Interview questions

daigo

These came up for a job interview and they had to be answered relatively quickly (most of them should be answered within one minute):

1) Prove the Law of Cosines (For any triangle: a^2=b^2 + c^2 - 2abcos(theta))

2) How much would you pay to play this game: You roll a die and are paid whatever amount comes up on the die. You are allowed to roll again if the number is 4 or above. You do not get to roll again if the number is 3 or below.

3) Give an algorithm to test if a number is prime in time better than O(n)

4) If you pick two numbers between 0 and 1, what is the probability that the product of those two numbers will be greater than .5

5) If you have a fair coin and want to simulate an event that has probability 1/3 and probability 2/3, how can you do that?

6) You have two robots placed randomly on the number line. When they land, they place a marker. You are to program the robots so that they meet, and you are given the following 3 commands: Go left, go right, or if you are on a marker, change strategy. Specify the two strategies so that the robots eventually meet.

7) Give an algorithm to reverse the order of the letters of each word in a sentence. Do not change the order of the words. For instance if your sentence is "I like cookies", this algorithm should return "I ekil seikooc"

8) What is happening in Greece? What countries are in trouble? Why is the Republic of Ireland in trouble? Why are the rest of the countries in trouble? Why do all the european banks have so much Greek debt?

9) There is a 5 game series, and you would like to bet on the outcome of the series. You have 100 dollars. If your team wins, you want to get 200 dollars at the end of the series, if they lose you want 0. The problem is that you can only bet on each individual game. How do you bet on each game?

10) You have a 6 barrel revolver with 2 bullets in it, placed side by side. You are going to play Russian Roulette. You play once and don't die. Do you spin the barrel again and then pull the trigger, or do you just pull the trigger?

11) You have two options. One has a strike price of 1300, one has a strike price of 1400. Which is cheaper and why?

12) What parameters would you need to price an option?

How many could you answer and how quickly?

Hare

Wow. What kind of job was it?

Evo

What kind of job was this for? How do you have a copy of the test? When I've taken employment tests, you were not allowed to take anything with you so that it can't be given out.

Jimmy Snyder

I just picked a few low hanging fruit.

Spoiler

2) 3.5 because the rule that makes you stop playing has no effect on the expected value.

7) While there are input letters take an input letter and see if it is a space. If it is not a space, put it into a LIFO queue. If it is a space, then take the letters off of the LIFO queue one at a time and print them, then print the space. When there are no more letters, take the letters off of the LIFO queue one at a time and print them. Stop.

10) Spin the barrel again for a 2/3 chance of surviving. If you pull the trigger without spinning you will have a 1/2 chance of surviving.

11) 1400 is cheaper because you subtract the strike price from the sale price to determine the value.

12) This one is weird. Options sell in a market that is independent of their underlying securities. However, in general, there is some correlation to: The underlying security, the strike price and the expiration date.

Evo

The OP is a student, I'd be careful about giving answers.

daigo

Quote by Evo

What kind of job was this for? How do you have a copy of the test? When I've taken employment tests, you were not allowed to take anything with you so that it can't be given out.

FIG @ GS, memory

Quote by Evo

The OP is a student, I'd be careful about giving answers.

Didn't ask for solutions, just wanted to discuss the aspects of getting jobs at these types of firms.

Here's some others asked at another company:

How many ridges are on a quarter?
How many libraries are in the U.S.?
How many traffic lights are in Manhattan?
Rank yourself from 1-10, 10 being the best in the following 5 qualities. The total cannot be greater than 35: Intellect, teamwork, communication, finance, attitude

jtbell

Quote by daigo

Here's some others asked at another company:

How many ridges are on a quarter?
How many libraries are in the U.S.?
How many traffic lights are in Manhattan?

Physicists know this kind of question as "Fermi questions," after Enrico Fermi who liked to spring them on his students. The point is not the actual question or answer, but rather the process that you use to estimate an answer, within an order of magnitude or so.

A classic Fermi question is "How many piano tuners are there in Chicago?"

BobG

I wouldn't work there. I'd rather work somewhere they ask you easy questions - like, "How high can you count on your fingers and toes?" Except I'd need a slide rule to even answer that question.

Actually, some of these are easy; some I'd at least know how I wanted to start them, but would need to think about them for a few to refine my answer (the robot question, for example), and I wouldn't have a clue about #11 or #12. Plus, I couldn't answer #5, but at least I knew that immediately.

Biosyn

Quote by daigo

FIG @ GS, memory

FIG? Does that stand for Fortress Investment Group?...

Astronuc

Quote by daigo

These came up for a job interview and they had to be answered relatively quickly (most of them should be answered within one minute):

How many could you answer and how quickly?

From the math, probability, economis and financial questions and terms, I'd imagine this was a financial services company.

*MarcoD*

Well, I wouldn't qualify, but I like the questions. #5 is interesting, for example. Best I could come up with that with a fair coin you can chose between four things A,B,C, and D. So you flip until you hit either an A, or a B or C. So it has an answer as a limit. Can it be done easier?

BobG

Quote by MarcoD

Well, I wouldn't qualify, but I like the questions. #5 is interesting, for example. Best I could come up with that with a fair coin you can chose between four things A,B,C, and D. So you flip until you hit either an A, or a B or C. So it has an answer as a limit. Can it be done easier?

With enough coin flips, you could get close to 1/3 and 2/3 by merging several possible results into one category (4 heads & 3 heads out of 4 flips, for example), but it's impossible to get an exact multiple of 3 using only powers of 2.

*MarcoD*

Quote by BobG

With enough coin flips, you could get close to 1/3 and 2/3 by merging several possible results into one category (4 heads & 3 heads out of 4 flips, for example), but it's impossible to get an exact multiple of 3 using only powers of 2.

Yeah, I had the same conclusion. The answer has to be a 'limit.'

Jimmy Snyder

Quote by MarcoD

Yeah, I had the same conclusion. The answer has to be a 'limit.'

No, just flip twice, 2 heads is A, 1 head, 1 tail is B, 0 heads is ignored.

*MarcoD*

Quote by Jimmy Snyder

No, just flip twice, 2 heads is A, 1 head, 1 tails is B, 0 heads is ignored.

That's the same answer as I gave. (Chose between A,B,C and D with chance 1/4, but try again on D. )

lisab

Clearly, you use the coin to buy a 2/3-headed coin.

*MarcoD*

What about #2? Very sloppily I came up with less than 7, but I am very unsure about it.

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Evo Mentor Blog Entries: 4	What kind of job was this for? How do you have a copy of the test? When I've taken employment tests, you were not allowed to take anything with you so that it can't be given out.

MarcoD	Well, I wouldn't qualify, but I like the questions. #5 is interesting, for example. Best I could come up with that with a fair coin you can chose between four things A,B,C, and D. So you flip until you hit either an A, or a B or C. So it has an answer as a limit. Can it be done easier?

lisab Mentor	Clearly, you use the coin to buy a 2/3-headed coin.