Vanguard Interview Questions and Answers

I want to join GS because of their reputation for excellence and the opportunity to work on challenging projects.

• GS is known for its prestigious reputation in the financial industry

• I am attracted to the opportunity to work on complex and challenging projects

• I admire GS's commitment to innovation and cutting-edge technology

• I believe GS will provide me with valuable learning and growth opportunities

Find max path from bottom left to top right in a matrix using only up and right steps.

• Start from bottom left corner and move towards top right corner.

• At each step, choose the maximum value between the cell above and the cell to the right.

• Keep track of the sum of values in the chosen path.

• The final sum is the maximum possible sum of values in a path from bottom left to top right.

The most likely number to occur as the final sum is 100.

• The sum of the outcomes of the dice rolls will keep increasing until it reaches or exceeds 100.

• Since the dice have equal probabilities for each outcome, the sum will have a higher chance of reaching 100.

• The probability of rolling a sum greater than 100 decreases as the sum gets larger.

Finding probability of point (1,0) lying in longest cut of three random points on circle of radius 1 centered at (0,0)

• The longest cut will be the one that spans the smallest angle between two of the three points

• The probability can be found by calculating the area of the region where the longest cut includes point (1,0)

• This can be done by finding the angle between (1,0) and the two other points and using trigonometry to...read more

Find the magic number in a sorted array where value and index are same.

• Iterate through the array and check if the value and index are same

• If found, return the value

• If not found, return -1

Searching an element in a sorted 2D matrix

• Start from the top-right corner or bottom-left corner

• Compare the target element with the current element

• Move left or down if the target is smaller or move right or up if the target is larger

Design a newspaper subscription system

• Create a user registration system

• Allow users to select subscription plan and payment method

• Provide options for delivery frequency and start/end dates

• Send reminders for subscription renewal

• Allow users to modify or cancel subscription

• Track subscription history and payment records

Number of ways to jump n stairs if a person can climb 1 or 2 stairs.

• Use dynamic programming to solve the problem.

• The number of ways to jump n stairs is equal to the sum of ways to jump n-1 stairs and ways to jump n-2 stairs.

• Base cases: if n=0, return 1 and if n=1, return 1.

An LRU cache can be made using a doubly linked list and a hash map.

• Create a doubly linked list to store the cache items.

• Create a hash map to store the key-value pairs.

• When a new item is added, check if the cache is full. If it is, remove the least recently used item from the linked list and hash map.

• When an item is accessed, move it to the front of the linked list.

• When an item is removed, remove it from both the linked

Probability of winning a dice game where the one with lesser number wins.

• The probability of winning depends on the number of sides on the dice.

• If the dice has an odd number of sides, the probability of winning is higher for the second player.

• If the dice has an even number of sides, the probability of winning is equal for both players.

Compute working days using given functions f, g, and h.

• To compute the 3rd working day, apply function g three times to function f.

• To compute the 2nd working day of the previous month, apply function h to function f, then apply function g twice.

• To compute the 4th working day of the next month, apply function g four times to function f.

I am a highly motivated individual with a passion for learning and a strong work ethic.

• I have a degree in computer science and have worked as a software developer for 3 years.

• I am proficient in multiple programming languages including Java, Python, and C++.

• I am a quick learner and enjoy taking on new challenges.

• In my free time, I enjoy hiking and playing guitar.

Flip the coin twice and consider the outcome as follows.

• Flip the coin twice and consider the outcome as follows:

• - If both flips are heads or both are tails, discard and flip again.

• - If the first flip is heads and the second is tails, consider it as heads.

• - If the first flip is tails and the second is heads, consider it as tails.

• This method ensures a 50-50 chance of getting either heads or tails.

• Alternatively, use a phy...read more

Count number of ways to reach 20 on number line starting from 0 in steps of 1 or 2. Derive recursive formula for n+1.

• Use dynamic programming to count number of ways for each step.

• For each step, number of ways is sum of number of ways for previous 1 or 2 steps.

• Recursive formula: ways[n+1] = ways[n] + ways[n-1]

Yes, I have applied to several PhD programs in the past.

