2. Brain Teasers & Puzzles (20 questions)

| # | Question | Difficulty | Key Insight | |---|----------|------------|--------------| | 36 | How many times a day do clock hands overlap? | ★ | 22 times | | 37 | You have a 3-gallon and 5-gallon jug. How to measure 4 gallons? | ★ | Fill 5, pour to 3, empty 3, pour remaining 2 into 3, fill 5, pour 1 into 3, left 4 | | 38 | 100 prisoners and a light bulb. Find a strategy to know all have been in room. | ★★★ | Designated counter | | 39 | You have 12 balls, one heavier or lighter, balance scale. Minimum weighings? | ★★ | 3 weighings | | 40 | Why are manhole covers round? | ★ | Can’t fall through | | 41 | How many golf balls fit in a Boeing 747? | ★ | Estimate volume & packing fraction (~0.74) | | 42 | You have a 7-minute and 4-minute hourglass. How to measure 9 minutes? | ★★ | Start both, flip 4 when done, etc. | | 43 | Two trains 100 miles apart approach at 50 mph each. A bee flies 75 mph back and forth. Total bee distance? | ★ | 75 miles (bee flies for 1 hour) | | 44 | You have 10 stacks of 10 coins each, one stack all counterfeit (lighter). One weighing on a scale? | ★★ | Take 1 from stack 1, 2 from stack 2, etc. | | 45 | You have a 5x5 grid of lights. Pressing toggles row & col. Can you turn all off? | ★★ | Linear algebra mod 2 | | 46 | Three ants on corners of triangle, move along edges. Probability no collision? | ★★ | 1/4 | | 47 | You have 2 eggs and 100 floors. Find highest safe floor. Minimum drops? | ★★ | 14 | | 48 | A rope burns unevenly in 60 mins. How to measure 45 mins? | ★ | Light both ends of one rope, one end of other | | 49 | How many trailing zeros in 100! ? | ★ | floor(100/5)+floor(100/25)=24 | | 50 | You have 4 liters of water, need 2 liters. You have 3L and 5L jugs. | ★ | Fill 5, pour to 3, leave 2 in 5 | | 51 | Light switches and bulbs in another room. One flip. How to match? | ★ | Turn one on for long, then off, another on, go check | | 52 | You have 8 coins, one lighter, 2 weighings on balance scale? | ★★ | Divide into 3,3,2 | | 53 | One honest and one liar guard, two doors (life/death). One question? | ★ | Ask “What would the other guard say is the safe door?” | | 54 | You have 9 marbles, one heavier, balance scale in 2 weighings? | ★★ | 3 vs 3 first | | 55 | 100 coins, one counterfeit lighter, no scale, just balance? | ★★ | Binary search |

Part 3: Probability Theory (Questions 41–70)

This is the heart of quant interviews. If you fail probability, you fail the interview.

What is the expected number of coin flips to get two heads in a row? (6).

You have two envelopes. One contains twice as much money as the other. You pick one. Should you switch? (The paradox – standard answer: no difference).

What is the probability that a random chord in a circle is longer than the radius? (Bertrand’s paradox).

You roll a die until you get a 6. What is the expected number of rolls? (6 – geometric distribution).

What is the probability of getting exactly 3 heads in 5 fair coin flips? (10/32 = 5/16).

State the Central Limit Theorem.

What is the difference between correlation and covariance?

What is the Law of Large Numbers?

What is the Martingale property?

You have a bag with 3 red and 3 blue marbles. You draw two without replacement. What is P(both red)? (3/6 * 2/5 = 1/5).

What is the expected value of a standard normal variable? (0).

What is the variance of a standard normal? (1).

What is the moment generating function (MGF) of a normal distribution?

What is the probability that a Brownian motion ever hits 1, starting from 0? (1 – recurrence).

Explain the Monte Carlo method.

What is the difference between weak and strong convergence?

You have 100 people. What is the probability two share a birthday? (~99.97%).

What is the expected number of times you must roll a die to see all six faces? (14.7 – coupon collector).

What is a Poisson process?

What is the Gamma distribution?

What is the difference between probability mass function (PMF) and probability density function (PDF)?

What is a conditional expectation?

What is the Tower property of expectations?

What is the Markov property?

What is the probability that two random numbers between 0 and 1 sum to less than 1? (1/2).

You play a game where you roll a die and receive that many dollars. How much will you pay to play? ($3.50).

What is the St. Petersburg paradox?

What is the probability of drawing a royal flush in poker? (1 in 649,740).

What is the difference between Bayesian and Frequentist probability?

What is a conjugate prior? Give an example for a binomial likelihood. (Beta distribution).

