Friday, January 4, 2013

McKinsey Case Interviews and Unit Conversions - An Easy, 3-step Method

One of the most common causes of math errors during case interviews is unit conversions.  Here's a method I learned as an engineering undergrad that helped me get through all of my case prep and interviews without making any unit conversion errors.  I've also used this method countless times at McKinsey and even after leaving the Firm...

There are three critical elements for getting your unit conversions right during case interviews.  The method I'm suggesting to make unit conversions foolproof will be introduced in Step 2, with visual examples.

STEP 1 - Gather all of the relevant information

The "quant" part of any case test both a) your ability to perform mathematical calculations and b) understanding the implications of the numbers on the case.

Let's suppose this case interview is about agriculture and you're being asked "how much revenue can be generated by Supplier X's average seed?"  During the interview, you ask the right questions and have the following information:

  • For every 10 seeds planted, 3 plants typically grow  (Fact A)
  • It typically takes 14 plants to produce 1 pound of fruit  (Fact B)
  • For every 100 pounds of fruit, 10 pounds are usually not suitable for sale  (Fact C)
  • Every pound of fruit can be sold for $7  (Fact D)
Keep in mind that you might get some extraneous data.  If you find that you're missing a piece of data, you can always ask questions to get it.  Just don't ask something like "do I have everything I need to know?" because figuring that out is part of your job.

STEP 2 - Set up the calculation

As you can see from this example, even if each piece of data is straightforward, how to manipulate them to get to the final answer can be challenging.  The technique I'm recommending is powerful because it makes it easy to organize your information and clarifies how to apply each number (e.g., should you be multiplying or dividing?).

First, set up what looks like a "+" sign that has a longer horizontal line.  In the top left, enter in your starting point.  In this case, "1" and the units, "seed"

Then, to the right of the vertical line, start adding the data elements that will help you cancel out the "seed" unit and get you closer to the desired "$" unit.  Thinking about your unit cancellation goals will help you see which numbers go above or below the line.




STEP 3 - Cancel units and do the math

After you've set up the problem, cancel out the units one at a time.  When you finish, the remaining unit(s) should align with the the answer you're seeking - in this case, "$" (of revenue per seed purchased).  If the units don't cancel out the way you intended, you've either made an error in the set-up or are missing information.  In either case, you've laid out your thinking clearly so you and your interviewer can discuss next steps.

Now, you can begin reducing to make the math easier.  Look for numbers above the line that are easily divide into numbers below the line.  Often, cases are designed so that the arithmetic becomes easy - we're looking for problem-solvers who are comfortable with numbers, not human calculators.

Finally, multiply the numerators, multiply the denominators, and divide.  You now have a numerical answer in the correct units.





Throughout the case math, keep these additional tips from a previous post in mind.



REMEMBER - It's not just about getting the right number

I've seen plenty of candidates forget about the implications of the final answer.  They're so amped up about the case and relieved that they got the calculation right, that they don't think about what this number might mean to the case.  Always remember the context - that's why I encourage people I case coach to write the question down at the top of the paper.

In this example, you now know that the average seed from Supplier X will yield about 13.5 cents of revenue.  Can you tie that to other facts you might know about the case?

For example, on the one hand, suppose you learned earlier that your client is a farming cooperative and Supplier X wants to charge $200 for every 1,000 seeds, or 20 cents per seed.  At this point you might mention that each seed generates less revenue than it costs to buy the seed.

On the other hand, suppose you were told previously that your client is Supplier X and they are thinking about selling every 1,000 seeds for $70, or 7 cents per seed.  You might want to mention that farmers are going to generate a lot more revenue (13.5 cents) than they're paying per seed (7 cents) so there might be opportunity for Supplier X to raise the price.  You would get bonus points if you added the caveat that your simple calculation has not yet taken into account costs - other than seeds - that farmers might incur (e.g., planting, growing, harvesting) that would be taken out of the revenue, impacting how much more Supplier X might be able to charge for their seeds.



While this method can't protect you from errors in arithmetic, it will reduce the likelihood that you'll make a math mistake by:
  • Increasing the likelihood of setting up the calculations correctly
  • Ensuring your answer is in the correct units
  • Simplifying the arithmetic by giving you chances to reduce some of the numbers


  1. Why does the text say "For every 10 seeds planted, 3 plants typically grow" but the diagram has 20 seeds for 3 plants?

  2. I'm not sure what you mean - I've checked all 6 examples and plants and seeds always seem to be in a 3 to 10 ratio. Is there a specific diagram to which you're referring?

  3. Fabulous ideas you have still provided to us, anyway this blog is really wonderful for all.