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Goldman Sachs engineering interview questions

Here are some interview questions I got during my various rounds of Goldman interviews for engineering. Hope this is helpful!

-A class of 17 children needs to be separated into groups for a game. They must be broken into one group of seven one group of six, and one group of four. How many different ways are there to partition the class?
-In one turn of the game, a player throws three ordinary dice, their score being the largest of the numbers appearing face up. What is the probability that a player scores 2?
-Stock A has a volatility of 22% per year, Stock B has a volatility of 17% per year and the price spread of the two stocks has a volatility of 31% per year. What do the volatilities imply about the historical relationship between the stocks?
-What is the limit of (Cos(x)-1)/x^2 as x approaches 0?
-Alice and Bob choose an integer each in the range of [1, 10]. All choices are equally likely. What is the probability that neither of the chosen numbers will be the square of the other?
-If the probability of a random variable X with space R_x = {1, 2, 3, …, 12} is given by f(x) = k*(2x-1), then, what is the value of the constant k?
-f(x) = integral of (1+t^4) dt from 3 to x. Find f^(-1)’(0), the derivative of the inverse of f, evaluated at 0.

Thanks for sharing these with the community!