McKinseyProblem Solving TestPractice Test A 2013 APTMetrics, Inc.
1InstructionsMcKinsey Problem Solving TestPractice Test Overview and InstructionsThis practice test has been developed to provide a sample of the actual McKinseyProblem Solving Test used for selection purposes. This test assesses your abilityto solve business problems using deductive, inductive, and quantitative reasoning.This practice test contains a total of 26 questions. The actual test contains 26questions 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. Thisinformation is presented in shaded areas and is distributed in sections throughoutthe scenario. The questions ask you to find the most appropriate answer to theproblem as described using only the information presented. You should select oneand 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 testadministration. Also during the actual test administration, you may use allblank space in the test booklet as scratch paper to assist you in performing anycalculations and recording any notes. No scratch paper will be allowed. Bookletswill be destroyed after you complete the test and will not be used in any way todetermine your test scores. Your final test score will be based on the number ofquestions you answer correctly.The practice scenarios begin on the next page of this booklet. Only considerinformation contained within the scenario when determining your answer.Considering all information presented within the scenario is critical to answeringquestions correctly.After you have completed the test, score your answers using the answer key locatedat the end of this booklet. Add the number of correct answers to determine yourfinal total score.
2Innovation CapitalInnovation CapitalThe Group of Eight or G8 is a group comprised of political representatives of eightof the world’s largest eleven economies: United States, United Kingdom, Canada,Germany, France, Italy, Japan and Russia. The G8 meet periodically to discuss issuesof importance to member states and agree upon measures to address these issues.The countries that comprise the G8 have been experiencing slow economic growthin recent years, and this is an important topic to be discussed at the next meetingof G8 Finance Ministers. In preparation for this meeting, a McKinsey team,working together with a group of external thought leaders and academics, arepreparing a report on the importance of Innovation as a contributor to economicgrowth. The team intends to introduce a concept to the G8 representatives knownas ‘Innovation Capital’, which is the value of all innovation-related assets whichcontribute to growth in productivity in the economy.The team further defines three types of Innovation Capital: Physical Capital: Investments in information and communicationequipment Knowledge Capital: Investments that build the intellectual property andbrand value of a company or organization Human Capital: Investments that build individual or group abilities andskills within companies or organizationsExhibit 1 shows the main components of Innovation Capital and their total valueacross 16 countries that the team has been studying, including the members ofthe G8.Exhibit 1Total innovation capital, (US trillions)Information and communications infrastructureComputerized informationScientific research and developmentOther research and developmentAdvertising and market researchEducationEmployee developmentOrganizational developmentTotal18.104.22.168.22.214.171.124.513.8
3Innovation Capital1.Which of the following MOST accurately describes the reason for the team’swork in preparing for the G8 meeting?A.The team has discovered a new economic measure known as InnovationCapital and wants to introduce itB.The team wants to explain how Innovation can drive economic growthC.The team wants to explain how Innovation can represent a large proportionof an economy’s sizeD.The team wants to convince the group to invest more in Innovation Capitalin the future2. Which of the following analyses would be LEAST appropriate in betterunderstanding the size of investments in Innovation Capital in the countries theteam has been studying?A.Analysis of expenditure by organizations on training programs for theiremployeesB.Analysis of expenditure by organizations on activities which buildawareness of their aims and purposeC.Analysis of expenditure by organizations on networking and socializationmeetings and eventsD.Analysis of expenditure by organizations on the management of theirdatabases and information systems3. Which of the following can be concluded based on the information provided inExhibit 1 regarding the countries being studied?A.45% of all Human Capital is invested in Organizational DevelopmentB.51% of all Innovation Capital is Knowledge CapitalC.More than 10% of Innovation Capital is invested in ComputerizedInformationD.More than a quarter of Innovation Capital is Scientific Research &Development
