Here's a sample data sufficiency mini-case question that at McKinsey partner asked me many years ago. See my reply below.
Volvo – The Safest Car in the United States*
* New US government report shows that fewer people die in a Volvo than in any other car brand in America
Assess the validity of this statement, you have 3 – 5 minutes to do so. Go!
BEFORE you look at the answer below (I know it's tempting), I strongly recommend you try ANSWERING the question yourself first.
To do so, click here to post an anonymous answer and to see how 1,300+ other people answered the question... THEN come back and look at the answer below. You will get a lot more value out of it this way because frankly there are very FEW practice opportunities available. So don't use them up by just reading them, use them by ATTEMPTING to answer them first.
Click Here to Submit an Answer to This McKinsey Problem Solving Test - Example Test Question
The validity of the claim that Volvo has the safest car in the US because fewer people die in it is at best ambiguous. I have several concerns about this claim:
1) The definition of "safe" -- the statement assumes that a safe car is only one where someone does not die IN the car. But it's possible the passenger died later or suffered severe injury.
Now lets assume that a safer car really is one where fewer people die in it, the next concerns I have are:
2) # cars on the road - Perhaps Volvo has FEWER cars on the road and you'd expect them to have FEWER deaths in their cars because of it. To test this, I would need to know how many cars from Volvo are on the road vs. other brands, and compare the relative market share of cars to share of deaths.
3) # passengers in the car - Perhaps single people drive Volvo's so there's only one person in the car, compared to say a Toyota which is perhaps a family car which perhaps carries more passengers. So maybe when a Volvo crashes it kills the 1 person in the car more OFTEN, but in other car brands people die LESS OFTEN, but there are MORE passengers. To test this, I would need to know the average number of passengers per trip in Volvo cars vs. other manufacturers.
4) # accidents - Perhaps Volvos get in more accidents a lot more often than other cars, but perhaps once you get in an accident you're less likely to die. For example, maybe Volvo brakes don't work so you crash all the time, but the Volvo body frame construction and airbags are excellent. To test this, I'd need to know how many accidents involve Volvos compared with other cars -- especially in comparison to their relative market shares.
5) Mileage - Perhaps Volvos are driven less often for shorter distances than cars from other manufacturers. If Volvo's are driven less often, for fewer miles, then it's possible Volvos have less time a risk of being in an accident -- so it's possible the car is actually more dangerous, but used less. To test this, I'd need to know how many miles per year the average Volvo is driven compared to other car brands.
6) The driver - Perhaps Volvo's are not actually safer cars, but perhaps Volvo DRIVERS are safer. This might be hard to test with data, but to start it would be useful to get the accident history of drivers who own Volvos when they drive NON-Volvo cars.
So to summarize conceptually
# deaths* =
(# Volvos on the road) X
(# passengers in the car) X
(% chance of having an accident) X
(% likelihood of dying in the event of an accident**) X
(Miles driven per year) X
(Driver's Likelihood of getting into an accident)
* assuming fewer deaths = safe car
** this can be computed from the original statement
Critiquing Other People's Answers
In reviewing the hundreds of answers people submitted for this question, here are a few observations.
1) Many people fixated on just one or two problems with the statement. To really answer this question correctly, you need to be more thorough and complete.
2) Some people gave only philosophical answers -- you can't really trust the government, it's an overly narrow definition... etc.
In consulting and in case interviews, you need to be more specific.
3) The answers that I would rate as pretty good are ones that included at least 4 of the items above and did so preferably in some systematic way
(Note the formula above wasn't necessary to state explicitly (I didn't in my interview and still passed), but the formula-like approach is consistent with how the top candidates tend to think about ANY kind of problem)
4) Many people said the claim was "incorrect". I don't think this is a factually supported statement. It is more accurate to say the validity of the claim is ambiguous or unclear, because additional information is needed or it depends on how certain words like "safe" are defined. So if you said the claim was "wrong" or "incorrect" on the McKinsey Problem Solving Test or if asked verbally in the middle of a case interview, I would consider the response as "imprecise" (consulting speak for "wrong").
Some people object that they said the claim was "wrong" they really meant the argument is flawed and therefore the conclusion may or may not be correct. BUT, they didn't SAY (or in our case write) that. And if you don't say (EXACTLY) what you mean, then you don't mean what you say.
Does this seem picky? ABSOLUTELY.
And it IS actually that important. If you tell a client they are "wrong" when what you really mean is their rationale has a logical flaw or ambiguity in it, they will take offense and be unconvinced at the former, but would be persuaded by the latter. So, the big takeaway is:
CHOOSE YOUR WORDS VERY, VERY PRECISELY.
