Akuna Interview Questions - Complete List

Quant Interview Questions

232 questions

What is 15% of 235?

Junior Trader Interview

What is the fair value of a game where you receive $14 if you roll a total of 11 or 12 in two dice rolls, and $0 otherwise?

Junior Trader Interview

What is 19% of 270?

Junior Trader Interview

What is 12% of 240?

Junior Trader Interview

If there are exactly 5 people and exactly 5 seats around a round table, what is the probability that those 5 people will sit in perfectly ascending or descending age order?

Junior Trader Interview

You roll a 100-sided die and receive a payout equal to the number on the top face. What is a fair price to pay to play this game? Now, suppose you may re-roll the die any number of times for $1 per re-roll. What is the fair price to pay to play this modified game?

Junior Trader Interview

What is the expected value of the random variable corresponding to a fair six-sided die roll? What is the expected value if you can choose to reroll the die once, keeping the higher result to maximize your value?

Junior Trader Interview

On an infinitely large chessboard, a knight can move two squares in one direction (up, down, left, or right) and then one square perpendicular to that direction. After 10 moves, how many unique squares can the knight land on? Provide both a confidence interval and an estimate for the number of unique squares.

Junior Trader Interview

What is the result of 141 minus 54?

Junior Trader Interview

Given the sequence M, J, J, A, S, O, what is the next element in the series?

Junior Trader Interview

A colony of bacteria doubles in size every minute. After 60 minutes, it reaches its full size container. At what minute was the container half full?

Junior Trader Interview

It is currently 3:00 PM. After how much time, to the nearest second, will the hour and minute hands of a clock overlap?

Junior Trader Interview

You have 1000 1x1x1 cubes and form a 10x10x10 cube with them. You remove the outer layer of small cubes. How many cubes have you removed?

Junior Trader Interview

Multiply 94 and 48 in your head.

Junior Trader Interview

Describe two probabilistic scenarios that have the same expected value but different variances.

Junior Trader Interview

Calculate 57 multiplied by 22 and 3230 divided by 34.

Junior Trader Interview

Calculate the product of 47 and 75.

Junior Trader Interview

What is the result of subtracting 53.9 from 84.2?

Junior Trader Interview

What is the sum of the interior angles of an octagon?

Junior Trader Interview

What is the angle between the hour hand and the minute hand of a clock when the time is 3:15?

Junior Trader Interview

What is the result of subtracting 28.3 from 45.1?

Junior Trader Interview

What is the result of multiplying 38 by 79?

Junior Trader Interview

What is the result of multiplying 19 by 32?

Junior Trader Interview

Given the sequence M, J, J, A, S, O, what is the next letter in the sequence?

Junior Trader Interview

What is thirty-five times thirty-five?

Junior Trader Interview

What is the probability of getting three heads in a row when tossing a fair coin five times?

Junior Trader Interview

Game 1 pays $20 if you flip at least one heads when flipping a coin 4 times, while Game 2 pays $500 if you flip heads on all 4 flips. Which game should you choose?

Junior Trader Interview

A 10 × 10 × 10 cube has all its surfaces painted red. If the cube is broken into 1000 unit cubes, how many of those unit cubes have at least one red face?

Junior Trader Interview

You have 3,000 apples and one truck that can carry a maximum of 1,000 apples at a time. For every mile the truck travels, one apple is lost (destroyed) from the load. What is the maximum number of apples you can transport to a city 1,000 miles away?

Junior Trader Interview

You have 50 white marbles and 50 black marbles. You can distribute these marbles into two buckets in any way you choose. Afterward, you will randomly select one bucket, and then randomly select a marble from that bucket. How should you distribute the marbles to maximize the probability of drawing a black marble?

Junior Trader Interview

Given a list of projects, each with a profit value, calculate the number of pairs of projects whose combined profit exceeds a certain threshold. Use binary search to efficiently determine the count of such pairs.

Quantitative Researcher Interview

Output all permutations of size n.

Quantitative Researcher Interview

1. X and Y are independent normal random variables with standard deviations a and b, respectively. What is the possible range of standard deviations for X+Y? 2. If you flip a fair coin 4 times, what is the probability of getting an even number of heads? What about 10 times? What is the probability of getting an even number of heads when flipping n coins, if only one of them is fair?

Quantitative Researcher Interview

You break a stick into two pieces at a random point, then break the longer segment again at a random point along its length. What is the probability that the resulting three segments can form a triangle?

Quantitative Researcher Interview

Implement a class that stores values and provides methods to get the mean, max, and mode of the values. How can you optimize your solution for efficiently computing the mean, max, and mode?

Quantitative Researcher Interview

1. What is the derivative of the function f(x) = x^x? 2. Find the eigenvectors and eigenvalues of an n x n matrix with n on the diagonal and ones in every off-diagonal entry.

Quantitative Researcher Interview

Implement gradient descent in Python.

Quantitative Researcher Interview

Given a list, return a new list containing only the non-repetitive (unique) elements from the original list.