4Innovation Capital4. If total Innovation Capital in Exhibit 1 were to grow by 5% per year in the future,which of the following would be the MINIMUM required annual growth inHuman Capital that would see it represent more than half of total InnovationCapital in 10 years?A.10%B.15%C.20%D.25%The team proceeds to examine changes in business sector growth in a numberof European countries in recent years, that is, the change in the total value ofgoods and services produced by the business sectors in these countries.Growth in the value of goods and services can be driven by two factors: Hours: Changes in the total hours worked can drive changes in the totalgoods and services produced Productivity: Even if the same number of hours have been worked, a moreor less productive workforce can generate greater or lesser goods and services.Exhibit 2 shows the average contribution of these two factors towards businesssector growth in ten European countries over the last 12 years. Average annualbusiness sector growth is given at the top of each bar. Within each bar, thelight grey portion represents the proportion of this growth driven by changesin Productivity, while the dark grey portion represents the proportion of thisgrowth driven by changes in Hours.Exhibit 553.846.2Netherlands Denmark1.533.966.1Italy3.820.179.9Spain
5Innovation Capital5. Which of the following statements, if true, would BEST explain why theinformation in Exhibit 2 is important for the team?A.Most of the countries in Exhibit 2 have experienced negative economicgrowth in the last 2 yearsB.In most countries, the business sector is the biggest contributor towardsInnovation CapitalC.Growth in Hours is mostly driven by growth in the size of the workingpopulationD.Growth in Productivity is mostly driven by growth in Innovation6. Which of the following statements is TRUE based on the information providedin Exhibit 2?7.A.Hours grew by 24% across all ten countries over the last 12 yearsB.Slovenia had the greatest growth in Productivity over the last 12 yearsC.Spain had the least growth in Productivity over the last 12 yearsD.Germany had the least growth in Hours over the last 12 yearsTo the nearest tenth of a percentage point, what is the differencebetween Germany’s and Spain’s average annual business sector growth due toproductivity over the last 12 years?A.0.1 percentage pointsB.0.5 percentage pointsC.0.9 percentage pointsD.1.3 percentage points8. Which of the following, if true, LEAST explains the data for Slovenia and CzechRepublic in Exhibit 2?A.Over the last 20 years, the average age of the population in these countrieshas been steadily increasingB.Prior to the period in Exhibit 2, these countries were emerging from Communisteconomies with comparatively poor infrastructure and productivityC.Net migration into these countries has been negative over the last 12 yearsD.Changes in employment laws in these countries have led to greaterflexibility for employers in setting working hours for their employees
6Innovation CapitalIn preparing further for the G8 meeting, the team decides that it would be a goodidea to use some specific examples of recent major innovations to help betterexplain the importance of Innovation Capital.A team member suggests using Apple’s iPod music player as such an example. Theteam readily agrees to this suggestion. They believe that the development of theiPod not only illustrates all three types of Innovation Capital, but it also shows howup-front investment in Innovation Capital can lead to follow-on advantages for theinvestor that accumulate over time.9. Which of the following statements LEAST illustrates the Innovation Capitalunderlying the development of Apple’s iPod?A.New software and technology was required to allow the distribution ofmusic through online channelsB.New pricing was negotiated with the music industry to encourage onlinemusic purchasingC.New design concepts were developed that gave the product an appealinglook and feelD.A new way of working with the music industry was developed to allow rapiddistribution of new music to iPod users10. Which of the following analyses would BEST illustrate the team’s beliefsregarding Apple’s iPod?A.An analysis of the market share achieved by Apple for its productssubsequent to the iPodB.An estimate of the size of the investment made by Apple in the developmentof the iPodC.An estimate of the profit margins of the music industry subsequent to thelaunch of the iPodD.An analysis of the reactions of technology experts to the iPod andsubsequent Apple products
