Book Summary - Heard On The Street - Quantitative Questions from Wall Street Job Interviews

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#Book Summary - Heard On The Street: Quantitative Questions from Wall Street Job Interviews by Timothy Falcon Crack

Heard On The Street is a collection of interview questions (and their answers) asked on Wall Street for quant positions. I never worked on Wall Street, so I cannot talk about whether the questions are indeed often used. I just read it for fun, kind of like puzzling, as most questions are of logical nature that can be answered in a really short elegant way.

I won't post the answers here because 1) it's better if you find a solution on your own and 2) to still give you an incentive to buy the book if you find these kind of questions interesting. That being said, I've heard most of the questions before so you can probably just look up the answers on the internet if you're really curious.

My favourite questions:

#Logic Questions

Q 1.5: Picture a 10 x 10 x 10 "macro-cube" floating in mid-air. The macro-cube is composed of 1 x 1 x 1 "micro-cubes," all glued together. Weather damage causes the exposed (outermost) layer of micro-cubes to become loose. This outermost layer falls to the ground. Нолу many micro-cubes are on the ground?

Q 1.10: There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 stockbrokers lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. Each stockbroker is numbered consecutively from 1 to 100.
Broker number 1 enters the room, switches on every bulb, and exits. Broker number 2 enters and flips the switch on every second bulb (turn- (turning off bulbs 2, 4, 6, ...). Broker number 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, ...). This continues until all 100 brokers have passed through the room.
What is the final state of bulb number 64? Further question: How many of the light bulbs are illuminated after the 100th person has passed through the room, and which light bulbs are they?

Q 1.28: In a certain matriarchal town, the women all believe in an old prophecy that says there will come a time when a stranger will visit the town and announce whether any of the menfolk are cheating on their wives. The stranger will simply say "yes" or "no," without announcing the number of men implicated or their identities. If the stranger arrives and makes his announcement, the women know that they must follow a particular rule: If on any day following the stranger's announcement a women deduces that her husband is not faithful to her, she must kick him out into the street the next day. This action is immediately observable by every resident in the town.
It is well known that each wife is already observant enough to know whether any man (except her own husband) is cheating on his wife. However, no woman can reveal that information to any other. A cheating husband is also assumed to remain silent about his infidelity.
The time comes, and a stranger arrives. He announces that there are cheating men in the town. On the morning of the tenth day following the stranger's arrival, some unfaithful men are kicked out into the street for the first time. Ноw many of them are there? (Come up with a strategy for the women to find out how many cheated.)

Q 1.34: You are standing at the center of a circular field of radius R. The field has a low wire fence around it. Attached to the wire fence (and restricted to running around the perimeter) is a large, sharp- fanged, hungry dog who likes to eat any humans he can catch. You can run at speed v. Unfortunately, the dog can run four times as fast, at 4v.
The dog will do his best to catch you if you try to escape the field. What is your running strategy to escape the field without feeding yourself to the dog?

Q 1.40: We are to play a game on a table in the next room. We each have an infinite bag of identical quarters (i.e., American 25-cent pieces). We will take it in turns to put one quarter on the table. Quarters may not overlap on the table. When there is no room left on the table to put another quarter, the winner is the last person to put a quarter on the table. Let me tell you that there does exist a strategy for winning and that this strategy is independent of the size of the table.

  1. What is the shape of the table?
  2. Do you start?
  3. What is your strategy for winning?
  4. Is there any case where this does not work?

(I skipped the financial questions as I don't have a financial background and was not interested in them.)

#Statistics Questions

Q 4.3: Two sealed envelopes are handed out. You get one and your competitor gets the other. You understand that one envelope contains m dollars, and the other contains 2m dollars (where m is unstated).

  • If you peek into your envelope, you see $X. However, you do not know whether your opponent has $2X or $0.5X. Without peeking, what is your expected benefit to switching envelopes? What is your opponent's expected benefit to switching envelopes (assuming your opponent sees $Y)? Should you switch? If you do, do you do it again for the same reason (assuming neither of you peeked)?
  • Suppose that you both peek into your envelopes initially. What is the payoff to switching? Should you switch? If you do, do you do it again for the same reason?

Q 4.14: Welcome to your interview. Sit in this chair. Excuse me while I tie your arms and legs to the chair. Thank you. Now we are going to play "Russian roulette."
I have a revolver with six empty chambers. Watch me as I load the weapon with two contiguous rounds (i.e., two bullets side-by-side in the cylindrical barrel). Watch me as I spin the barrel. I am putting the gun against your head. Close your eyes while I pull the trigger. Click! This is your lucky day: you are still alive! Our game differs from regular Russian roulette because I am not going to add any bullets to the barrel before we continue, and I am not going to give you the gun.
My question for you: I am going to shoot at you once more before we talk about your resume. Do you want me to spin the barrel once more, or should I just shoot?