Goldman Sachs Analyst Interview Questions, Process, and Tips

The Convex Hull is the smallest convex polygon that encloses all given points.

• Sort the points based on their x-coordinate.

• Find the upper hull by starting from the leftmost point and moving clockwise.

• Find the lower hull by starting from the rightmost point and moving counterclockwise.

• Combine the upper and lower hulls to form the convex hull.

The strategy is to always subtract the number chosen by the friend from 4 to ensure reaching 16 first.

• Start with 20 and subtract the number chosen by the friend from 4.

• Continue this strategy until reaching 16 before the friend reaches 17-19.

• Ensure the friend ends up at any number between 17 to 19 before reaching 16.

The problem involves finding an element in a matrix that is sorted both row-wise and column-wise.

• Start from the top-right corner of the matrix

• Compare the target element with the current element

• If the target is smaller, move left; if larger, move down

• Repeat until the target is found or the matrix boundaries are crossed

To create a uniform distribution from 1 to 200 using an unbiased coin, we can use the rejection sampling method.

• Divide the range into equal parts based on the number of outcomes of the coin toss.

• Toss the coin and select the corresponding part of the range.

• If the selected number is outside the desired range, reject it and repeat the process.

• Repeat until a number within the desired range is obtained.

• Example: If the coin ...read more

Expected number of tosses of a fair coin to get 3 consecutive heads.

• The probability of getting 3 consecutive heads is 1/8

• The expected number of tosses to get 3 consecutive heads is 14

• This can be calculated using the formula E(X) = 2^k + 2^(k-1) + 2^(k-2) + ... + 2^2 + 2^1 + 2^0, where k is the number of consecutive heads required

Go second. The probability of winning is higher when going second.

• The probability of winning when going first is (1/n+1), while the probability of winning when going second is (n/n+1)

• This is because the first player has a chance of drawing the black ball on their turn, while the second player has a chance of drawing the black ball on their turn or the first player's turn

• For example, if there are 10 red balls and 1 blac...read more

What is the most likely value of the last roll in a game where a die is rolled until the sum of all rolls is at least 100?

• The last roll must be at least 4 to reach a sum of 100

• The probability of rolling a 4, 5, or 6 is 1/2

• The most likely value of the last roll is 4 or 5

Algorithm to search for a number in an n x n matrix with sorted rows and columns.

• Start from the top-right corner of the matrix

• If the current element is greater than the target, move left

• If the current element is less than the target, move down

• Repeat until the target is found or the bottom-left corner is reached

Algorithm to find largest common subarray of two arrays of size n

• Create a 2D array to store the lengths of common subarrays

• Traverse both arrays and fill the 2D array with lengths of common subarrays

• Find the maximum length and its corresponding ending index in the 2D array

• Use the ending index to retrieve the largest common subarray from either of the arrays

I am excited to join Goldman Sachs because of its reputation for excellence and the opportunities it offers for professional growth.

• Goldman Sachs is a leader in the financial industry and has a strong reputation for excellence.

• I am impressed by the firm's commitment to innovation and its focus on delivering value to clients.

• I believe that working at Goldman Sachs will provide me with the opportunity to learn from some ...read more

I have experience in marketing and sales, with a focus on digital marketing and lead generation.

• Started career as a marketing intern at XYZ company

• Managed social media accounts and email campaigns for ABC company

• Implemented SEO strategies and increased website traffic by 30%

• Led a team of 5 sales representatives and exceeded quarterly sales goals by 20%

• Currently working as a digital marketing specialist at DEF company

Probability of a randomly dropped rod of length L intersecting a line on a 2D plane with infinite parallel, vertical lines.

• The probability depends on the length of the rod L.

• The probability can be calculated using geometric probability.

• The probability is 1 - (2L - 1) / infinity.

• For example, if L = 1, the probability is 0.5.

• If L = 2, the probability is 0.75.