Quantitative Researcher Interview

Describe an algorithm to count the number of strongly connected components in a directed graph.

Quantitative Researcher Interview

Given a building with 10 doors, and for each door, you know the probability of escaping, dying, and returning to the same point. Which strategy would you choose to maximize your chances of escaping the building, and why?

Quantitative Research Interview

Let X be the sum of N independent random variables, each following a uniform distribution. What is the distribution of X?

Quantitative Research Interview

Given four independent and identically distributed uniform random variables on [0,1], we form two line segments by connecting the first two and the last two. What is the probability that these segments overlap?

Quantitative Researcher Interview

Given two arrays of n strings each, compare corresponding strings from both arrays. For each pair, print 'yes' if for every character, the absolute difference in the number of occurrences of that character in both strings is less than 3; otherwise, print 'no'. For example, if string 1 is 'aaabbb' and string 2 is 'aabb', their character counts are {a:3, b:3} and {a:2, b:2}; since all counts differ by 1, output 'yes'.

Quantitative Researcher Interview

Find the integral points inside a triangle that have the shortest total distance to the three vertices.

Quantitative Researcher Interview

What is the probability that three random points on a unit circle will form a triangle that includes the center of the unit circle?

Quantitative Researcher Interview

Given an n x n matrix, write a function to rotate the matrix by 90, 180, and 270 degrees clockwise. Return the resulting matrices for each rotation.

Quantitative Researcher Interview

Write a program to determine whether two triangles are equivalent. Equivalence is defined as one triangle being able to exactly cover the other after applying rotations and translations (i.e., rigid motions).

Quantitative Researcher Interview

Let X and Y be independent, identically distributed standard normal random variables (X, Y ~ N(0, 1), iid). What is the conditional distribution of X given that X + Y = 1?

Quantitative Researcher Interview

Design a URL shortening system.

Software Engineer Interview

What is the difference between uncorrelated and independent random variables? Give an example of two random variables that are uncorrelated but not independent.

Quantitative Researcher Interview

Given a two-dimensional array representing positions of stones and a rope of a known length, determine the maximum number of stones that can be enclosed by the rope. The rope must form a closed loop.

Quantitative Researcher Interview

How many numbers between 1 and 10,000 inclusive contain the digit zero at least once?

Quantitative Researcher Interview

What are the eigenvalues of the n x n matrix where each diagonal element is n and all off-diagonal elements are 1?

Quantitative Researcher Interview

Implement a thread-safe Least Recently Used (LRU) cache.

Software Engineer Interview

Implement your own version of the STL vector data structure.

Software Engineer Interview

Given an array of stocks, exchanges, and timestamps, design an algorithm to detect evidence of front running.

Software Engineer Interview

What is the time complexity of accessing an element from a vector?

Developer Interview

Design a class that efficiently computes the running mean, mode, and standard deviation for a stream of data.

Software Engineer Interview

Given a list of items with varying weights and a maximum weight capacity per box, design an algorithm from scratch that packs all the items into as few boxes as possible.

Software Engineer Interview

Implement a vector class that supports initialization and a push_back method to add elements to the vector.

Software Developer Interview

How can you optimally distribute food to various groups of people, considering the time it takes to reach each group and the rate at which the food cools during transport?

Software Developer Interview

Read a list of word strings from standard input. Output each unique word along with its count, and also output the frequency of each letter from 'a' to 'z' across all the input words.

Software Engineer Interview

Describe how you would insert a node into a binary search tree in a thread-safe manner without requiring locking mechanisms.

Software Engineer Interview

Implement the longest common subsequence (LCS) algorithm.

Software Developer Interview

Given an array A, sort it so that A[0] < A[1] > A[2] < A[3] > A[4] < A[5] ... and so on. Provide an efficient algorithm to perform this unusual sort.

Software Engineer Interview

Given an array of integers, find the largest product that can be obtained by multiplying any two numbers from the array.

Software Engineer Interview

Given an integer, find the number of 1 bits in its binary representation.

Software Engineer Interview

List three ways to check if a number is a power of 2.

Developer Interview

Why might multiple threads calling a simple function involving array access or possible modification be much slower than a single thread calling the function?

Software Engineer Interview

What is a deadlock, and how can deadlock be prevented?

Software Engineer Interview

What is virtual memory?

Software Engineer Interview

An hour is to a minute as a minute is to what?

Trader Interview

What is 0.6 divided by 0.03?

Trader Interview

What is the angle between the hour and minute hands of a clock at 3:15?

Trader Interview

After 3 o'clock, at what time do the hour and minute hands of a clock next coincide?

Trader Interview

What is the expected value of a die? What would you pay to play the game if you only played once? What if you played a thousand times? Now, if you get a chance to reroll, what would you set as the price of the game?

Trader Interview

Find the next letter in the sequence: A, C, E, G, ?

