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McKinsey Problem Solving Test - Example TestQuestion #1by Victor Cheng

by Victor Cheng

Like 12 people like this. Be the first of your friends. One of the skills that's being tested during a caseinterview is something I call data sufficiency.

Basically, you have a bunch of data and the question is do you have ENOUGH data to make aparticular conclusion.

This is certainly something that is tested during a live, in-person, face-to-face case interview.

It is also a skill that is often tested in a variety of formats including written tests before the first in-personcase interview question is asked.

An example of this is the McKinsey Problem Solving Test which evaluates your data sufficiency skills(among others).

In parts of the McKinsey Problem Solving Test, you are given a bunch of data and some possibleconclusions.

Your job is to figure out which conclusions are or are NOT supported by the facts presented.

Now this test is not intended to torture you (though I know some people might argue with me on thisone).

It turns out this is a very important skill once you're on the job as a management consultant, especially asa first year analyst or associate.

In addition to a live case interview, the McKinsey Problem Solving Test, other firms have used similar

tests (Monitor has done this from time to time) OR have given an in-person case interview where thecandidate is presented with a written document consisting of various facts, figures and other data… andthe data sufficiency skill is tested verbally.

These are all variations of the same thing.

Given a set of data, will you determine the correct, logical, and factually supported conclusion everytime?

So bottom line, this skill is pretty important and based on the many emails I've been receiving fromaspiring consultants around the world, it seems many people are having a difficult time figuring out howto practice these skill.

So just for kicks, I thought I'd give you an actual data sufficiency type question that a McKinsey Partnerin the Los Angeles office asked me when I interviewed there for my final round several years ago.

Before I give you the question (which is posted on my blog), I strongly recommend that you read thequestion and then immediately hit the "post comment" button to post your answer on my blog.

(You can do so with just your first name or initials if you want to be a anonymous)

The key is to post your answer WITHOUT seeing other people's answers!

(otherwise it sort of defeats the purpose of practicing, and there really are very few opportunities topractice this skill.).

I will be "grading" all the answers posted in a day or two.

Here's the question:

Volvo recently ran an advertisement that said:

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 inAmerica

(Note: A prior version of this blog post indicated that Volvo was the Safest Car in the World. Myintention was to write U.S., so some of the answers you see may reflect this.)

Assess the validity of this statement, you have 3 - 5 minutes to do so. You are NOT permitted to ask anyclarifying questions. Please be SPECIFIC in your answers. Go!

Click Here to Post Your Response(Remember: Don't cheat by looking at everyone else's response first, look at them AFTER you post yourresponse.)

Scroll down to see the hundreds of answers submitted by readers of my blog.

To see my answer to this question (ideally AFTER you try to answer the question yourself FIRST),click here: McKinsey Problem Solving Test - Example 1 Answers.

Additional Resources

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{ 3245 comments… read them below or add one }

← Previous Comments

R October 31, 2013 at 2:27 pm

This statement assumes that safety is only compromised when the accident is fatal to the driverand passengers. Severe injuries as well as light accidents are not taken into account. Thus it couldsimply be playing on the meaning of "safe". There is no quantitative data shown in the statementto illustrate the point clearly to the reader. It does not explore safety in terms of a car's strength,ability to crumple and absorb shock when colliding, i.e. results from crash tests.

Reply

Knk October 31, 2013 at 7:39 pm

False. Having fewer number of people dying in Volvo cars may not mean its the safest. There areother factors such as drivers' profile, where they drive and the add-ons they may have in the car toprotect them.

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Marina November 2, 2013 at 7:24 am

The U.S. government's report does not prove the causal link that is advertised by Volvo as Volvobeing the safest car in the U.S. because there might be other reasons for why fewer people die in aVolvo: For example it is possible that less people drive a Volvo and therefore there are also lessaccidents which involve al Volvo. We would need to look at relative instead of absolute numbersin order to make a more accurate statement.It could also be that Volvo cars are more sold in rural areas where less accidents happen ingeneral.Consequently, Volvo's conclusion cannot be drawn from the report.

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Eric November 2, 2013 at 7:39 am

Although the number of Volvo-related deaths is an important piece of information to have, I feelthat the statement might be misleading because it is based on a single value.Many more factors must be accounted for when considering whether or not a a car can be deemedthe “safest”:- number of cars in circulation- frequency of use of said cars / number of trips- age of cars- number of accidents- number of casualties- number of fatalities- NCAP (or rather the American equivalent... sorry, I'm from Europe and only familiar with theEuropean organization) test results- history of car maintenance- driver experienceAnd many more other values, if given more time

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VV November 2, 2013 at 7:50 am

There are a few factors that signal that Volvo indeed is the safest car on the US market. Such as:

It's made in Sweden, one of the most prosperous counties in Europe and the world, where highquality standads are carefully looked after. Volvo ensures that it's cars are build to last-constructed from scratch with safety in mind and are branded as more of family cars than sportscars.

