In an email to my newsletter recipients (through https://www.caseinterview.com), I made a glaring math mistake. And I received more emails than I ever have pointing it out!
This is actually quite an interesting teaching opportunity on so many levels, let explain what I mean.
While I received many more emails than I normally do pointing out this math error, I was shocked I didn't receive more.
Only 0.5% of those receiving the email I sent out both noticed my error and replied to "clarify" (a.k.a. politely tell me I was wrong).
Now, this is a big problem for one of two reasons. First off, if you're really paying attention, you really should have caught the error.
Second, if you did notice the error, but you didn't reply to let me know... why didn't you?
Had I sent my last email to a group of 100 of my former McKinsey consultants, I'm pretty sure 50% would have replied back telling me I was wrong. Yet, when I sent the email to the thousands of aspiring consultants, only 0.5% replied back.
That's 100 times difference.
And why does this matter to you?
First, top consultants at the McKinsey, BCG, Bain level are very, very sharp. They notice these kinds of things. And they don't trust anybody's numbers unless they verify it themselves.
Now I'm pretty sure everyone who gets my emails has the math skills to have noticed my error (and in a minute, if you didn't notice the error the first time around, I will give you another chance to find it). So it's not an issue of not being skilled enough to find the problem, the problem is not being in the habit of using those skills to verify numbers.
In my experience, the top consultants are in the habit of using those skills constantly.
Second, lets say you did notice my math error but did not bother emailing me to "clarify", it's worth asking yourself why not?
If you were busy and didn't want to bother, I can certainly understand that, and that's probably a reasonable reason. But, I suspect some people didn't feel comfortable doing so for one reason or another.
Maybe some people were intimidated by me, maybe others didn't want to embarrass me, or maybe some people figured someone else would contact me to point out the error.
Now, at the risk of being a bit harsh with you... all those reasons above are just a bunch of lame excuses.
How you act right now is how you will likely act in an interview... which is highly correlated with how you will act on the job.
At McKinsey in particular, one of the firm's values is the "obligation to dissent"... meaning when you factually KNOW that someone (a director, a partner, a client) is wrong or about to make a mistake, it is your obligation to point it out.
If you're not willing to point out a little math mistake that I made, what are the chances you're going to stop a partner from recommending to a client to make a $1,000,0000,000 ($1 Billion) decision that you believe to be wrong (and have the facts to back up your perspective)?
That takes a certain level of self confidence, (not to mention knowing your numbers) and some guts to do that. And you'd better get used to it!
When I first joined McKinsey and even during the interview process, I was thoroughly intimidated. Looking at the recruiting brochure, I saw all these people with two PhD's, or MD's + MBA (both from Harvard), those who were Fulbright scholars, those who worked for the U.S. Presidential Administration, etc...
But, once I started working at McKinsey (and arguably one of the best life lessons I learned there), all these very impressive people and the clients are just people -- even the ones where Hollywood has made movies about them.
And when I had done my homework for a client, I had a legitimate perspective to share... and knowing your data (whether it be quantitative and numerical, or qualitative, such as having interviewed the clients top 10 customers) gave you the opportunity to contribute to the discussion.
The facts prevailed while things like title / stature / reputation / credentials didn't really matter.
So when you have the FACTS, Use Them!
Okay, next lesson.
Clearly many of those who had emailed me to point out my mistake had paid attention to my video on client skills. My favorite one was something like this...
I was going through your example the other day... and I was just working through the math, and I just didn't get the same answer as you did. Could you look it over and let me know if I did something wrong?"
(And the guy writing the email has a PhD in Physics from Harvard... or something along those lines... clearly the guy knows how to do basic math.)
Now there are several useful things to point out about how many people pointed out my mistake. First, the tone of the email was written such that the assumption was the writer of the email made the mistake... not me.
(Now clearly, he knows that I screwed up the math... I now know that I screwed up the math... and let's be honest I know that he knows I screwed up the math.)
But, rather than say, "Hey Victor, I think you made a mistake on your math," he framed it in such a way as to not embarrass me... or rather he created an opportunity for me to notice my own mistake and for me to correct it.... as opposed to having him correct me, which creates a superiority aspect to the relationship.
This is an excellent demonstration of really good client skills. And if memory serves, I probably used the exact same approach with clients on numerous occasions.
Now in real life, I really could care less. At this point in my career, I have nothing left to prove, so if I screw up some basic math, no big deal.
I'm at a point in my career where this kind of mistake has no consequence.
(Though rule #1 for those starting in consulting jobs soon -- never make the kind of mistake I made in front of a client... or allow a partner to present your work in front of a client with a mistake like the one I made... your career will be set back big time.)
Here's why I'm making a big deal out of it.
Often when you come in as a consultant, before you arrive, you are positioned on a pedestal. Some people resent people on a pedestal. So if I'm the VP of Finance for a client, and some guy with a PhD in Physics from Harvard points out my math mistake... in front of my subordinates... what does this accomplish?
All it accomplishes is the guy now hates you.
Now at the same time, you can't just ignore the mistake either, for the sake of having the person like you more... you have to do both: correct errors (especially if the consequence of the error is extremely high), and still havethe client like you. Hence the need for good "client skills".
Alright, so by now you're probably wondering what was the math mistake that I made that warranted this long essay about it.
So if you didn't catch it the first time around, the original post is:
**** THE ANSWER ****
In my comparison of "fast" vs. "slow" candidates, I indicated that if you knew profits were down 20%, sales were down 10%, then you could automatically conclude that costs were up 10%.
Because % are by definition relative numbers... a ratio of what they are being multiplied against, this is incorrect. The simplest example of this phenomenon is if you have a $100 stock price, and the stock price falls by 50% and then increases by 50%, the final stock price is $75.... not $100.
What I had intended to write (but didn't) was if you knew profits were down $20 million, sales were down $10 million, then you could automatically conclude that costs were up $10 million.
Using an actual dollar amount is an absolute number, and unless I'm mistaken (and I'm sure if I am mistaken, I will get a few dozen emails pointing this out), the logic of what I wrote previously should hold when using absolute dollar amounts.
And for what it is worth, math mistakes are most often made when one is tired or in a rush... (you'd be wise to remember that for both your interviews and on-the-job) and in my case, I was both tired and in a rush to finish up that email.
I reply to case interview emails and do my case interview Q&A email newsletter after I finish my client work, sales calls, staff meetings, client travels, press interviews, and tucking my three girls into bed... so basically almost by definition when it comes to this newsletter, I'm pretty much always tired and always in a rush to finish it.
If I were to wait until I had free time, wasn't tired, and wasn't in a rush to finish this newsletter, you would pretty much never see a single issue ever. So hopefully an occasional math mistake (which I'm sure some people found quite amusing) is a small price to pay to get everything else.
So bottom line, you're probably going to see more mistakes in the future! 🙂
And for those who took the time to point out my mistakes, a quick thank you and congratulations for exercising your "obligation to dissent". And for those who dissented with great diplomacy, nice job on using your client skills - well done.