Trader Interview

You and your friend continuously toss a fair coin. If the sequence HH (two consecutive heads) appears first, you win. If the sequence TH (tail followed by head) appears first, your friend wins. Who is more likely to win?

Trader Interview

What is the value of 8415 divided by 85? Provide your answer using mental math.

Trader Interview

Calculate the product of 4.3 and 3.43.

Trader Interview

Find the next number in the sequence: 1, -1, 3, -2, 5, -3, 7.

Trader Interview

What is 299 multiplied by 17? Calculate the answer using mental math.

Trading Interview

What is the expected value of a standard six-sided die?

Trading Interview

What is the result of adding 1940.42 and 4392?

Trading Interview

If you have a 10x10x10 cube and you paint its outside, how many of the smaller cubes have paint on them? (Solve in 90 seconds.)

Trading Interview

Given a 10×10×10 cube made up of 1×1×1 smaller cubes, how many 1×1×1 cubes are there in the outer layer?

Trading Interview

What is the product of 27 and 37?

Trading Interview

What is the probability of getting 3 heads when tossing 3 coins, given that at least 1 head has occurred?

Trading Interview

Find the next value in the sequence: M, A, M, J, J.

Trading Interview

What is a fair payout for a game where you draw a number from 1 to 12 and win the amount of the number you draw, but you can either keep the first card or discard it and draw a second card (which you must keep)?

Trading Interview

If it is now three o'clock, at what time will the minute hand and hour hand next coincide?

Trading Interview

A lily pad doubles in size every day and takes 30 days to cover a pond. If you start with 8 lily pads instead of 1, how many days will it take to cover the pond?

Trading Interview

If I flip 3 coins and tell you that at least one is heads, what is the probability that all 3 are heads?

Trading Interview

Divide 472,865 by 2,324.

Trading Interview

A coin is flipped 4 times. You can receive $20 for each heads, or $500 if all 4 are heads. Which option would you choose, and why?

Trading Interview

What is 23 + 45?

Trading Interview

100

Design a class that can handle streaming price data. Implement a function to get the top 5 prices and another function to get the most frequent price.

Quantitative Developer Interview

101

What is the expected number of steps for a robot to walk from one vertex of a cube to the opposite vertex, moving only along the edges of the cube, if the robot picks an adjacent vertex uniformly at random at each step?

Quantitative Developer Interview

102

How many ways are there to arrange the digits 0 through 9 in a sequence so that each digit is either an integer multiple or a divisor of each of its neighbors?

Quantitative Developer Interview

103

Create a Python class that keeps track of the score in a bowling game and updates the score based on inputs representing how many pins were knocked over in each turn.

Quantitative Developer Interview

104

Find the eigenvalues and eigenvectors of an n by n matrix where every entry is 1.

Quantitative Developer Interview

105

Write a Python function to rotate the elements of an N x N matrix by 90, 180, or 270 degrees, in either a clockwise or counterclockwise direction.

Quantitative Developer Interview

106

Write a program that compares the words in two text documents.

Quantitative Developer Interview

107

1. Compare the value of two hands of cards. 2. Find the maximum among the shortest paths from a source to all other nodes in a directed graph. 3. Determine if there exist three collinear points in a given list of points.

Quantitative Developer Interview

108

Given an array of digits where numbers may appear multiple times, write a function to return a sorted array containing each unique digit only once. For example, input: [0,0,0,1,1,2,3,3,3,3] output: [0,1,2,3].

Quantitative Developer Interview

109

Given a set of lines, return the count of unique words and unique letters. A word is defined as any sequence of one or more lowercase letters, and words are separated by white spaces.

Quantitative Developer Interview

110

N coffee chains are competing for market share through advertising. Each day, a percentage of customers switch from one chain to another. You are given the current market share vector and a daily customer switching probability matrix. If advertising continues indefinitely, what will be the final (steady-state) distribution of market share? Assumptions: N is an integer less than 25. Total market share is 1.0. The probability that a customer switches is independent across customers and days. Example: 2 coffee chains: A and B Initial market share: A: 0.4, B: 0.6 Switching matrix: [[0.8, 0.2],[0.1, 0.9]] where the element at row i, column j represents the probability a customer of chain i switches to chain j each day. Output: [0.3333, 0.6667]

Quantitative Developer Interview

111

A coin is repeatedly tossed until there is a winner. Player A wins if two heads appear consecutively. Player B wins if the first toss is heads and the second toss is tails. Who has a better chance to win?

Quantitative Developer Interview

112

Given a string containing brackets (such as '{}', '[]', '()'), determine if the sequence is valid. For example, '{{}}' is valid (true); '{)}(' is invalid (false); '{}[]' is valid (true).

Quantitative Developer Interview

113

Given a string containing the characters '(', ')', '[', ']', '{', and '}', determine if the parentheses are correctly matched and properly nested.

Quantitative Developer Interview

114

There are N satellites that can deliver messages. Each satellite can only send messages to a specific subset of satellites, and each message transmission has an associated time delay. Given the starting satellite that initiates the message, return the minimum time required for all satellites to receive the message. If it is not possible for all satellites to receive the message, return -1.