When I posted this question previously, I received 1,300+ answers from other readers of my blog (aka your potential competitors in interviews). You can see how others answered the same question here McKinsey Problem Solving Test Example 1 and see how your response stacked up to others.
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Tagged as:case interview questions, mckinsey problem solving test, problem solving test
Case Study Interview Examples: Questions and AnswersYou will need to prepare for an interview where case study questions will be asked. While preparation is required for every job interview, extra time is required to adequately prepare for case study interviews.
Providing an answer to a case study question involves much more than simply recounting the issues and problems set forth, it includes identifying the most important issues, employing sound and logical analysis, developing an action plan for addressing the problem(s) and making recommendations. Depending on the firms you're interviewing with, and the industry you work in, case study questions can be presented in verbal or written format, and address a number of topics.
In case interviews, it's not uncommon for interviewers to exclude important details when asking candidates to resolve hypothetical business problems presented. It's okay to ask interviewers for more information, and it's expected. They want to see if you can identify what information is important, and what is not.
Occasionally, interviewers provide no detail at all to test your analytical skills when adequate resources are unavailable. In these situations, it's okay to make assumptions, but they must be based on sound logic and analysis of information that is provided.
Interviewers asking case study questions are primarily concerned with how effectively you can analyze a problem, determine key factors, brainstorm ideas, and propose workable, pragmatic solutions that are supported by your analysis.
Answering Case Interview QuestionsIn the case interview, coming up with the "correct" answer isn't nearly as important as the process you use for getting there. When answering a case interview question, you want to showcase your ability to analyze a situation or business dilemma, identify the important issues, and develop sound conclusions that flow from your analysis. For this reason, it's important to use a logical framework for breaking down and analyzing the case. Some of the more common business analysis frameworks that can be employed include Porter's Five Forces, Value Chain Analysis, Four P's of Marketing, and SWOT Analysis. The framework you decide to use should be a function of the type of case you're presented.
Where a specific framework for analysis isn't readily available or applicable, a general framework or analytical approach can be applied. The most important thing is that your approach to answering the case interiew question is structured and logical.
Regardless of the type of case you're presented, there will likely be a few main parameters and several factors that influence those parameters. The first thing you want to do is identify the parameters and factors, the then determine which are key to the case output.
For example, assume the case involves a company's declining profitability. From your initial review of the case information you determine the main parameters to consider are total revenues and total costs.
After defining the two main parameters, you'd then drill down further to the factors influencing each of the parameters you've identified. You determine the factors influencing total revenues are average price of goods sold and volume of goods sold. And for total costs, fixed costs and variable costs.
With both the case parameters and factors clearly identified you give yourself the ability to steer the conversation and begin to identify possible solutions. To identify areas of concern, you'll want to explore the history of the four influencing factors. At the end of your discussion with the interviewer you may determine that it's rising variable costs that are having the biggest impact on profitability. You'll then drill down even further to determine what is causing variable costs to rise and come up with more specific recommendations.
Building a graphic representation (tree, decision diagram, etc.) of parameters, factors and other influencing elements will help you structure your thought process, keep from missing key aspects of the case, and make a strong argument for the recommendations you'll make.
Using a framework or structured approach to developing a recommendation for a case study interview question provides the added benefit of giving the interviewer something to take back and present to his or her superiors to make the case that you're the right person for the job.
Whatever you do, don't force-fit frameworks. If a particular framework doesn't apply to the case, don't use it. Most frameworks incorporate universal concepts that can be applied to various business issues. Use the concepts you've learned in school or through prior work experience to support your analysis of the case. Show your interviewer that you understand these business concepts well enough that you can apply them to the specifics fo the business issue being presented in the case.
Below we're going to present several case interview questions organized by question type. To perfect your ability to perform well in case interviews, we recommend reviewing each question and then developing a logical framework or approach for answering each one.
Standard Case Interview QuestionsAs is the case in real life, there is usually no single correct answer to standard case interview questions. As long as you're able to prove your case, using sound analysis and by demonstrating an understanding of the main case issues, you're likely to do well. Below are some common standard case interview questions that provide great practice for case interviews.
- What would be your approach for introducing a product into a foreign market? What are the risks and benefits to consider i.e. producing in your own country vs producing in the new country, etc?
- Company ABC is struggling, should it be restructured? Identify the three main problems it's facing. What is the most important problem the company is facing? How would you recommend the company address this problem? How would you turn this company around? Provide your reasoning for your recommendation(s).
