McKinsey Problem Solving Test – Example Question and Answer

One of the skills that's being tested during a case interview is something I call data sufficiency.

Basically, you have a bunch of data and the question is do you have ENOUGH data to make a particular 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-person case 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 possible conclusions.

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 this one).

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

In addition to a live case interview, the McKinsey Problem Solving Test, other firms have used similar tests OR have given an in-person case interview where the candidate is presented with a written document consisting of various facts, figures and other data… and the 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 every time?

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

Below is an actual data sufficiency type question that a McKinsey Partner in the Los Angeles office asked me when I interviewed there for my final round.

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 in America

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

BEFORE you look at the answer below (I know it's tempting), I strongly recommend you try ANSWERING the question yourself first. Write your answer down then look at my answer below.

You will get a lot more value out of it this way because frankly there are very FEW practice opportunities available. Don't use them up by just reading them, use them by ATTEMPTING to answer them first.

My Answer:

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 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.

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

For more information on the McKinsey PST and how to prepare click here

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