Quantitative Developer Interview

115

1. Given a list of numbers with some repeated elements, return a new list in which each element appears only once. For example, input list: [1, 2, 2, 3, 4, 4], output: [1, 2, 3, 4]. 2. Return the powers of 2 in the inclusive range [low, high], where 'low' and 'high' are positive integers. 3. Define a class with the following methods: (1) insert(value): insert a value into its internal attribute; (2) get_max(): return the maximum value; (3) get_mode(): return the mode; (4) get_mean(): return the mean.

Quantitative Developer Interview

116

1. Rotate a matrix anti-clockwise; the matrix may be rectangular. 2. Given a sorted array, find the median of the subarray containing values greater than or equal to k. 3. Given multiple lines of text, count all words and alphabetic characters. 4. Design an order book.

Quantitative Developer Interview

117

1. Given an array, find the median of the elements that are less than a given number k. Assume k exists in the array. 2. Find the number of palindrome dates in the format MMDDYYYY in a given century (for example, 1000-9999). 3. You are given an array of numbers representing old trades, each labeled as 'good' or 'bad'. Predict the label for a new array of trades. 4. Given a grid containing 0s, -1s, and 1s, where you can walk only on 0s, determine if you can reach any of the cells with value 1, starting from any location. Print yes or no.

Quantitative Developer Interview

118

What are the names of some sorting techniques and what are their algorithms?

Quantitative Developer Interview

119

What is the probability that a randomly chosen integer from 1 to 60,000 does not contain the digit 6?

Quantitative Developer Interview

120

How would you implement a data structure to efficiently compute the median of a stream of numbers as new numbers are added?

Quantitative Developer Interview

121

What is the time complexity of inserting an element into a heap?

Quantitative Developer Interview

122

What is the inverse of the covariance matrix?

Quantitative Analyst Interview

123

Find all 'special primes' less than a given number N, where a 'special prime' is defined as a prime number that has both 3 and 5 as factors. Explain the algorithm you would use and analyze its time complexity.

Quantitative Analyst Interview

124

Given the coordinates of the three vertices of a triangle, find all the integer coordinate points (lattice points) that lie inside or on the boundary of the triangle.

Quantitative Analyst Interview

125

How many numbers contain the digit 7 in the range from 1 to 1 billion, exclusive?

Quantitative Trader Interview

126

What is the expected value of the sum when rolling three fair six-sided dice?

Quantitative Trader Interview

127

A clock was dropped and broke into three pieces. Each piece has a set of consecutive numbers such that the sum of the numbers on each piece is equal. What numbers are on each piece?

Quantitative Trader Interview

128

You have a 100-sided die with numbers 1 to 100 on each side. You get paid an amount in dollars equal to the number you roll (e.g., $50 for rolling 50, $75 for 75, etc.). If you are unsatisfied with your roll, you can pay $1 to roll again. You may roll as many times as you want. What is the maximal amount you should be willing to pay to play this game (i.e., for the first roll)? What is the optimal strategy?

Quantitative Trader Interview

129

There is a clock with the numbers from 1 to 12. It breaks into 3 pieces such that the sum of the numbers on each piece is equal. What are the three pieces the clock broke into?

Quantitative Trader Interview

130

Calculate 58 multiplied by 65 without using a calculator.

Quantitative Trader Interview

131

What is the square root of 918?

Quantitative Trader Interview

132

Given up to two drones, each assigned to a unique housing grid in SimpleTown USA, and a delivery sequence consisting of 'grid-home' identifiers, determine the minimum total time (in minutes) required for the swarm to complete the deliveries in exact order. Each drone starts at home 1 on its grid and can, in one minute, move to the next house, make a delivery, or wait. All deliveries must occur in the provided order. For each test case, you are given the number of packages and the delivery sequence.

Quantitative Trader Interview

133

What is the result of multiplying 11.45 by 3?

Intern Interview

134

You have a 10x10x10 cube composed of 1x1x1 smaller cubes. If you remove the entire outer layer, how many 1x1x1 cubes remain?

Intern Interview

135

How can you divide the numbers on a clock (1 to 12) into groups such that the sum of each group's numbers is equal?

Intern Interview

136

Design a class that can be used to track and calculate bowling scores.

Python Developer Interview

137

Which computer architecture might encounter problems due to deep recursive function calls, and why?

Python Developer Interview

138

Given an array of integers, find the minimum number of cuts required to split the array into subarrays such that the greatest common divisor (GCD) of each subarray is greater than 1.

Python Developer Interview

139

What is garbage collection in Python?

Software Developer (Python) Interview

140

What is the 'yield' keyword in Python and how is it used?

Python Developer Interview

141

Given a train schedule and a source and destination (point A to point B), write a program to calculate the minimum time required to catch the trains to travel from point A to point B. Assume the schedule includes departure and arrival times for each train, and you can transfer between trains where schedules permit.

