Quant interview questions
1,322 questions in the style trading and research firms ask, from probability and brainteasers to options, statistics and coding. Every question is open to read; the 50 in the free sample show their worked solutions here.
149 questions · page 1 of 4 · Clear filters
- How many integers from 1 to 100 share no common factor with 100 other than 1?Counting and combinatorics · Applied
- How many subsets of {1,2,…,10} contain no two consecutive integers? Count the empty set.Counting and combinatorics · Advanced
- X and Y are independent standard normals. What is Pr(Y > 3X)? Give a decimal.Probability · Foundation
- A coin is drawn at random: with probability 1/2 it is fair, otherwise it lands…Probability · Advanced
- You note the height of the first person to walk past, then count how many more…Probability · Advanced
- A coin lands heads with probability 0.6.Probability · Advanced
- You draw independent uniforms on [0,1] until their running sum exceeds one.Probability · Expert
- You estimate π by drawing points uniformly in the unit square and counting the…Probability · Expert
- One of 1000 bottles of wine is poisoned, and the poison kills within a day.Games, decision theory and puzzles · Applied
- A balance, and coins of which exactly one is counterfeit and either heavy or light.Games, decision theory and puzzles · Advanced
- A shuffled deck of 26 red and 26 black cards is turned over one card at a time.Games, decision theory and puzzles · Expert
- You join the best bid behind 1,200 shares already queued at that price.Market making · Foundation
- The best bid is 100.00 for 900 shares and the best offer is 100.10 for 100 shares.Market making · Applied
- Your passive fills capture a half-spread of 2 cents a share and earn a rebate of 0.2 cents.Market making · Applied
- On 6 May 2010 US equities fell several percent and recovered within minutes.Markets and products · Applied
- You solve for implied volatility by bisection on the bracket [0.01,2.00] to a…Option pricing models · Applied
- A Monte Carlo pricer uses 10,000 paths, and the discounted payoffs have a…Option pricing models · Applied
- A matrix has largest singular value 100 and smallest 0.5. What is its condition number?Linear algebra · Applied
- A symmetric matrix has eigenvalues 10, 6 and 2.Linear algebra · Advanced
- Gradient descent with momentum uses a learning rate of 0.01 and β = 0.9.Machine learning · Applied
- The best bid has 300 lots and the best offer 100.Research case studies · Foundation
- You buy 100 shares at $10.00, 300 at $10.20 and 100 at $10.50.Research case studies · Foundation
- You buy at $100.03 when the mid-quote is $100.00.Research case studies · Foundation
- You need to classify trades as buyer- or seller-initiated from trades and quotes.Research case studies · Applied
- Successive trade-price changes have autocovariance −0.0004 (in dollars squared).Research case studies · Advanced
- Daily true variance is (1%)².Research case studies · Advanced
- You need the 100 largest values from a stream of 10⁹ numbers you cannot store.Data structures and algorithms · Foundation · Free solution
- How many comparisons does a binary search need, in the worst case, over a…Data structures and algorithms · Foundation
- A balanced binary search tree holds one million keys.Data structures and algorithms · Foundation
- What is the maximum number of edges in a directed acyclic graph on ten vertices?Data structures and algorithms · Foundation
- How many set bits does the integer 90 have?Data structures and algorithms · Foundation
- How many non-empty contiguous subarrays does an array of length ten have?Data structures and algorithms · Foundation
- How many times does the inner body run in for i in range(1000): for j in range(i): body()?Data structures and algorithms · Foundation
- What is the height (edges on the longest root-to-leaf path) of a binary heap…Data structures and algorithms · Foundation
- A dependency graph has edges a → b, a → c, b → d, c → d.Data structures and algorithms · Foundation
- You climb a staircase of 10 steps, taking one or two steps at a time.Data structures and algorithms · Foundation
- For a positive integer x, which test is true exactly when x is a power of two?Data structures and algorithms · Foundation
- What does the recurrence T(n) = 2T(n/2)+O(n) solve to?Data structures and algorithms · Applied · Free solution
- A hot-path buffer is a dynamic array with O(1) amortised push.Data structures and algorithms · Applied
- Using an unlimited supply of coins worth 1, 3 and 4, in how many ways can you…Data structures and algorithms · Applied