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86,625 junior interview questions shared by candidates

-If the radius of a sphere is expanding at a rate of 4 metres/second, and the starting radius is 0.25 metres, what is the volume of the sphere after 2 1/2 minutes? -if the mean of X=4 and the variance of X is 9, and the mean of Y=5 and the variance of Y is 16, what is the standard deviation of X + Y given a relationship of -3/8 (x to y)? - there are 3 faucets. Faucet #1 can fill a sink in 20 min, F#2 can fill a sink in 12 min, and F#3 can fill a sink in 5 min. If all 3 faucets are running at the same time, how long will it take for the sink to fill?
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Junior Trader

Interviewed at TransMarket Group

4.1★
Feb 12, 2014

-If the radius of a sphere is expanding at a rate of 4 metres/second, and the starting radius is 0.25 metres, what is the volume of the sphere after 2 1/2 minutes? -if the mean of X=4 and the variance of X is 9, and the mean of Y=5 and the variance of Y is 16, what is the standard deviation of X + Y given a relationship of -3/8 (x to y)? - there are 3 faucets. Faucet #1 can fill a sink in 20 min, F#2 can fill a sink in 12 min, and F#3 can fill a sink in 5 min. If all 3 faucets are running at the same time, how long will it take for the sink to fill?

There are 100 prisoners on an island. Starring from Day 1, a guard will play the following game with them. On the n th day, a random prisoner will be brought into a room, which contains a switch that is either on or off. After he left the room, the guard will then ask the prisoner if everybody has been to the room. He can answer either "Yes" or "I dun know". If he answered "yes" and he is correct, everyone is free' otherwise everyone dies. If he answered "I dun know", the game continues: a prisoner will be choosen at random on (n+1)-th day and so on. Now these 100 prisoners are free to meet and discuss a strategy on the night of 0th day. Afterwards they will not be able to see anyone else at all. No other communcation is possible except the binary switch in the room. Is there a sure-fire strategy to free all of them?
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Junior Proprietary Trading Intern

Interviewed at D. E. Shaw & Co. - Investment Firm

3.8★
Feb 24, 2013

There are 100 prisoners on an island. Starring from Day 1, a guard will play the following game with them. On the n th day, a random prisoner will be brought into a room, which contains a switch that is either on or off. After he left the room, the guard will then ask the prisoner if everybody has been to the room. He can answer either "Yes" or "I dun know". If he answered "yes" and he is correct, everyone is free' otherwise everyone dies. If he answered "I dun know", the game continues: a prisoner will be choosen at random on (n+1)-th day and so on. Now these 100 prisoners are free to meet and discuss a strategy on the night of 0th day. Afterwards they will not be able to see anyone else at all. No other communcation is possible except the binary switch in the room. Is there a sure-fire strategy to free all of them?

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