Junior Quantitative Developer Interview

142

Design a class that supports the following methods: add, remove, get_mean, and get_mode. Additionally, if a range is given, implement a method to find the mode (get_mode) for that interval.

Junior Quantitative Developer Interview

143

Given two sentences, find and return the words that appear in both sentences.

Junior Quantitative Developer Interview

144

Given an integer input n, determine whether it can represent the volume of a 3-dimensional figure with integer side lengths, where each side is at least 2 (i.e., n can be factored into three integers each greater than or equal to 2). For example, 8 = 2 x 2 x 2 -> Yes; 10 = 5 x 2 -> No; 12 = 2 x 2 x 3 -> Yes.

Junior Quantitative Developer Interview

145

Verify if two triangles are similar by checking if one can be obtained from the other through 1) translation and 2) rotation.

Junior Quantitative Developer Interview

146

Given a random, unknown population from which you draw one billion samples, how would you estimate the 99th percentile of the population?

Junior Quantitative Developer Interview

147

What is the value of 0.45 multiplied by 62? Solve this using mental math.

Trading Intern Interview

148

What is 64 plus 37?

Trading Intern Interview

149

Implement an order book that supports Good-Til-Canceled (GTC) and Fill-and-Kill (FAK) order types.

C++ Software Engineer Interview

150

Implement a vector data structure using a dynamic array.

C++ Software Developer Interview

151

Implement a C++ string class from scratch, including memory management, copy/move constructors, assignment operators, and relevant string manipulation methods.

C++ Software Engineer Interview

152

Given a set of numbers and an integer k, count the number of all arrays of size k composed of numbers from the input set such that the first number in each array is coprime to every other number in the array.

C++ Developer Interview

153

Implement a thread-safe circular buffer.

C++ Developer Interview

154

Describe the difference between a mutex and an atomic variable.

C++ Developer Interview

155

Describe what a smart pointer is and explain what determines the size of a smart pointer.

C++ Developer Interview

156

1. Check if a number is a power of 2. 2. Write code for the pair-sum problem: given an array, determine if there are two numbers whose sum equals a target value. Explain how to solve it in O(n log n) and O(n) time. 3. What is the difference between a pointer and a reference in C++? When should you use each?

Software Developer C/C++ Interview

157

What is the result of multiplying 123 by 57?

Quant Trader Interview

158

Given a biased coin that lands heads 70% of the time, how can you use it to generate a random outcome with a 50-50 probability?

Quant Trader Interview

159

What is the result of multiplying 89 by 23?

Quant Trader Interview

160

What is the result of 18 multiplied by 56? Solve this mentally, without using a calculator, in under 10 seconds.

Quant Trader Interview

161

Given an initial market share vector and a transition probability matrix, what is the final market share after many transitions?

Quant Trader Interview

162

What is the sum of all numbers from 1 to 100, excluding numbers that contain the digits 7 or 8?

Junior Quant Developer Interview

163

Given an unsorted array, remove duplicate elements while maintaining the original order of appearance.

Junior Quant Developer Interview

164

Given a set of points in a plane, find the point that has the minimum sum of distances to all the given points.

Junior Quant Developer Interview

165

Given the sequence: 12, 1112, 3112, 132112, what is the next term in the sequence?

Quant Trader Intern Interview

166

Given the official rules of 10-pin bowling, implement a program that calculates the score for a player, handling all scoring rules including strikes, spares, and the final frame nuances.

Internship Interview

167

What is 58 multiplied by 29.3?

Internship Interview

168

Design a URL shortening system.

Software Engineer Interview

169

Implement a thread-safe Least Recently Used (LRU) cache.

Software Engineer Interview

170

Implement an STL-like vector from scratch.

Software Engineer Interview

171

Given an array containing stocks, exchanges, and transaction times, design an algorithm to detect front running activities.

Software Engineer Interview

172

What is the time complexity of accessing an element from a vector?

Developer Interview

173

How would you design a controller for a set of traffic lights?

Software Engineer Interview

174

Design a class that efficiently computes the running mean, mode, and standard deviation for a stream of data.

Software Engineer Interview

175

Given a list of items with varying weights, and a weight limit per box, design an algorithm from scratch that packs the items into as few boxes as possible.

Software Engineer Interview

176

Implement a vector class that supports initialization and the push_back operation.

Software Developer Interview

177

How can you optimally distribute food to various groups of people, given the time it takes to reach each group and the rate at which the food cools?

Software Developer Interview

178

Implement a BuyOrder class. Orders should be maintained in a collection sorted by price.

Software Engineer Interview

179

Read word strings from standard input, and output each word along with its count and the frequency of letters 'a' to 'z'.

Software Engineer Interview

180

Describe how to insert a node into a binary search tree in a thread-safe manner without using locks.

Software Engineer Interview

181

Implement the Longest Common Subsequence (LCS) algorithm.

