Goldman Sachs Test

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.