Goldman Sachs test for "Quant Strategist" position was one of the lengthiest test I have given till date.

400+ students appeared for the test out of which around 25 students were shortlisted for final rounds of interviews.

Test was for a total of 3.5 hours. I don't remember many questions, but here are a few :

**Section 1 :**(Probability + Linear Algebra, Subjective)

**1) Two points are chosen randomly in a unit square. What is the probability that the circle formed using the diameter of the 2 points contains the square's center ?**

2) Choose any 9 points on or within a unit square. Prove that there always exists 3 points such that triangle formed by them has area 1/3.

3) Find Eigen values of a matrix which has all entries equal to 1, except the diagonal entries.

4) Prove : Summation(k * p(n,k)) = n! over k=1 to n, where p(n,k) is the number of permutations of {1,2, .. n} which have exactly k fixed points.

**Section 2 :**(Algorithms + Probability, Subjective)

1) Given 2 integers a, b. Calculate probability that a^2 + b^2 is divisible by 10.

2) Given a number N, find the smallest palindrome number greater than N in O(lgN)

3) Check whether we can form N/2 pairs from an array of length N, such that each pair's sum is divisible by k.

**Section 3 :**(Computer Science Concepts, Subjective + Objective)

The 3rd paper tested our knowledge on core cs concepts. It mainly consisted of questions on Networks.

are m.tech students in cse allowed for goldmann sachs, morgan stanley. worldquant etc?

ReplyDeletepls can u tell the approach to solve the probability questions

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