Software Developer Interview

182

Given an array A, rearrange it so that A[0] < A[1] > A[2] < A[3] > A[4] < A[5] ..., alternating between less than and greater than for consecutive elements.

Software Engineer Interview

183

Given an integer, find the number of 1 bits in its binary representation.

Software Engineer Interview

184

List three different ways to check if a given number is a power of 2.

Developer Interview

185

Why might multiple threads calling a simple function involving array access or modification be much slower than a single thread calling the same function?

Software Engineer Interview

186

What is deadlock? How can deadlock be prevented?

Software Engineer Interview

187

What is the difference between a process and a thread?

Software Engineer Interview

188

What is virtual memory?

Software Engineer Interview

189

Describe the garbage collector in Python and explain how it manages memory.

Junior Python Developer Interview

190

What is a named tuple?

Junior Python Developer Interview

191

What is a defaultdict?

Junior Python Developer Interview

192

How would you make an object instance callable?

Junior Python Developer Interview

193

What do the @property, @classmethod, and @staticmethod decorators do in Python?

Junior Python Developer Interview

194

How does Python manage memory?

Junior Developer (Python) Interview

195

How do you remove duplicated items from a list? What is the time complexity of your algorithm?

Junior Developer (Python) Interview

196

1. Profitable Project Pairs: Calculate the number of profitable pairs using binary search. 2. Maximum Swaps: Given two lists, and a limited time, swap elements between the two lists to maximize the number of unique elements in the first list. 3. Binary Circuit: Given a binary string, calculate the cost of moving all 1s to the right.

Quantitative Researcher Interview

197

Implement gradient descent to solve an optimization problem.

Quantitative Researcher Interview

198

Given a positive integer n, output all possible permutations of the numbers from 1 to n.

Quantitative Researcher Interview

199

1. Let X and Y be independent normal random variables with standard deviations a and b, respectively. What is the possible range of standard deviations for X + Y? 2. If you flip a fair coin 4 times, what is the probability of getting an even number of heads? What about flipping the coin 10 times? For n flips with only one fair coin, what is the probability of getting an even number of heads?

Quantitative Researcher Interview

200

A stick is broken at a random point into two pieces. Then, the longer segment is broken again at a random point into two pieces. What is the probability that the resulting three segments can form a triangle?

Quantitative Researcher Interview

201

Implement a class that stores values and provides methods to get the mean, maximum, and mode of the values. Can you optimize your solution to efficiently compute the mean, max, and mode?

Quantitative Researcher Interview

202

Find the eigenvalues and eigenvectors of an n x n matrix where all diagonal entries are n and all off-diagonal entries are 1.

Quantitative Researcher Interview

203

Implement gradient descent in Python.

Quantitative Researcher Interview

204

Given a list of elements, return a new list containing only the elements that appear exactly once in the original list.

Quantitative Researcher Interview

205

Describe stochastic gradient descent (SGD) and stochastic gradient descent with momentum, highlighting the differences between the two optimization algorithms.

Quantitative Researcher Interview

206

Describe an algorithm to count the number of strongly connected components in a directed graph.

Quantitative Researcher Interview

207

A building has 10 doors. For each door, you know the probability of escaping, the probability of dying, and the probability of returning to the same point. Which strategy would you choose to maximize your chance of escaping the building, and why?

Quantitative Research Interview

208

Let X be the sum of N independent random variables each following a uniform distribution. What is the distribution of X?

Quantitative Research Interview

209

Given four independent and identically distributed uniform random variables on [0,1], we create two line segments: one connecting the first two variables and one connecting the last two variables. What is the probability that these two segments overlap?

Quantitative Researcher Interview

210

Given two arrays, each containing n strings, compare corresponding strings from both arrays. For each pair, build a frequency map of characters. If for every character present in either string, the absolute difference in counts for that character between the two strings is less than 3, print 'yes'. Otherwise, print 'no'. For example: string1 = 'aaabbb', string2 = 'aabb'; the difference for 'a' is 1, for 'b' is 1, both less than 3, so the result is 'yes'.

Quantitative Researcher Interview

211

Find the integer-coordinate points inside a triangle that have the shortest total distance to the triangle's three vertices.

Quantitative Researcher Interview

212

What is the probability that three random points on a unit circle form a triangle that contains the center of the unit circle?

Quantitative Researcher Interview

213

Given a square matrix, write code to rotate the matrix by 90, 180, and 270 degrees clockwise.

Quantitative Researcher Interview

214

Write a program to determine whether two triangles are equivalent, where equivalence is defined as one triangle being able to exactly cover the other after rotation and translation.

Quantitative Researcher Interview

215

What is the probability that the sum of N independent and identically distributed uniform random variables on [0, 1] is less than 1?

Quantitative Researcher Interview

216

Let X and Y be independent and identically distributed random variables with a standard normal distribution, i.e., X, Y ~ N(0,1). What is the conditional probability density function of X given that X + Y = 1, i.e., p(X | X + Y = 1)?

