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Quantitative researcher Interview Questions

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a, b, c are integers. Such that a^2 + 2bc = 1; b^2 + 2ac=2012, find all the possibles values of c^2 + 2ab.

7 Answers

2011 is prime

More details in addition to the last post. 1) subtracting the 1st equation from the 2nd one gives: (b-a)*(b+a-2c)=2011 2) 2011 is prime, so there are only two possibilities: b-a=1, b+a-2c=2011; or b-a=2011, b+a-2c=1 3) subtracting the 1st equation from the 3rd equation gives: (c-a)(c+a-2b)=x-1 4) plugging c-a=0.5*[(b-a)-(b+a-2c)], c+a-2b=(c-a)-2(b-a) into 3) gives you x

In 2) there should be four rather than two possibilities. Both terms could be negative.

First round: basic probability, combinatorics. A bear wants to catch 3 fish from a river. when he has caught 3 fish, he'll leave. when a fish comes, there is a 1/2 chance he'll catch it. what's the probability that the 5th fish will not be caught?

4 Answers

Why did you leave the job before your last job.

2 Answers

Assume that you have an NxN Matrix, filled with decreasing numbers if you go from left to right and from top to bottom. Can you design an efficient search algorithm on this matrix. Hint: the most efficient one should have a Log(N) complexity...

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100 sided die question was difficult

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given a series of stock prices, describe an algorithm to find the best buy and sell point. ( only one buy and one sell, buy before sell)

2 Answers

I met a coule of quants with average MSc degrees from average schools, sub-par work experiences but with egos of Nobel Prize winners. I was very surprised to see the mediocrity of these two quants because I had read that GSA had only recruited 25 profiles out of 10000 in the last few years so I was expecting people working there to be Quants from the top 10 schools with Quantitative PhDs (which is my case). The recruiter had mentioned to me prior the interview that GSA looked as much at personality fit than skills so I was really on my best behaviour and within the Quant community I am usually known to be pleasant and easy to work with. However, both of these interviewers had severe personal issues. The first one wouldn't tell me about his background because "he was the one asking the questions" and the second thought that a multi linear regression (MLR) was the best Machine Learning Techniques and would scowl at me when I would confront him with the fact that the assumptions behind an MLR around returns being i.i.d were violated by the observed data and that as a result taking a Bayesian approach had more potential in my opinion. As a result of giving my honest opinion and seing through his facial expression the kind of tantrum anger you see on pre-adolescent children, he then went on a rampage trying to make me fail in his next few questions which I answered correctly but instead of moving on to the next ones quickly, he tried to make me fail with stupid details instead of help me show my best through asking additional conceptual questions and bringing the conversation to an interesting level of abstraction in which interesting trading ideas could emerge. I lost interest in GSA as a result of these interviews (GSA was amongst my top 10 preferred places to work for before that). It's a shame. I don't understand why management decided to put these two clowns as the face of GSA. They really give a poor image of the company. Currently, my best offers are with Goldman Sachs and the Man Group. It would have been good to be able to compare an offer with GSA.

2 Answers

throwing a dice until the face 6 comes up two times, what is the expected stopping time

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If I break a stick of unit length into three random pieces, what’s the expected length of the largest piece?

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If I throw two regular dice and tell you one of them is a six, what is the probability that I got two sixes?

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