Investment Banking Job Interview Question: The Growing Lily Pad

Investment banking job interviews can take many directions. One thing is for sure, your logic and quantitative abilities will be tested. Here is a common question that asks the candidate to dip their toe in the water – so to speak.

Q: You start with a single lily pad floating in an empty pond. If that pad grows and the surface area of the pad doubles every day, it will take 30 days to cover the entire surface of the pond. If instead of one lily pad you start with eight lily pads (each identical in characteristics to the original lily pad), how many days will it take for the surface of the pond to become covered?

A: The trick here is to figure out the relationship between …
… a single lily pad and eight pads. If you think the answer is 3.75 days, work on that relationship before reading the answer.

The lily pads grow at the same rate. Think of the eight pads as one large pad. When a single pad is 3 days old, it has the same surface area as the eight lily pads do at the beginning. You may think of the eight lily pads as a single lily pad that is 3 days old. It takes another 27 days for a 3 day old single lily pad to cover the pond, so it also takes 27 days for the eight pads to cover the pond.

Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews

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