7MarcadiaMarcadiaMarcadia is an online store which offers a wide range of goods to customers viamail order. Marcadia has been in existence for five years and has seen rapidgrowth in sales during this period, as more and more new customers signed up.However, recently Marcadia’s customer numbers have plateaued and this hasresulted in slower sales and profit growth.The Managing Director of Marcadia has engaged McKinsey to help her betterunderstand the purchasing behavior of her customers. She believes that abetter understanding of customer purchasing can lead to more targeted andsuccessful marketing. She tells the team: ‘I’m sure that our most valuablecustomers have certain purchasing behaviors that we can identify. If we canencourage more of our customers to adopt those behaviors, we can makethem more valuable to us and this can inject a new source of growth into ourbusiness.’Exhibit 3 shows some data which the team has collected regarding a sampleof 500,000 Marcadia customers who signed up in the last calendar year.The customers are split into quintiles according to their one year customervalue, from lowest to highest. ‘One year customer value’ is defined as theprofit made by Marcadia on purchases made by a customer in their first yearsince signing up. Also presented is data on purchasing by customers in eachquintile in their first 90 days since signing up, namely the average number ofpurchase transactions and the total revenue received by Marcadia from thosetransactions.Exhibit 3Average One Year ValueUS Quintile 1Quintile 2Quintile 3Quintile 4Quintile 5Average after 90 daysNumber ofTransactions1.01.53.08.026.0TotalRevenue1.1 791.3 1111.5 1202.6 2525.7 490
8Marcadia11. Which of the following statements BEST describes why the Managing Directorof Marcadia has engaged McKinsey?A.She believes that Marcadia can become better at identifying customers whostop making purchasesB.She believes that Marcadia can become better at identifying ways toencourage customers to spend moreC.She believes that, by focusing on the customers of greatest value, Marcadiacan drive renewed growth in their businessD.She believes that Marcadia can predict the purchasing behavior of itscustomers better12. Which of the following CANNOT be concluded from the information presentedin Exhibit 3 regarding the sample of customers analyzed?A.Purchasing by customers in their first 90 days is an indicator of their valueto Marcadia in their first yearB.Quintile 1 are the customers with the lowest profit margin for MarcadiaC.The average customer makes between 2 and 3 transactions in the first90 days since signing upD.The average one year customer value is 7.9013. What is the correct ranking of the five quintiles in Exhibit 3 according to theaverage transaction revenue, from lowest to highest?A.1, 2, 4, 3, 5B.1, 2, 3, 4, 5C.1, 3, 2, 4, 5D.1, 3, 2, 5, 414. If Marcadia had driven higher purchasing from the new customers in Exhibit 3so that the one year value of customers in Quintiles 1 thru 4 were each to increaseto the next highest quintile, how much greater would Marcadia’s total one yearcustomer value have been?A. 250,000B. 650,000C. 2.5 millionD. 6.5 million
9MarcadiaThe team designs an email marketing pilot for 100,000 new customerswho have made at least one purchase since joining. In this pilot, these newcustomers are split into two equal groups: a ‘pilot’ group and a ‘control’ group.The pilot group receives a specially designed email to encourage furtherpurchasing, while the control group does not receive the email. All emails aresent to the pilot group at the same time, and the emails are designed differentlyaccording to the demographics of the customer and his or her prior purchasingbehavior.Following the pilot, the team constructs Exhibit 4. This shows the ‘lift’ in thepurchasing behavior of the pilot group compared to the control group after theemails were sent to the pilot group. Horizontally, the information is dividedaccording to how long ago the customer made their first Marcadia transaction,measured from the time the emails were sent to the pilot group. Vertically, theinformation is divided according to what kind of product was purchased in thecustomer’s first Marcadia transaction. Within each box, the upper left portionshows the lift in the number of transactions, while the lower right portion showsthe lift in the number of customers who made transactions. All data in Exhibit 4is in percentage points.Exhibit 4% lift in numberof transactions% lift in number ofcustomers makingtransactionsWeeks since 1st l2.04.43.12.00.4-126.96.36.199-0.8-0.41.90.92.41.7