The price range of the Volvos ( which is close to Audi's and BMW's) and the fact that it's animported brand suggest that these vehicles won't be massively available on the market. Thepeople who are likely to and can buy the car, would be mostly upper middle class, possibly withfamily and children and are prone to be risk-averse on the road.

These individuals would drive short distances and are likely to value their time and to use planewhen travelling within in the county. Consequently, the amortization of the car is minimized aswell as the risk of failure on the road.

But really, one must examine the statistics and see whether they confirm the statement.

Reply

sfm November 2, 2013 at 7:53 am

The above statement is not valid as we do not have enough info as to how many volvos arerunning on US streets vs other car brands.

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Juan Sarmiento November 2, 2013 at 12:23 pm

Volvo’s statement is not valid and would require further analysis to probe it accurate, the factspresented are not enough to conclude that Volvo is the safest car in the US. Here are key pointsthat would be important to understand to come to a more accurate conclusion:

- What is the numbers of accidents involving Volvo cars and how does it compared to other

brands? Of these accidents what percentage of them resulted in fatalities? Volvo could have theleast number of deaths but as a percentage of deaths per accident this may not be lower amongother card brands.- What is the number of Volvo cars in the US compared to other brands? Fewer number of Volvocars in the US will lead to fewer number accidents but not necessarily make them the safest car.- What is the most predominant age group of people that drive Volvo cars, this age group couldbe one that is less likely to be involved in accidents bringing to fewer changes of being involvedin a fatal accident.

Understanding the points above will help support or reject Volvo’s statement that their cars are thesafest in the US.

JC

Reply

Sla gl November 2, 2013 at 1:37 pm

This U.S report just shows that fewer people die in a volve than any other car in u.s. But does itnecessarily show volve is safe ? Of course not. We should how many people have volvos andhow many ones have the others?This may be because there there are very few volves.

We should ask that in this report which class-cars were compared to each other ? (Whether all ofthe cars were in the same class or not)

Reply

VP November 3, 2013 at 6:35 am

Maybe Volvo has better safety features than other cars but this does not mean that people don'tdie from their injuries later at the hospital. There isn't a figure telling us how big or which datasetwas used nor what other car companies have been compared hence we don't know whether thisstatement falls only in a small segment of a report. Also, whether the car size/type we looking at isonly within a certain category of cars that Volvo trumps its competitors.

Reply

Ash I November 3, 2013 at 8:12 am

I would like to see the stats of all the cars by brand involved in fatal car accidents over the last 5 to10 years in the United States of American.I would like a further concentration on the fatalities involving the brand Volvo verses otherbrands.How many passengers per car, lastly out of the accidents how may people died after the accidentas a result of their injuries?

Reply

OV November 3, 2013 at 6:48 pm

Fewer people dying in a Volvo does not make a Volvo the safest car in the US. This could just bea factor of very few people owning and driving volvos. The incidence rate of death from a caraccident may be exactly the same for a Volvo or a Ford, however, if there there are less Volvoscirculating than Fords, there will logically be a lower volume of deaths in a Volvo.

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 brandin America

Reply

B. November 4, 2013 at 6:33 am

The conclusion drawn (that Volvo is the safest car in the US) is not valid.

First, we don`t have a clear definition of safety: Does it mean not getting into an accident in thefirst place, merely surviving an accident in any condition, including severly injured, or does itmean surviving an accident unscathed?

Second, we are lacking critical information to draw conclusions about the safety of Volvo cars:How many people own a Volvo compared to other car brand? How often do people drive aVolvo compared to other car brands? How often are Volvos involved in accidents compared toother cars? How often do mechanical problems of a Volvo (for instance, the breaks notfunctioning) cause an accident, compared to other brands? What are the survival chances inside aVolvo compared to other brands?

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Romer November 4, 2013 at 8:56 am

The conclusion is not supported by data to prove that Volvo is the safest car in the US. Here arethe information that I will need to jump into this conclusion:

1. Statistics of Accident per Car Maker, Model and year to include categorization of the intensityof accident (no-injury, injury needing hospitalization, death) and the force of impact (function ofspeed and weight)2. Number of Cars produced and sold per Car Maker, Model and year. To include thedemographics of the drivers.

It is critical that there is an apple to apple comparison per car maker, per model per year in termsof accidents. I would like to see the ratio of accidents per total new car sold , per make /model inthe market.