- A toy company has been experiencing decline sales for the last two seasons. Research suggests that introducing several new product lines is the solution. Develop a marketing strategy for the company's largest product line, including pricing, product packing, etc.
- A large chain of retail clothing stores is struggling with profitability. Bases on your review fo the company's financial statements, what problems can you identify? Can this company be turned arounds? How would you go about deciding?
- A new Eddie Bauer Store is being opened up in London. Discuss all the marketing issues regarding the opening of this new location.
- Take in information quickly and remember what you hear.
- Identify key issues, prioritize and logically solve problems.
- Make quick, yet accurate, decisions.
- Manage time efficiently.
- Perform under pressure.
- Be aware of resource constraints.
- Identify customer needs.
- Be original and creative.
Market Sizing Case Interview QuestionsA market sizing case interview question is one where you're asked to determine the size of market for a particular product. These types of case interview questions are popular, and actually not difficult to answer if you practice. The following a few examples of market sizing case interview questions.
- Please provide the total weight of a fully loaded Jumbo Jet at the time of take off.
- How many light bulbs are there in the United States?
- How many photocopies are taken in the United Kingdom each year?
- How much beer is consumed in the city of New York on Fridays?
- How many people sell AMWAY products in the United States?
- If there are 7,492 people participating in a tournament, how many games must be played to find a winner?
- How many golf balls will fit in the Empire State Building?
- How many car tire are sold in Canada each year?
- Given thhe numbers 5 and 2000, what is the minimum number of guesses required to find a specific number if the only hint you're given is "higher" and "lower" for each guess made?
- How do you determine the weight of a blue whale without using a scale?
- Take time to think before you answer the question.
- If given a pen and paper, take notes and write down key information. Use the paper to make calculations, write down ideas and structure your answer.
- Ask additional questions if you feel you are missing information. The interviewer is often expecting you to ask to find missing information.
- Use lateral thinking and be creative. There isn't always just one right answer. Just make sure your answer is backed up by sound logic and numbers that make sense.
- Make sure you know your math. At minimum you'll need to perform some basic arithmetic or mathematical calculations.
- These quesitons are often used to test your ability to structure, as well as your ability to think laterallly, make logical links and communicate clearly.
- Make mental calculations quickly by making sensible estimates and rounding numbers up or down.
- Does your answer make sense? If you're answer doesn't make sense, chances are you've made a bad assumpation, estimate or calculation. Go back and carefully check your work and provide a new answer.
- You can use business frameworks (SWOT, Porter's Five forces, etc.) or mind mapping to support your analysis and answers, as long as it makes sense.
- Many market sizing questions revolve around issues being faced by an organization or industry. Commercial awareness can be very important to answering market sizing questions.
Logic ProblemsQuestions involving logic problems are designed to test your ability to think quickly and logically. These questions also require you to be able to perform numeracy quickly, while under pressure. The following are a few logic problems followed by their answers. Review the questions, develop your own answers, and then check your answers to see how well you did.
1. At 3:15, how many degrees there between the two hands of a clock? (J.P. Morgan interview question).
2. A fire fighter has to get to a burning building as quickly as he can. There are three paths that he can take. He can take his fire engine over a large hill (5 miles) at 10 miles per hour. He can take his fire engine through a windy road (7 miles) at 9 miles per hour. Or he can drive his fire engine along a dirt road which is 8 miles at 12 miles per hour. Which way should he choose?
3. You spend 21 dollars on vegetables at the store. You buy carrots, onions and celery. The celery cost half the cost of the onions. The onions cost have the cost of the carrots. How much did the onions cost?
4. You spend a third of all the money you have on a piano. Half of your remaining money you use to buy a piano chair. A quarter of the rest of your money you use to buy piano books. What porportion of you original money is remaining?
5. Why are manhole cover always round, instead of square?
6. In the Chicago subway system there are two escalators for going up but only one for going down to the subway. Why is that?
7. You find three boxes at the store. One contains onions. Another contains potatoes. The third contains both onions and potatoes. However, all three of the boxes are labeled incorrectly so it's impossible to tell which box contains what. By opening just one box (but without looking in) and removing either a potatoe or onion, how can you immediate label the contents of all the boxes?
8. There are 8 bags of wheat, 7 of which weigh the same amount. However, there is one that weighs less than the others. You are given a balance scale used for weighing. In less than three steps, figure out which bag weighs less than the rest.
9. There are 23 rugby teams playing in a tournament. What is the least number of games that must be played to find a tournament winner?