10Marcadia15. When comparing the pilot group to the control group, which of the followingCAN be determined from the information provided in Exhibit 4 for customerswho purchased Electronics in their first transaction?A.Percentage difference in average number of transactions per customerB.Difference in number of customers making transactionsC.Two week time segment which had the greatest difference in number oftransactionsD.Percentage of total lift in number of transactions represented by each twoweek time segment16. If 10% of customers in the control group made transactions during the pilot, howmany of the customers in the pilot group made transactions during the pilot?A.5,085B.5,850C.10,170D.11,70017. Which of the following CANNOT be concluded from the information presentedin Exhibit 4?A.The pilot had no overall impact on the likelihood of making furthertransactions among customers whose first purchase was in Clothing/ApparelB.The pilot had a positive impact on the number of transactions per customerfor customers who made their first transaction 4-6 weeks before emailswere sentC.The pilot had greatest impact among customers whose first transaction wasin ElectronicsD.Among customers whose first transaction was in ‘Other’, the pilot hadgreatest impact among those whose first transaction was more recent
11Marcadia18. Which of the following data from the pilot period would be LEAST useful to theteam in further investigating the impact of the pilot on Marcadia’s business?A.Average transaction value for pilot group and control group customersB.Percentage of pilot group emails that were not delivered and bounced backC.Breakdown of data in ‘Other’ category to further levels of detailD.Breakdown of two week time periods into weekly time periodsThe team calls a meeting with the Managing Director of Marcadia to updateher on the results of the pilot. While presenting the results of the pilot, one ofthe team members reminds the Managing Director that all new customers mayhave received emails from Marcadia which were not related to the pilot.19. Which of the following is MOST LIKELY to be the reason for the statement by theteam member to the Managing Director?A.The Managing Director is concerned that customers in the control groupwere neglectedB.The team are concerned about how well Marcadia’s staff executed the pilotC.Customers who receive too many emails from the same company becomeless likely to open and read themD.Customers may discover that they were not selected for the pilot and may beunhappy about this
12WFGLAWay Forward Greater London Area(WFGLA)Way Forward (WF) is a non-profit organization that consists of more than 50local offices in the United Kingdom. Way Forward Greater London (WFGLA)is one of these local offices based in the Greater London Area, a metropolitanarea surrounding the city of London. Typically the local offices work togetherwith private and social sector organizations to pool efforts in fundraisingcampaigns. These campaigns typically address pressing community issues,usually around education, income or health. WF first seeks to educate thepopulation about these campaigns, then solicits donations.Currently, there is an economic downturn in the United Kingdom. Thispresents a challenge for WFGLA, because donations are decreasing whencommunity need is at its highest. The President of WFGLA has reached out toMcKinsey to ask for support. He tells the team: “I need your help on improvingour campaign effectiveness, which we define as the number of pounds donatedper pound spent on the campaign. We really need to focus on increasingdonations in these times!”A campaign is usually organized by a group of people called a “campaigncabinet”. This group includes WFGLA staff, as well as volunteers from thegeneral public; the actual campaign work is conducted by volunteers.20. Given the aims of the President of WFGLA, which would be the LEAST relevantquestion for the team to answer?A)How can WFGLA get better at targeting people who are likely to donate?B)How can WFGLA engage with people in ways that are more likely to resultin donations?C)How can WFGLA contact and communicate with their donors in a lowercost way?D) How can WFGLA improve the execution of campaigns by the campaigncabinet?
