Market size - How many three letter words are there in the English language?

Hey Justin,

This is a super hard one!

Let's look at the two approaches.

Top Down (preferred here)

1. How many words are in the English language period. About 100,000?
2. 80/20 rule...surely longer words are rarer
   1. There would be the most 3-5 letter words with a sharp dropoff on either end
   2. 80% of words are probably 3-5 letters
   3. Half of those are probably 4 letter? (most common)
   4. So, around 25% would be 3 letter
   5. Leaving us with approx 25,000

Bottom-up

1. Write a few random sentences that pop into your head
2. Count the # of 3 letter words and get a rough %
3. Multiply this by how many words are in the English language in total (around 100k)

Where did you get asked such question? It's an interesting one but it also feels more like a brain teaser that an investment bank would ask to watch you squirm vs. an actual market sizing where you can build a logic with assumptions. 

Hello !

This is a GMAT question, not one you would get asked in an MBB interview, 99% sure. 

In any case, you will need to first rescue your combinatory math knowledge from high school/uni to calculate the number of combinations that are possible. 

Then, you would need to reduce that number, since most of those wouldn´t make sense in English, by applying a % reduction -that you should justify by reasoning with number of vowels/non vowels that a normal word has, etc.-. 

Again, this one is too hard to worry about it. 

Hope it helps!

Cheers,

Clara