Wednesday, December 5, 2012

McKinsey case interviews - 6 common math mistakes and how to prevent them

Everyone applying to McKinsey knows case prep, but I’m always surprised to see how poorly some of them prepare to do math during their interviews.  In this post, I’ll go over the six most common quant errors I’ve seen and some tips on how to avoid them


Quantitative skills are table stakes during case interviews – the scoring rubric used to evaluate your interview performance does not allow candidates to “spike” on the case based on math alone.  That means you can’t get passed to the next round or offered a job on the strength of your quant skills alone.  But, you can get dinged if you screw them up. 



1.  Fumbling mathematical calculations

We realize that almost any time you would be asked to do calculations at McKinsey you would have access to Excel and don’t need to do math.  We also know that it’s probably been years since you had to multiply or do long division on paper.  Fair or not, being able to do arithmetic is part of how your quantitative abilities will be assessed during the case interview.  If you've done practice cases, you should know you have to do math - yet every interview cycle, I watch candidates fumble these basic calculations.  One candidate even asked me if he could use a calculator... in case you're wondering, the answer was "no"!


How to prevent this mistake:

Now that you know you'll be expected to add, subtract, multiply, and perform long division, you have no excuse to not practice.  Your ability to do math is like a muscle - if you have to exercise it or it will atrophy.

Make sure you can add several numbers together, including reminding yourself how to carry digits.  Practice subtracting and remember how to borrow a oneMultiply large numbers together.  Practice long division.  Based on my experience, long division is the one that gives candidates the most trouble.  It's obvious to me when I'm interviewing someone who has forgotten how to divide and it's interesting to see what methods they invent on the spot to try to get around it.  Don't be that candidate.  Practice.


2.  Descending the Spiral of Death

This sometimes happens after a candidate fumbles a math calculation.  Some candidates who know they've screwed up the math will start to get flustered.  When the next calculation comes up, they want to make up for their earlier mistake, psych themselves out, and make another mistake.  This leads to a vicious cycle and it's not a pretty sight.


How to avoid this mistake:

In the event that you make a miscalculation, relax.  One math error will not get you dinged, especially if you have the presence of mind to catch your mistake, ask for a moment to go over your work, find your error, and correct yourself.  Even if you miss your chance to correct yourself, shake it off, and move on to the next part of the case.

3.  Doing math in your head

On its own, doing math in your head is not a mistake.  But if you happen to make a miscalculation, having done the math in your head is a big problem for several reasons.  First, you can't go back and find your mistake because there's no record of your calculations.  Second, we can't help you by letting you know if or where you went off track.  Finally, we can't give you credit for the parts of the calculation you did correctly, because you never showed them.

How to avoid this mistake:
This is probably the easiest of the errors to avoid - show your work.  No one is going to be impressed because you were able to do some calculations in your head - in fact, it might cause us to wonder if you were able to set up the numbers properly or just got lucky.  Do what's called "public math" - explain and write out each and every step of the calculation.  Turn your paper to face your interviewer so he or she can follow along and help you, if necessary.  You'll need to do your public math quickly to avoid running out of time to finish the case, so you should practice this in advance.


4.  Losing units

Keeping track of the units of the numbers you're using is important for two reasons.  First, the units make the answer meaningful.  If you ask me how fast I run and I say "6", what does that mean?  Am I fast or slow?  Do I run 6 miles per hour, or do I run a 6-minute mile (10 miles per hour)?  Clearly the units associated with the 6 are important.  Second, working with units can help you realize if you're making a mistake.  If you find yourself multiplying $/unit by miles per hour, chances are you've made an error somewhere along the line. 


How to avoid this mistake:

Keeping your public math clearly labeled and well organized will prevent you from losing track of your units.  Make sure each number in your calculation is labeled, then carry or cancel out the units as you work with them.  When you finish your calculation, present your answer with the appropriate units.  Be sure to refer to this post on unit conversions in case studies.


5.  Not relating the numbers to the business case

Your McKinsey interviewer is never going to ask you to do math for the sake of doing math.  Calculations performed during a case are always part of solving of business problem.  Unfortunately, many candidates get wrapped up in the math, get an answer, but have no idea what the answer means

One practice case I liked to give required candidates to determine the value of a company they were selling.  Once they got the relevant facts and figures from me, they were off to the races, setting up their calculations, doing the math, and telling me they'd sell the company for no less than $50 million.  Unfortunately, the $50 million figure they had calculated was the annual profit from the company's product.  They lost sight of the goal and offered to sell me their company for about 1/10 of its value.

How to avoid this mistake:

The key here is to remember the significance of the numbers you're calculating in the context of the business case you're discussing.  One tactical way to do this is to write the question being asked at the top of your sheet of paper.  As you go through your math and as you prepare to present your solution, continue to remind yourself of the question at hand and ask yourself if you're answering it.  Then when you present your answer, do so in a way that shows you understand what your number means.  One way to do this is to explain the implications of the answer on the case you're cracking.

6.  Giving an incorrect answer that makes no sense

As I mentioned before, it's perfectly acceptable to make a math error.  What's not acceptable is to not catch your math error even though the answer you got makes no sense in the context of the case.  Now you've added poor judgment to your miscalculation.

One example of this is the candidate who told me, during an education case, that in this district, there were 30 classrooms per student.  Clearly, this candidate lost track of units - the correct answer was 30 students per classroom.  It didn't matter to me that the math had been done right - any candidate who thought 30 classrooms per student was a reasonable answer was either not paying enough attention to detail or lacked common sense.

How to avoid this mistake:

Every time you reach the end of a calculation, perform a "sense test" or "sniff test".  This means taking a moment to ask yourself:  "does this answer make sense?"

Some examples of questions you might want to ask yourself, depending on the nature of the question:  Is it the right order of magnitude given the other numbers and facts in the case?  Should it be positive or negative?  Should a ratio be greater than or less than one?  Should a cash flow be positive or negative?


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