The following are the answers to the 9 logic problems above:
If you thought the answer was zero degrees, you'd be incorrect. At 3:15, the clock's minute hand will be pointing at 15 minutes, exactly 90 degrees clockwise from vertical. At 3:15, the clock's hour hand will exactly one quarter of the distance between 3 O'clock and 4 O'clock. Each of the 12 hours on the clock represents 30 degrees (360 degrees divided by the 12 hours on the clock). Consequently, one quarter of an hour is exactly 7.5 degrees, so at 3:15 the minute hand will be at 97.5 degrees. So there is a difference of 7.5 degrees between the hour hand and minute hand at 3:15.
Driving his fire engine 5 miles at 8 miles per hour takes 37.5 minutes. Driving his fire engine 7 miles at 9 miles per hour takes about 47 minutes. Driving his fire engine 8 milles at 12 miles per hour takes 40 minutes. So he should choose to drive his fire engine over the hill.
Answering this problem just requires some simple algebra. If we assume the cost of celery = x, then the cost of onions = 2x, and cost of the carrots is 4x, such that the total cost of all vegetables = x + 2x + 4x = 7x = 21 dollars. Consequently, x = 3 dollars. Hence, the onions cost 6 dollars.
You spend a third of all the money you have on a piano, so you're left with two thirds (2/3). You spend half (1/2) of the remaining two thirds on a piano chair, which leaves you with just one third of what you started with (1/2x2/3=1/3). You spend a quarter (1/4) of what you have remaining (1/3) on piano books, which leaves you with one twelth of the original (1/4x1/3=1/12).
A square manhole cover can be dropped down the hole if turned diagonally to the hole, where round covers can't be dropped down manholes.
People coming into the subway tend to arrive at different times, so the flow of people down the escalators is a more even stream. Conversely, when people get off the subway they typically all arrive at the escalators at about the same time. Consequently, two escalators are need to handle people leaving the subway, where only one is required for people arriving.
Just open the box that is labeled "Onions and Potatoes". Since none of the boxes are labeled correctly, this box must contain only onions, or only poatatoes. If you remove a potatoe from this box, the box must be the "Potatoes Only" box.
One of the remaining two box has to be the "Onions Only" box. However, the only you currently have it labeled "Potatoes Only", and the other is label "Onions Only". So the box labled "Potatoes Only" must be the box that contains only onions, and the box labeld "Onlions Only" must be the box that has both potatoes and onions.
Bags of Wheat
Immediately, take any 2 of the bags and place them to the side. Weigh 3 of the remaining six bags against the other 3 bags. If these bags weigh the same, that means the bag that weighs less must be one of the two that you immediately placed to one side. If this is the case, weigh the 2 bags you placed to one side against each other to find out which one weighs less. You've now found in your bag.
However, upon weighing the sets of 3 bags against one another you find that one set weighs more than the other set, place one of the bags from the set of heavier bags aside and weigh the remaining two bags to find out which one is heavier. If they are of equal weight, the you know that the bag you place to one side is the bag you're looking for.
In a tournament, every rugby team except the winner is eliminated from the tournament after being defeated just once. Hence, the number of games required to find a tournament winner is going to be one less than the number of teams, or 22 in this case.
Business Case Interview QuestionsThe following are examples of common business case interview questions:
- How would you work with a subordinate who is underperforming?
- You're consulting with a large pharmacy with stores in multiple states. This company has improved sales but experienced a decrease in revenue. As a result, it is contemplating store closings. Explain how you'd advise this client?
- You are working directly with a company's management team. It is organizing a project designed to significantly increase revenue. If you were provided with data and asked to supervise the project, what steps would you take to ensure it's successful?
- You have been assigned to work with a small company that manufactures a popular product. However, a competitor begins selling a very similar product which incorporates state of the art technology. What would you advise your client to do?
- You have been assigned to advise a company with a large Western European market. Company management wants to open the Chinese market. What advice do you have for this company?
- The firm has assigned you to consult a company intending to drop a product or expand into new markets in order to increase revenue. What steps would you take to help this company achieve its objective?
- You have been assigned to consult a shoe retailer with stores throughout the nation. Since its revenue is dropping, the company has proposed to sell food at its stores. How would you advise this client?
Case Interview ResourcesIn addition to the guides and articles presented on our website, there are several other good resources, including workshops, mock interviews, books and interactive online resources, that will prepare you for case interviews. Some of the resources we recommend are listed below.
- Vault Guide to the Case Interview
- Vault Career Guide to Consulting
- Case in Point: Complete Case Interview Preparation
- Mastering the Case Interview
- Ace Your Case! Consulting Interviews (series 1-5)
Interactive Online Resources