13WFGLA21. Which of the following pieces of information would be LEAST helpful in betterunderstanding the current WFGLA situation?A)Total amount of donations, in British pounds, collected by other WF officesacross the U.K.B)Comparison of donations made to WFGLA by one-time donors versusregular donors over the past 5 yearsC)Market research on the public awareness generated by WFGLA campaignsover the past 5 yearsD) Comparison of campaign effectiveness with other local WF officesThe team gathers more data on WFGLA and on other WF offices. Exhibit 5shows the total donations and total campaign costs in million British pounds( ) for various WF offices last year.Exhibit 5WF OfficesDonationsCampaign costWFGLA20.835.7Region ARegion B1.940.9Region D23.61.338.1Region G3.243.816.42.02.117.6Region FRegion H4.415.8Region CRegion E3.01.91.122. How should Regions A to E in Exhibit 5 be ranked according to their campaigneffectiveness from highest to lowest?A)C, E, D, B, AB)C, A, D, E, BC)C, E, D, A, BD) A, B, D, E, C
14WFGLA23. Assuming WFGLA could reach the highest campaign effectiveness of allother regions on Exhibit 5, by what percentage could their current campaigneffectiveness be increased?A)196%B)235%C)296%D) 335%One potential opportunity the team explores is a segmentation of potentialdonors according to the type of work they do, with the aim of taking differentfundraising approaches for employees working in different occupations. Theteam identifies 3 segments of workers: Blue Collar: Employees doing mostly manual work White Collar: Employees doing mainly office work Executive: Employees who mostly have college or advanced degrees, andwho typically work as senior managers in businessExhibit 6 shows the number of employees in thousands in each segmentin the Greater London Area. Employees are categorized by the size of thecompany they work for, as well as their level of contact with WFGLA so far, or‘relationship intensity’. The goal is to subsequently increase the relationshipintensity for each segment, so that each segment moves closer to the ‘frequentcontact’ group.Exhibit 6Relationship intensityNo 6Large50.0Little 137.540.0125.6ExecutiveFrequent 83.23.4318.7100.420.714.914.1ExecutiveExecutive
15WFGLA24. Which is most likely to be TRUE based on the information given on Exhibit 6?A)WFGLA has had contact with slightly more than 50% of all employees in theGreater London AreaB)Small companies have received the least attention by WFGLA in the pastC)The biggest proportion of the total amount donated has come fromemployees with frequent contactD) The biggest opportunity to increase donations is to get in touch with thoseemployees who work for large companies WFGLA is not in contact with yetThe team explores the donation potential for each of the segments accordingto the company size. The team concludes that a medium Blue Collar companyemployee with frequent contact currently donates double the amount of amedium Blue Collar company employee with little contact. They also determinethat, if targeted with the right approach, all employees of medium Blue Collarcompanies would increase their donation by 50 per person per year. This willinclude employees who do not have any current contact with WFGLA, whom doNOT make any donations currently.25. If WFGLA implements the targeted approach, the expected total donationestimate for Blue Collar employees in medium companies will be 6.13 million.What is the current annual donation of a Blue Collar employee with frequentcontact in a medium company?A) 50B) 100C) 150D) 200
16WFGLA26. In addition to donation potential, which would be the LEAST helpfulinformation to consider when deciding the prioritization of the differentemployee segments to WFGLA?A)The amount of disposable income of the various employee segmentsB)The number of volunteer hours to be invested per segment to increaseemployees’ relationship intensity to the next levelC)The effectiveness of past campaigns with similar employee segmentsD) The additional budget amounts WFGLA would need per segment toincrease employees’ relationship intensity to the next level
17AnswersAnswer KeyInnovation Capital1.B – The introductory paragraphs state that the team is preparing a report on theimportance of innovation as a contributor to economic growth. Option B is theonly statement that mentions the connection between innovation and economicgrowth.2. C – Referring to the three types of Innovation Capital defined in theintroductory paragraphs, Option C is the only option that does not fit into anyof the three types. Option A is an educational activity which fits into HumanCapital, Option B relates to building an organization’s brand, which fits intoKnowledge Capital. Option D is related to building the intellectual property ofan organization, which also fits into Knowledge Capital.3. A – Observing Exhibit 1 and relating the categories to the three types ofInnovation Capital, it can be seen that the final three categories representHuman Capital, which totals 3.3 trillion. Of this, Organizational Developmentrepresents 1.5 trillion, which is 45% of 3.3 trillion. The 2nd thru 5thcategories represent Knowledge Capital, which can be calculated as 60% of thetotal, rendering Option B incorrect. Option C is incorrect as ComputerizedInformation represents 8.7% of the total. Option D is incorrect as ScientificResearch and Development represents 23.2% of the total.4. B – At 5% per year growth over 10 years, total Innovation Capital would grow to 22.5 trillion. At 10% per year growth, Human Capital would only grow to 8.6trillion. However, at 15% per year growth, Human Capital would grow to 13.4trillion, which would be more than half of total Innovation Capital.5. D – The original aim of the team is to show how Innovation Capital can driveeconomic growth. From Exhibit 2, in most countries, business sector growth isdriven mostly by improvements in productivity. Combining Option D with thisobservation establishes a direct link between Innovation Capital and businesssector growth, hence economic growth.
