Friday, January 18, 2013

Interview: How many cows are in Canada?

How many cows are in Canada?

I was surfing around stumbled on this interview question. At first, this appeared to be one of those break down the problem to smaller more manageable parts, like "How many quarters would you need to reach the height of the Empire State building," or "Estimate how many windows are in New York." But then I quickly realized, I do not have the faintest idea what the base case should be. Below is my thought process to answer the question with my current knowledge without looking up facts.

I think the premise of the question is really how I troubleshoot or go about the question more than the correct answer like the questions mentioned above. There are many factors that cannot be used because I do not know the start or end points of such data, like how much milk is produced or how much beef is consumed. I do not know how much is consumed domestically nor how much is exported for the former data point. I do not know how many people eat beef nor even the frequency.

To start, I think my solution would be some sort of range that I slowly refine as much as I can with smaller error. This will cause a wider range, but at least it is some information that can be used. Assuming there are cows that are kept for recreational purposes, I will assume this number is negligent. With that assumption, cows are raised for the purpose of consumption or to produce goods for consumption (ie milk).

Starting with calculating the upper range and consumption, I will assume cows (around 500 - 1000 pounds) weight about 750 pounds [from memory]. A person who normally eats beef will eat about 1 pound per week. Because most hamburgers and steaks are served in units of quarter pounds to one pound, and on rare occassion 32 ozs. Anything larger is assumed negligent [round up for upper range, down for lower range if necessary]. 1 pound seems like a lot of beef. So for 50 weeks (slightly less than a year but makes it easier to calculate), a person will eat about 50 pounds per year. So a cow will feed at most 15 people.

I do not know the population of Canada, but the US is about 300M (I actually know this number). Canada is about the same size but a good amount of the land area is not populated. I'd guesstimate that is is about a third of the US, so the population is 100M (also a nice round number). 100M / 15 = 6.67M, so approximately 6.67M cows are needed for consumption assuming all people eat approximately 1 pound / week. Another assumption is that Canadians eat as much or less than Americans.

Now, I have to compensate the number for actual population because cows do not grow instantly. Thus, 7M is a good starting low range for number of cows in Canada. Now I have to figure how long cows live for.... and I have no idea. Hmmmmmmmmmmm.... Cows eat grass... You can buy beef for approximately $5-20 per pound... I'll use $10 (pure guess and an easy number to use). Thus, $7500 worth of grass, feed, etc. Minus profit of middle stores, probably a third or even a quarter... so $2000. This is going now where quickly...

At this point, I will realize I am taking too much time, so I'll guess that it is about 5 years. My answer would be between 7M and 35M cows. With some sanity check that it is less than a billion cows and more than hundreds of cows.

As good practice, I would email research afterwards to show that I am also capable of following up and doing research. Provide online resources if you need to demonstrate that you can web search.

After minimum research, there are approximately 13M cows in Canada. Canada has a population of 35M. Approximately 91M cows in US. US has a population of 311M. US consumes 26B pounds of beef. 0.012 pounds of beef per person per year. Although the final number fell into the range I provided, using the calculations above, I should have come between 2.3M and 11.5M. A cow's life is between 1-2 years for meat and 15 years for dairy. An easier way to remember is that there are about a third of the country's population. I'd estimate less for other countries unless they export cows, but that's enough research for a blog.


Also see post on other methods I would answer the question
After doing a few more practices of other forms of this question, I've found that I do have some idea approximately what the number should be. There may be some tendency to fidget which metrics to use to estimate the final number because my final numbers tend to be within a range that surprises even myself. So just remember, typically these questions is just your process of thinking. You may come up with the worst guess but may have the best explanation, and it is the latter that has greater weight and for some interviews may be the only weight.


7/31/2014 - Checking on some old subjects and stumbled across a new link on how this question is not useful. I agree that there are more effective questions (as I've noted in My Take on Odd Questions). It does have its use but has too many variables to consider. Either way, a candidate should still be prepared for these questions because there will be some companies that will ask this type of questions. For me, I still enjoy thinking of different variants. It kind of has a nice intention to test one's imagination.