S&T quantitative interview questions
I am looking to start a new thread on the types of quantitative/logic/brainteaser types of questions that people have recieved in recent S&T interviews.
Anyone ever heard of the gold bar problem? Here it is..
I have contracted a carpenter to replace the roofing on my house. The project will take 1 week and he requires that I pay him in equal amounts of gold each day for the entire week. All I have is a bar of gold. If I can only cut the gold bar twice how do I pay this carpenter..(given his requirement)?
You worded the question wrong. The brainteaser goes a worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?
You cut the bar at 1/7 and 2/7 which leave a 4/7 bar left.
Day One: You make your first cut at the 1/7th mark and give that to the worker. Day Two: You cut 2/7ths and pay that to the worker and receive the original 1/7th in change. Day three: You give the worker the 1/7th you received as change on the previous day. Day four: You give the worker 4/7ths and he returns his 1/7th cut and his 2/7th cut as change. Day Five: You give the worker back the 1/7th cut of gold. Day Six: You give the worker the 2/7th cut and receive the 1/7th cut back in change. Day Seven: You pay the worker his final 1/7th.
And there you go.
assuming he doesn't spend the 1/7ths...
Do people actually get these correct in interviews if they have never heard them before?
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There's a good book that helps out with these types of questions -- to ensure that interviewees can actually answer these types of questions. really, there are only a handful of trick-types and thousands of variations to the wordings.
Heard on the Street - Timothy Falcon Crack
I've got no problem admitting that there's no way in hell I'd pull the answer to the above question out of my ass during an interview without ever seeing it before. Glad I never got grilled with brainteasers.
the only way to pay him on the first day is to have a piece that is 1/7. so that is one cut the only way to pay him on the second day is to have a piece that is 2/7 or a second that is 1/7, so that is the second cut.
try to make other combos 3/7-7/7 to double check. done.
Who would want to be paid in gold in this environment?
J/ks.
Interesting read.
Does anyone have any good expectation or probability problems they have recieved or know of? It seems like alot of trading firms ask alot of these types of questions.
anything with Bayes' Rule: given P(A given B) and p(B), find P(B given A). Questions like this are often asked in a false-positive / false-negative context.
Here's a question for you - it's a favorite.
Say I offer to play the following game with you. You get to roll a die, and I'll pay you the number of dollars equal to the number of dots facing up.
How much would you pay to play this game?
Answer: 1/6 * (1+2+3+4+5+6) = 3.5
Now, suppose I give you the option of taking the prize money after 1 roll, or if you prefer, you can have another roll and hopefully get more money.
How much would you pay for this option?
Answer: First we calculate the value of this game. Since the expected value of the final roll is 3.5 (above), any first roll less than that will result in the player of the game rolling again. So the value of the game is 1/6 * (3.5 + 3.5 + 3.5 + 4 + 5 + 6) = 4.25
The value of the option is 4.25 - 3.5 = .75
That was mad easy. How was that quant?
Heres an option question..
Suppose that c1, c2, and c3 are the prices of European call options with strike prices K1, K2, and K3, respectively, where K3>K2>K1 and K3-K2=K2-K1. All options have the same maturity.
Show that c2= 0.5 (c1+c3)
(Hint: Consider a portfolio that is long one option with strike price K1, long one option with strike price K3, and short two options with strike price K2). What is the result corresponding to that in above for European put option?
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