18Answers6. B – Growth in productivity can be calculated by multiplying the overall growthrate by the proportion that is due to productivity. Observing that Sloveniahas the highest overall growth rate, and the second highest proportion dueto productivity is sufficient to establish that Option B is correct. Option A isincorrect as Hours growth can be calculated by multiplying overall growth bythe proportion due to Hours and in every country this can be seen to be muchless than 24%. Option C is incorrect as Italy has the least growth in productivity.Option D is incorrect as Slovenia has the least growth in Hours.7.C – The two growth figures for Germany and Spain can be calculated bymultiplying their total growth by the proportion due to Productivity. ForGermany, this figure is 1.7% ( 1.4 x 121.6%). For Spain, this figure is 0.8% ( 3.8x 20.1%). Therefore the difference is 1.7 – 0.8 0.9 percentage points.8. D – Option D states that employers have greater flexibility in setting workinghours, which is inconsistent with the trend in these countries that workinghours are declining. Option A would help explain the declining hours due to anageing population. Option B would help explain the comparatively high growthrates due to emergence from stagnant economies. Option C would help explaindeclining hours due to more people exiting these countries than entering.9. B – Referring to the three types of Innovation Capital in the introductoryparagraphs, Option B is least likely to represent any of these types, as pricingof products is not in itself a new technology or intellectual property. OptionA would represent either Physical Capital or Knowledge Capital. Option Cwould represent Knowledge Capital. Option D would be new organizationaldevelopment which would represent Human Capital.10. A – The team’s belief is that investment in Innovation Capital can lead to followon advantages for the investor. In the case of the iPod, the investor is Apple.Of the options presented, only Option A might illustrate follow-on advantagesfor Apple through establishing improvements in market share for subsequentproducts. Option B refers only to investment, which would not necessarilyestablish an advantage for Apple. Option C looks at the entire music industry,which would not necessarily show an advantage for Apple. Option D refers to theopinion of technology experts, which may not reflect an advantage for Apple inthe marketplace.
19AnswersMarcadia11. B – From the introductory paragraphs, the Managing Director is looking to findways to encourage customers to adopt purchasing behaviors that more valuablecustomers are known to have. Given that a customer needs to make morepurchases to become more valuable to Marcadia, this could be rephrased as‘encouraging customers to spend more’. Option A refers to customers who stoppurchasing, who are not mentioned by the Managing Director. Option C refersto driving growth purely through focusing on customers of greatest value, whichis also not a true reflection of the Managing Director’s opinion. Option D refersto ‘predicting’ purchasing behavior, which is not mentioned by the ManagingDirector.12. B – Profit margin cannot be calculated from the data in Exhibit 3 as revenuedata is only presented for the first 90 days. Option A is a reasonable conclusionbased on the relationship between revenue in the first 90 days and one yearvalue. Option C can be concluded by calculating the average of the ‘Numberof Transactions’ column, which equals 2.44. Option D can be concluded bycalculating the average of the ‘Average One Year Value’ column.13. D – Average transaction revenue can be calculated by dividing total revenueby number of transactions. The ranking, from lowest to highest. is 1 ( 71.82),3 ( 80), 2 ( 85.38), 5 ( 85.96), 4 ( 97.31).14. C – There are 100,000 customers in each quintile. For each of the first fourquintiles, calculating the difference in one year value versus the next highestquintile gives 0.50, 1.50, 5.00 and 18.00 respectively. Multiplying each by100,000 and summing gives 50,000 150,000 500,000 1,800,000 2,500,000.15. A – For customers purchasing Electronics, there was a 3.8% lift in transactions,and a 5% lift in number of customers making transactions. Therefore thenumber of transactions per customer compared to the control group was103.8%/105% 98.9%, ie a ‘lift’ of -1.1%. Option B is not possible to determine asthere is no data on the number of customers in each product segment. Similarly,Option C is not possible to determine as there is no data on the number oftransactions in each time segment. Finally, Option D cannot be de
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.