Quantitative Researcher Interview

217

What is the difference between uncorrelated and independent random variables? Provide an example of two random variables that are uncorrelated but not independent.

Quantitative Researcher Interview

218

Given a two-dimensional array representing the positions of stones and a rope of known length, determine the maximum number of stones you can fully enclose with the rope. The rope must form a closed loop around the stones.

Quantitative Researcher Interview

219

How many numbers between 1 and 10,000 inclusive contain at least one zero in their decimal representation?

Quantitative Researcher Interview

220

What are the eigenvalues of an n x n matrix with n on the diagonal and 1 elsewhere?

Quantitative Researcher Interview

221

You roll a 100-sided die. After each roll, you can either accept the value shown and win that amount in dollars, or pay $1 to roll again. What is the optimal strategy to maximize your expected winnings?

Intern Trader Interview

222

What is 97% of 2100? Approximate your answer within 5 seconds.

Trader Intern Interview

223

MVEMJS_ : What is the next letter in this sequence?

Trader Intern Interview

224

Given the sequence: J, F, M, A, M, J, J, A, (S), what is the next letter in the sequence, where each letter represents the first letter of the months of the year?

Trader Intern Interview

225

1. Compute P(X > 3Y), where X and Y are independent and identically distributed standard normal random variables (N(0,1)). 2. Compute P(X > 3Y | X > 0), where X and Y are independent and identically distributed standard normal random variables (N(0,1)). 3. How do your answers change if X and Y are correlated Gaussian variables? 4. Coding: Write a function to generate the power set of a given set.

Junior Quantitative Researcher Interview

226

1. Compute P(X > 3Y) where X and Y are i.i.d. N(0, 1). 2. Compute P(X > 3Y | X > 0). 3. How would your answer change if X and Y are correlated normal variables? 4. Coding: Write a program to find the power set of a given set.

Junior Quantitative Researcher Interview

227

1. Compute P(X > 3Y) for X and Y independent and identically distributed as N(0,1). 2. Compute P(X > 3Y | X > 0). 3. How does the probability change if X and Y are correlated Gaussian random variables? 4. Coding: Write code to find the power set of a given set.

Junior Quantitative Researcher Interview

228

How much would you pay to play a game where you win $32 if you flip 5 heads in a row with a fair coin?

Junior Quant Trader Interview

229

You have a fair 100-sided die and can roll it up to 20 times. What is the expected sum of the numbers rolled?

Junior Quant Trader Interview

230

What will happen if you pass a reference as an argument to std::thread in C++?

Junior Software Developer Interview

231

Given a binary string, determine if it represents a power of five. If not, break the string into substrings that each represent powers of five.

Junior Software Engineer Interview

232

Find a point inside a triangle that minimizes the sum of its distances to the three vertices.

Quantitative Research Analyst Interview

Quant Interview Questions

What is 15% of 235?

What is the fair value of a game where you receive $14 if you roll a total of 11 or 12 in two dice rolls, and $0 otherwise?

What is 19% of 270?

What is 12% of 240?

If there are exactly 5 people and exactly 5 seats around a round table, what is the probability that those 5 people will sit in perfectly ascending or descending age order?

You roll a 100-sided die and receive a payout equal to the number on the top face. What is a fair price to pay to play this game? Now, suppose you may re-roll the die any number of times for $1 per re-roll. What is the fair price to pay to play this modified game?

M, V, E, M, J: Which letter comes next in the sequence?

What is the next letter in the sequence: F, S, T, F, F, S?

What is the result of multiplying 45 by 22?

What is the expected value of the random variable corresponding to a fair six-sided die roll? What is the expected value if you can choose to reroll the die once, keeping the higher result to maximize your value?

What is the result of 141 minus 54?

Given the sequence M, J, J, A, S, O, what is the next element in the series?

A colony of bacteria doubles in size every minute. After 60 minutes, it reaches its full size container. At what minute was the container half full?

It is currently 3:00 PM. After how much time, to the nearest second, will the hour and minute hands of a clock overlap?

You have 1000 1x1x1 cubes and form a 10x10x10 cube with them. You remove the outer layer of small cubes. How many cubes have you removed?

Multiply 94 and 48 in your head.

Describe two probabilistic scenarios that have the same expected value but different variances.

Calculate 57 multiplied by 22 and 3230 divided by 34.

Calculate the product of 47 and 75.

What is the result of subtracting 53.9 from 84.2?

What is the sum of the interior angles of an octagon?

What is the angle between the hour hand and the minute hand of a clock when the time is 3:15?

What is the result of subtracting 28.3 from 45.1?

What is the result of multiplying 38 by 79?

What is the result of multiplying 19 by 32?

Given the sequence M, J, J, A, S, O, what is the next letter in the sequence?

What is thirty-five times thirty-five?

What is the probability of getting three heads in a row when tossing a fair coin five times?

