with or without tails, if any Since the Invariance Principle is a heuristic principle, Decision Making and Problem Solving Strategies THIS PAGE INTENTIONALLY LEFT BLANK Decision Making and Problem Solving Strategies John Adair Publisher’s note Every possible effort has been made to ensure that the information contained in this book is accurate at the time of going to press, and the publishers and author cannot accept responsibility for any errors or omissions, however caused No responsibility for loss or damage occasioned to any person acting, or refraining from action, as a result of the material in this publication can be accepted by the editor, the publisher or the author Previously published by the Institute of Personnel and Development as Decision Making and Problem Solving 1997 and 1999 First published in Great Britain and the United States in 2007 by Kogan Page Limited as Decision Making and Problem Solving Strategies Reissued 2010 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licences issued by the CLA Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned addresses: 525 South 4th Street, #241 120 Pentonville Road Philadelphia pa 19147 London n1 9jn United Kingdom usa www.koganpage.com 4737/23 Ansari Road Daryaganj New Delhi 110002 India © John Adair, 1997, 1999, 2007, 2010 The right of John Adair to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988 ISBN 978 7494 5551 E-ISBN 978 7494 5890 The views expressed in this book are those of the author, and are not necessarily the same as those of Times Newspapers Ltd British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Adair, John Decision making and problem solving strategies / John Adair 2nd ed p cm Originally published in 2007 Includes index ISBN 978-0-7494-5551-4 ISBN 978-0-7494-5890-4 (ebook) Decision making. Problem solving. Thought and thinking. I Title. II Title: Decision making and problem solving strategies HD30.23.A3 2010 658.4’03 dc22 Typeset by Jean Cussons Typesetting, Diss, Norfolk Printed and bound in India by Replika Press Pvt Ltd 2009031517 Contents About the author vii Introduction 1 Your mind at work Is your brain working now? 4; The functions of the mind 6; Introducing the Depth Mind principle 12; Key points 15 The art of effective decision making 17 Define the objective 18; Collect relevant information 18; Generate feasible options 21; Make the decision 23; Implement and evaluate 28; Key points 31 Sharing decisions with others 35 Your role as leader 35; Task need 36; Team maintenance need 36; Individual needs 37; The three circles interact 38; The functions of leadership 38; Key points 44 vi Contents Key problem-solving strategies 45 How problems differ from decisions 45; A unified model for decision making and problem solving 47; Asking the right questions 48; How to approach systems problems 50; Key points 53 How to generate ideas 56 Brainstorming 56; Guidelines for brainstorming 57; How to run a brainstorming session 59; Key points 61 Thinking outside the box 63 Towards a more creative approach 63; Look wider for solutions 65; How to use your Depth Mind 67; The creative thinking process 69; Mental roadblocks 70; Key points 72 Developing your thinking skills 75 What is an effective practical thinker? 75; Check that you are in the right field 78; Key factors in choosing your field of work 78; How to design your own learning strategy 79; Key points 83 Appendix 85 Further reading 89 ... mistake Section Summary • To solve problems involving Newton’s laws of motion, follow the procedure described: Draw a sketch of the problem 3/9 Problem- Solving Strategies Identify known and unknown... the car plus its occupants? Explicitly show how you follow the steps in the Problem- Solving Strategy 4/9 Problem- Solving Strategies for Newton’s laws of motion For this situation, draw a free-body... follow steps in the Problem- Solving Strategy for Newton’s laws of motion Use Newton’s laws since we are looking for forces Draw a free-body diagram: 7/9 F Problem- Solving Strategies The tension