While celebrating the U.S. holiday Halloween, I announced an estimation question contest.

As you might recall, I posed the following question:

“In today’s New York Times, I learned that in the weeks leading up to this holiday, Americans purchased \$2.7 BILLION dollars in candy.

So here’s my challenge for you.

Assuming all of that candy is consumed by someone in America, estimate the total number of calories represented by \$2.7 billion in candy.

Assuming 3,500 calories consumed results in a person gaining 1 lb (0.45 kg) in weight, estimate how many pounds (or kilograms) of weight the American population will gain.”

It turns out that Adrian also won my case structuring contest a year ago as well.

I will share Adrian’s answer to this contest and explain why I chose it amongst over 300 entries.

But first, some background on Adrian.

Adrian is in his 4th year at a non-Ivy, state college in the southern United States. His school is what’s known as a non-target school. Historically MBB do not recruit on campus.

Through extensive networking, Adrian worked hard to get opportunities to interview at McKinsey, Bain and BCG. He just finished a summer internship at Bain a few months ago. He will also be returning to Bain full time upon graduating.

Adrian started case preparation as a first year (freshman). He did 100-200 practice case interviews, and has given 60 or so practice cases to others. Of my resources, he used my book Case Interview Secrets, my flagship case prep program Look Over My Shoulder, and CaseInterviewMath.com.

Now let’s look at Adrian’s answer to my question and see why I (and Bain) liked his approach. I’ve added my comments in [BRACKETS].

“If we want to estimate the total amount of weight that the US population gained as a result of the candy sold for Halloween, there are a few steps that we should take.

First, since we’re given \$2.7B as the total dollar amount spent on candy, we need to determine the number of pieces of candy that represents by dividing by the average price of a piece of candy.

Then we need to multiply that number of pieces by the average calories of a single piece of candy to get the total calories consumed.

Once we have the total calories, we can divide by the calories per pound, given to us here as 3,500 to get the total number of pounds gained by people in the US as a result of Halloween candy.”

[VC Comment #1: Unlike 95% of the entries that started running computations immediately, Adrian outlined his approach conceptually first. This is an extremely effective way to communicate because it is client friendly.

But wait, you might be thinking, I didn’t say in my contest parameters that I would be judging your communication skills. This is because your communication skills are always being evaluated for client friendliness.

When you email the recruiting coordinator, when you write your cover letter, when you do a full blown case, or you do a simple math problem… anything and everything you do is always being judged on the standard of client friendliness.

Keep in mind that most clients will not have the same capacity to do mental math as you will. If you start diving into computations, you will lose 95% of your clients with the numbers.

However, if you explain your computational approach conceptually using mainly words first, most clients can see, “Oh that makes sense.” Then as you do your computations, they aren’t going to bother to check your specific computations. They will trust you can add, subtract, multiply or divide without their help.]

“1. To start off, let’s assume that we could buy a bag of candy with 50 pieces of candy for ~\$10. That would mean each piece of candy cost, on average, \$0.20. Then we can divide 2.7B by \$0.20 to give us 13.5B pieces of candy sold.
2. Then if we assume that a single piece of candy is ~50 calories, we can multiply the 13.5B pieces by 50 to get a total of 675B calories coming from the candy.
3. We can then divide the 675B calories by 3,500 which gives us ~190M pounds gained by people in the US.”

[VC Comment #2: Nice job stating assumptions explicitly. It would be better to explain the reasoning behind the assumptions. This allows me (and others) to evaluate the approach. In a real life engagement, we’d go send an analyst off to verify the assumptions with a Google search. We don’t need to test your ability to use Google. I would say 50% of the entries did.]

“Initially, that may seem high, but if we consider the fact that there are ~320M people in the US, that is just over half a pound per person which seems reasonable.”

[VC Comment #3: I liked that Adrian did a reasonableness check at the end. Does a 0.5 lb. gain in weight per person in America intuitively seem correct around a sugar-oriented holiday.]

1) Many people just submitted a number without showing their computations. This doesn’t work because the purpose of the exercise isn’t to get the number, it is to evaluate your thinking process — whether it is logical and whether it can be followed easily by others.

2) Half the entries did accurate calculations. This is important to do, but since over half of the people were able to do it, it’s not a differentiator.

3) Roughly 1%-2% of the participants outlined their approach conceptually FIRST before doing actual computations.

4) Roughly 2%-3% did a reasonableness check after doing the computations. They asked out loud, “Does this quantitative answer seem intuitive and qualitatively reasonable?” Then they answered their own question.

Two or three other participants did all of the above as Adrian did. A few justified their assumptions better than Adrian did, but I chose Adrian’s entry over the 3-4 others that were logically equal and even slightly better because Adrian’s response was more eloquent and concise.

I hope this contest has been a useful learning exercise. Congratulations to Adrian for winning two of my contests in a row. (Adrian: You officially aren’t allowed to participate anymore! Also congratulations on your full-time offer at Bain.) And congratulations to Bain, you’re getting a great new consultant.

Finally, Adrian — look out for my stash of Halloween candy that I got from my kids. I don’t need the calories or to gain any more weight. Now the sugar is your problem. 🙂

-Victor

P.S. The most amusing entries for the contest ended with “I’m going to go work out now.” I suspect I wasn’t the only one with a post sugar feeding frenzy guilt complex from the very sugary holiday.