Game 1 pays $20 if you flip at least one heads when flipping a coin 4 times, while Game 2 pays $500 if you flip heads on all 4 flips. Which game should you choose?

A 10 × 10 × 10 cube has all its surfaces painted red. If the cube is broken into 1000 unit cubes, how many of those unit cubes have at least one red face?

You have 3,000 apples and one truck that can carry a maximum of 1,000 apples at a time. For every mile the truck travels, one apple is lost (destroyed) from the load. What is the maximum number of apples you can transport to a city 1,000 miles away?

Given a list of projects, each with a profit value, calculate the number of pairs of projects whose combined profit exceeds a certain threshold. Use binary search to efficiently determine the count of such pairs.

Output all permutations of size n.

You break a stick into two pieces at a random point, then break the longer segment again at a random point along its length. What is the probability that the resulting three segments can form a triangle?

Implement a class that stores values and provides methods to get the mean, max, and mode of the values. How can you optimize your solution for efficiently computing the mean, max, and mode?

1. What is the derivative of the function f(x) = x^x? 2. Find the eigenvectors and eigenvalues of an n x n matrix with n on the diagonal and ones in every off-diagonal entry.

Implement gradient descent in Python.

Given a list, return a new list containing only the non-repetitive (unique) elements from the original list.

Describe an algorithm to count the number of strongly connected components in a directed graph.

Given a building with 10 doors, and for each door, you know the probability of escaping, dying, and returning to the same point. Which strategy would you choose to maximize your chances of escaping the building, and why?

Let X be the sum of N independent random variables, each following a uniform distribution. What is the distribution of X?

Given four independent and identically distributed uniform random variables on [0,1], we form two line segments by connecting the first two and the last two. What is the probability that these segments overlap?

Find the integral points inside a triangle that have the shortest total distance to the three vertices.

What is the probability that three random points on a unit circle will form a triangle that includes the center of the unit circle?

Given an n x n matrix, write a function to rotate the matrix by 90, 180, and 270 degrees clockwise. Return the resulting matrices for each rotation.

Write a program to determine whether two triangles are equivalent. Equivalence is defined as one triangle being able to exactly cover the other after applying rotations and translations (i.e., rigid motions).

Let X and Y be independent, identically distributed standard normal random variables (X, Y ~ N(0, 1), iid). What is the conditional distribution of X given that X + Y = 1?

Design a URL shortening system.

What is the difference between uncorrelated and independent random variables? Give an example of two random variables that are uncorrelated but not independent.

Given a two-dimensional array representing positions of stones and a rope of a known length, determine the maximum number of stones that can be enclosed by the rope. The rope must form a closed loop.

How many numbers between 1 and 10,000 inclusive contain the digit zero at least once?

What are the eigenvalues of the n x n matrix where each diagonal element is n and all off-diagonal elements are 1?

Implement a thread-safe Least Recently Used (LRU) cache.

Implement your own version of the STL vector data structure.

Given an array of stocks, exchanges, and timestamps, design an algorithm to detect evidence of front running.

What is the time complexity of accessing an element from a vector?

Design a class that efficiently computes the running mean, mode, and standard deviation for a stream of data.

Given a list of items with varying weights and a maximum weight capacity per box, design an algorithm from scratch that packs all the items into as few boxes as possible.

Implement a vector class that supports initialization and a push_back method to add elements to the vector.

How can you optimally distribute food to various groups of people, considering the time it takes to reach each group and the rate at which the food cools during transport?

Read a list of word strings from standard input. Output each unique word along with its count, and also output the frequency of each letter from 'a' to 'z' across all the input words.

Describe how you would insert a node into a binary search tree in a thread-safe manner without requiring locking mechanisms.

Implement the longest common subsequence (LCS) algorithm.

Given an array A, sort it so that A[0] < A[1] > A[2] < A[3] > A[4] < A[5] ... and so on. Provide an efficient algorithm to perform this unusual sort.

Given an array of integers, find the largest product that can be obtained by multiplying any two numbers from the array.

Given an integer, find the number of 1 bits in its binary representation.

List three ways to check if a number is a power of 2.

Why might multiple threads calling a simple function involving array access or possible modification be much slower than a single thread calling the function?

What is a deadlock, and how can deadlock be prevented?

What is virtual memory?

An hour is to a minute as a minute is to what?

What is 0.6 divided by 0.03?

What is the angle between the hour and minute hands of a clock at 3:15?

After 3 o'clock, at what time do the hour and minute hands of a clock next coincide?

What is the expected value of a die? What would you pay to play the game if you only played once? What if you played a thousand times? Now, if you get a chance to reroll, what would you set as the price of the game?

Find the next letter in the sequence: A, C, E, G, ?

You and your friend continuously toss a fair coin. If the sequence HH (two consecutive heads) appears first, you win. If the sequence TH (tail followed by head) appears first, your friend wins. Who is more likely to win?

What is the value of 8415 divided by 85? Provide your answer using mental math.

Calculate the product of 4.3 and 3.43.