The year to year comparison is critical to see the consistency of safety features in the car. I wouldalso categorized the type of accident to further analyze the effectiveness of the safety feature bylooking at the number of accidents and segmenting it to the no. of injury that is minor (notneeding hospitalization), severe (needing hospitalization) and death. I will correlate this to theassessed intensity of impact.

I will also further segment the drivers based on age, sex and education level. Younger people(teens) are statistically aggressive and the data should be adjusted based on risk given the spreadof the driver population based on age. I will look at the risk factor for sex and education level ifthis will pose the same issue as age and will consider this in the analysis if needed. This isnecessary for the analysis of the preventive collision effectiveness of the car.

To summarize this, two things are necessary for the analysis:

1. Preventive Safety Measure analysis adjusted based on risk2. Post Collision assessment of the Safety Measure based on severity of injury relative to impact.3. #1 and #2 should be done per Car Maker, Per Make and Model.

The ads should be specific to the make and model of the car as concluded by the analysis aftertaking into consideration the risk factors of the users and the occurence per make/model ratio. Theseverity of the accident relative to force of impact should be considered as part of deciding onwhat has the most effective safety features.

Reply

Chang November 4, 2013 at 11:55 am

First, i would confirm validity of the quote by looking into who or what units are responsible forNew US report? Is it trustworthy, or endorsed by neutral third party?

If so, we can move to second part. Find out definition of car safety and benchmark to set up fairstandard to testify validity of the quote ,ex: same series of cars or average standard?

Reply

L November 4, 2013 at 2:04 pm

First of all, 'safety' is defined as 'no/few deaths' in this advertisement. Which is of course notentirely true. People can get (seriously) injured in a car accident and still survive.

Second, this statement does not tell us anything about the relative amount of deaths. If there is onevolvo in the US and nobody ever died in it, then still the statement is true but does not say a lotabout the safety of the car. Besides, the demography also matters. Young people tend to drive lesssave than older people. So it would be better to express the safety of the car by the amount ofaccidents per mile driven in a volvo per age group.

Reply

Maros Cincura November 5, 2013 at 4:20 am

The statement says about how many people die in a Volvo car compared to the other car brandsabsolutely. However, the proportion of Americans driving Volvo is not perfectly the same, thanproportion of Americans driving other car brand. I would say, that there are way less peopledriving Volvo in the US, than another car. If there are few people driving Volvo, even though ifthey would all have died, it is still way less people in ABSOLUT measures, than people dying inFord. Weighted average rate of people dying in a particular car brand with car brand distributionrate would be relevant information in this context.

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AF November 5, 2013 at 4:58 am

You can't conclude that Volvo is the safest car in the US based on the premise because its onlystate the number and not the percentage. If Volvo only sells one car a year in the US then onlyvery few people could get killed in a Volvo. Also, safety doesn't automatically equal law deathrate and if people get seriously injured but stay alive it still can be an unsafe car.

Reply

Agrippa Sulla November 5, 2013 at 8:13 am

Disclaimer does not provide enough evidence to support claim for following reasons:a) Is the fatality number adjusted for car popularity?b) Has avg car usage per person been taken into account?

c) Have the stats been controlled for age and gender?d) Injury statistics not mentioned.

Reply

Nate November 5, 2013 at 8:34 pm

Volvo's claim of having the least number of people die in their cars may simply be because Volvohas significantly fewer cars on the road. It may also be because Volvo cars carry less people thanother cars.

Therefore, what I would really want to know is the number of accidents resulting in a death in aVolvo for each Volvo car that is on the road.

Reply

JD November 5, 2013 at 8:41 pm

Statement seems invalid because Volvo could be just 1% of all cars in the US, hence carries a tinyfraction of the population and therefore has the least number of people in an accident.

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Kad November 6, 2013 at 8:43 pm

First, people die in Volvo as they die in any other car. In this regard, Volvo is as dangerous as anyother car.

Second we don't have enough data to assess the number if volvo in circulation compared to otherbrands. We can assume Volvo is not the most famous brand, so maybe the number is just little.

Finally, with deep analysis it may be possible Volvo is a car driven by people of a certain age(oldies) who are more cautious than the others, young and adults.

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Sunil November 7, 2013 at 2:53 am

The available information is insufficient to conclusively determine the validity of this statement.

The first point is to determine how one 'measures' safety. Is the number of deaths occuring theonly valid measure? How about the nos. of accidents caused by the cars' mechanical or operatingfailures?

However, if the no. of people dying is accepted as the prime measure of safety, then it wouldmake sense to look at the proportion of people driving Volvos, who died in such accidents ratherthan the absolute nos. of deaths.

Reply

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