• I have applied to PhD programs in [specific field] at [specific universities].

• I have experience with the application process, including writing research proposals and obtaining letters of recommendation.

• I am currently waiting to hear back from the programs I applied to.

Probability of a rod of length L covering an integer on a number line.

• The probability depends on the length of the rod and the distance between adjacent integers on the number line.

• If the length of the rod is less than the distance between adjacent integers, the probability is zero.

• If the length of the rod is greater than or equal to the distance between adjacent integers, the probability is (L - d)/d, where d is the d...read more

There are (N-1)! ways to eat chocolates from left to right.

• The first chocolate can be chosen in N ways, the second in (N-1) ways, and so on.

• However, since the order of chocolates eaten matters, we need to divide by the number of ways to order N chocolates, which is N!.

• Therefore, the total number of ways to eat chocolates is (N-1)!

• For example, if N=4, there are 3! = 6 ways to eat the chocolates.

No, it is not possible for each person to give gifts to 3 people and receive a gift from them in a party of 9 people.

• In this scenario, each person would need to receive 3 gifts, which is not possible if there are only 9 people.

• This scenario would be possible if there were at least 10 people at the party.

• In general, for a party of n people, each person can give gifts to n-1 people and receive gifts from n-1 people.

Conditions for overflow and steady state in a tank with inflow and outflow

• Overflow occurs when the inflow rate is greater than the outflow rate

• Steady state is achieved when the inflow rate equals the outflow rate

• Overflow can be prevented by adjusting the inflow rate or increasing the outflow rate

• Steady state can be maintained by balancing the inflow and outflow rates

I am interested in data analysis, technology, and staying up-to-date with industry trends.

• Data analysis and visualization

• Machine learning and AI

• Technology advancements and innovations

• Industry conferences and events

• Networking with professionals in the field

The most probable number on the last toss is 6.

• The probability of getting a sum of 100 or more is highest when the sum is 99.

• The last toss will be made to reach the sum of 100, so the most probable number is the one that will take the sum closest to 100.

• The sum of 94 can be achieved by rolling a 6 on the last toss, which is the most probable number.

Options are financial contracts that give the buyer the right, but not the obligation, to buy or sell an underlying asset at a predetermined price.

• Options can be used for hedging or speculation

• There are two types of options: call options and put options

• Call options give the buyer the right to buy the underlying asset at a predetermined price, while put options give the buyer the right to sell the underlying asset at a ...read more

A call option is a financial contract that gives the buyer the right, but not the obligation, to buy an underlying asset at a predetermined price within a specified time period.

• Call options are bought by investors who believe that the price of the underlying asset will rise in the future.

• The buyer of a call option pays a premium to the seller for the right to buy the asset at a predetermined price, known as the strike ...read more

You can buy fuel from us through our fuel card program.

• We offer a fuel card program that allows you to purchase fuel from our network of stations.

• Our fuel card program offers discounts and rewards for frequent users.

• You can easily track your fuel expenses and usage through our online portal.

• We also offer customized fuel solutions for businesses and fleets.

• Our fuel is high-quality and meets all industry standards.

Increasing stock volatility increases the price of a call option.

• Higher volatility means higher potential for the stock to move in the option holder's favor, increasing the option's value

• The option's delta and gamma will also increase with higher volatility

• Example: If a call option on a stock with a strike price of $50 has a premium of $2 when the stock has a volatility of 20%, increasing the volatility to 30% may incr

The price of a call option is calculated using the Black-Scholes model which takes into account the underlying asset price, strike price, time to expiration, risk-free interest rate, and volatility.

• Determine the current price of the underlying asset

• Determine the strike price of the option

• Determine the time to expiration of the option

• Determine the risk-free interest rate

• Determine the volatility of the underlying asset

• Pl...read more

The price of a barrier option is generally less than a normal option.

• Barrier options have a condition that must be met for the option to be activated, which reduces the likelihood of the option being exercised.

• This reduced likelihood of exercise means that barrier options are generally cheaper than normal options.

• However, the price of a barrier option can vary depending on the specific conditions and terms of the optio...read more