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Quantitative Trader Interview Questions


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N points lie on a circle. You draw lines connecting all the points to each other. These lines divide up the circle into a number of regions. How many regions is this? Assume that the points are scattered in such a way as to give the maximum number of regions for that N.

12 Answers

n choose 4 + n choose 2 + 1

I don't think the above answer is right.What happens if N is less than 4? Even if N is at least four, it still doesn't work For example, take the case when 4 lines are drawn, you can make 11 regions, but Dimitar's formula gives 4c4+4c2+1=8 The way you do it, is you start out with 1 region with 0 lines. Then you draw 1 line to get 2 regions. When the maximum number of regions is created, each new line will cross every previous line and will create a new region each time it crosses line. It also creates a new region just by being created. So the 2nd line makes 2 new regions, the third line makes 3 new regions, the fourth line makes 4 new regions etc. So the answer is the sum of the first N natural numbers +1. In general this is the formula N(N+1)/2+1

Hi, I also get Dimtar's formula, you may use the recursion method to do it, which takes some time. Is there any easy way to get this one? Btw, when there are 4 dots on a circle, I think it shoud still give 8 regions. I think 11 is the answer to another problem. If you make n cuts on a circle, the max shares you can create.

You flip four coins. At least two are tails. What is the probability that exactly three are tails? Do this in your head, you are not allowed to write anything down for this question.

8 Answers

How many 0s in 100! ?

4 Answers

If I give you the opportunity to play a game at the end of which the loser pays the winner $10, and then partway through the game I ask that we each double our bets to $20 or that you must immediately pay me $10, what is the minimum probability of winning you must have to keep playing?

3 Answers

Devise a strategy of betting on a seven-game series such that if team 1 wins the series you win $1000 no matter what and if team 1 loses, you lose $1000.

1 Answer

You have all the clubs from a deck, 13 cards, and you can choose 2 from the deck and get paid their product, where all face cards are considered to be 0. You can pay $1 to reveal the difference of any two cards you choose, how much would you pay to play this game?

Draw payoff diagram of call and put option and explain. What is the advantage of call option? When do people want to buy a stock instead of option?

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