7. Finance & Derivatives (15 questions)

| # | Question | Difficulty | Key Idea | |---|----------|------------|-----------| | 136 | What is the Black-Scholes formula? | ★★ | C = S N(d1) – K e^-rT N(d2) | | 137 | What is a call option? Put option? | ★ | Right to buy/sell | | 138 | What is delta? | ★ | ∂C/∂S | | 139 | What is gamma? | ★ | ∂²C/∂S² | | 140 | What is implied volatility? | ★★ | Vol that makes BS price match market | | 141 | What is the volatility smile? | ★★ | IV varies with strike | | 142 | What is the risk-neutral measure? | ★★★ | Measure where discounted prices are martingales | | 143 | What is a swap? | ★ | Exchange cash flows | | 144 | What is a futures contract? | ★ | Standardized forward | | 145 | What is the difference between hedging and speculation? | ★ | Reduce risk vs seek profit | | 146 | What is value at risk (VaR)? | ★★ | Loss quantile | | 147 | What is the Sharpe ratio? | ★ | (Return – RF)/Volatility | | 148 | What is the Greeks for options? | ★ | Delta, Gamma, Vega, Theta, Rho | | 149 | What is a binomial tree for option pricing? | ★★ | Discrete-time model | | 150 | What is put-call parity? | ★ | C – P = S – K e^-rT |

Category A: Pure Logic

Sample Questions:

The Burning Rope: You have two ropes. Each takes exactly 60 minutes to burn, but they burn at inconsistent rates (e.g., half the rope might burn in 1 minute, the other half in 59). How do you measure exactly 45 minutes?

The Bear: A bear walks 1 mile South, 1 mile East, and 1 mile North, returning to its starting point. What color is the bear?

The Coins on a Table: You and an opponent take turns placing quarters on a round table. The quarters cannot overlap. The last person to place a quarter wins. Do you want to go first or second, and what is your strategy?

Three Ants: Three ants sit on the three corners of a triangle. Each ant randomly picks a direction and starts walking along the edge. What is the probability that none of the ants collide?

The Two Envelopes: You are given two envelopes containing money. One contains twice as much as the other. You pick one, open it, and see $100. Should you switch?

150 Most Frequently Asked Questions On Quant Interviews //free\\

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"150 Most Frequently Asked Questions on Quant Interviews" by Stefanica, Radoicic, and Wang is a key preparation resource for quantitative finance roles, covering topics like mathematics, programming, and brainteasers. The third edition (2024) expands on previous versions by adding over 200 questions, including new content on machine learning, option pricing, and stochastic calculus. For more details, visit FE Press. 150 Most Frequently Asked Questions On Quant Interviews

2. Brain Teasers & Puzzles (20 questions)

Part 3: Probability Theory (Questions 41–70)

This is the heart of quant interviews. If you fail probability, you fail the interview. Part 3: Probability Theory (Questions 41–70) This is

What is the expected number of coin flips to get two heads in a row? (6).
You have two envelopes. One contains twice as much money as the other. You pick one. Should you switch? (The paradox – standard answer: no difference).
What is the probability that a random chord in a circle is longer than the radius? (Bertrand’s paradox).
You roll a die until you get a 6. What is the expected number of rolls? (6 – geometric distribution).
What is the probability of getting exactly 3 heads in 5 fair coin flips? (10/32 = 5/16).
State the Central Limit Theorem.
What is the difference between correlation and covariance?
What is the Law of Large Numbers?
What is the Martingale property?
You have a bag with 3 red and 3 blue marbles. You draw two without replacement. What is P(both red)? (3/6 * 2/5 = 1/5).
What is the expected value of a standard normal variable? (0).
What is the variance of a standard normal? (1).
What is the moment generating function (MGF) of a normal distribution?
What is the probability that a Brownian motion ever hits 1, starting from 0? (1 – recurrence).
Explain the Monte Carlo method.
What is the difference between weak and strong convergence?
You have 100 people. What is the probability two share a birthday? (~99.97%).
What is the expected number of times you must roll a die to see all six faces? (14.7 – coupon collector).
What is a Poisson process?
What is the Gamma distribution?
What is the difference between probability mass function (PMF) and probability density function (PDF)?
What is a conditional expectation?
What is the Tower property of expectations?
What is the Markov property?
What is the probability that two random numbers between 0 and 1 sum to less than 1? (1/2).
You play a game where you roll a die and receive that many dollars. How much will you pay to play? ($3.50).
What is the St. Petersburg paradox?
What is the probability of drawing a royal flush in poker? (1 in 649,740).
What is the difference between Bayesian and Frequentist probability?
What is a conjugate prior? Give an example for a binomial likelihood. (Beta distribution).

7. Finance & Derivatives (15 questions)

Category A: Pure Logic

Sample Questions:

The Burning Rope: You have two ropes. Each takes exactly 60 minutes to burn, but they burn at inconsistent rates (e.g., half the rope might burn in 1 minute, the other half in 59). How do you measure exactly 45 minutes?
The Bear: A bear walks 1 mile South, 1 mile East, and 1 mile North, returning to its starting point. What color is the bear?
The Coins on a Table: You and an opponent take turns placing quarters on a round table. The quarters cannot overlap. The last person to place a quarter wins. Do you want to go first or second, and what is your strategy?
Three Ants: Three ants sit on the three corners of a triangle. Each ant randomly picks a direction and starts walking along the edge. What is the probability that none of the ants collide?
The Two Envelopes: You are given two envelopes containing money. One contains twice as much as the other. You pick one, open it, and see $100. Should you switch?