Photo: flickr: kevin dooley

Pencils down.Hopefully you’ve all thought long and hard (or even better, short and hard) about the answers to the Wall Street brain teasers yesterday.

If you didn’t, no matter, here are the answers anyway (along with the questions in case you missed them). We got most of these questions from IBankingFAQ, a site brilliantly recommended by our sources, so if you have a bone to pick, take it up with them.

Now, on to feeling either totally satisfied or totally crushed.

### How many quarters would it take to make a stack from the floor of this room to the ceiling?

Source: Former Wall Street Intern

### Answer: Assume the room is 10 feet high, and assume that 12 quarters is 1 inch tall ...

12 quarters / inch x 12 inches / feet x 10 feet room = 1440 quarters

Source: Former Wall Street Intern

### Three envelopes are presented in front of you by an interviewer ...

One contains a job offer, the other two contain rejection letters. You pick one of the envelopes. The interviewer then shows you the contents of one of the other envelopes, which is a rejection letter. The interviewer now gives you the opportunity to switch envelope choices. Should you switch?

Source: Former M&A analyst/IBankingFAQ

Originally, you had a 1/3 chance that envelope A contained the offer letter. There was a 2/3 chance that the offer letter was either in envelope B or C. If you stick with envelope A, you still have the same 1/3 chance. Now, the interviewer eliminated one of the envelopes (say, envelope B), which contained a rejection letter. So, by switching to envelope C, you now have a 2/3 chance of getting the offer and you've doubled your chances.

Note that you will often get this same question but referring to playing cards (as in 3-Card Monte) or doors (as in Monte Hall/Let's Make a Deal) instead of envelopes.

Source: Former M&A analyst/IBankingFAQ

### A windowless room has 3 light bulbs ...

You are outside the room with 3 switches, each controlling one of the light bulbs. If you can only enter the room one time, how can you determine which switch controls which light bulb?

Source: Former M&A analyst/IBankingFAQ

### Answer: Turn on two switches (call them A and B) and leave them on for a few minutes ...

Then turn one of them off (switch B) and enter the room. The bulb that is lit is controlled by switch A. Touch the other two bulbs (they should be off). The one that is still warm is controlled by switch B. The third bulb (off and cold) is controlled by switch C.

Source: Former M&A analyst/IBankingFAQ

### Four investment bankers need to cross a bridge at night to get to a meeting ...

They have only one flashlight and 17 minutes to get there. The bridge must be crossed with the flashlight and can only support two bankers at a time. The Analyst can cross in 1 minute, the Associate can cross in 2 minutes, the VP can cross in 5 minutes and the MD takes 10 minutes to cross. How can they all make it to the meeting in time?

Source: Former M&A analyst/IBankingFAQ

### Answer: First, the Analyst takes the flashlight and crosses the bridge with the Associate ...

This takes 2 minutes. The Analyst then returns across the bridge with the flashlight taking 1 more minute (3 minutes passed so far). The Analyst gives the flashlight to the VP and the VP and MD cross together taking 10 minutes (13 minutes passed so far). The VP gives the flashlight to the Associate, who recrosses the bridge taking 2 minutes (15 minutes passed so far). The Analyst and Associate now cross the bridge together taking 2 more minutes. Now, all are across the bridge at the meeting in exactly 17 minutes. Note, that instead of investment bankers, you'll often see the same question using members of musical bands (usually either the Beatles or U2).

Source: Former M&A analyst/IBankingFAQ

### A car travels a distance of 60 miles at an average speed of 30 mph. How fast would the car have to travel the same 60 mile distance home to average 60 mph over the entire trip?

Source: Former M&A analyst/IBankingFAQ

### Answer: Most people say 90 mph but this is actually a trick question!

The first leg of the trip covers 60 miles at an average speed of 30 mph. So, this means the car traveled for 2 hours (60/30). In order for the car to average 60 mph over 120 miles, it would have to travel for exactly 2 hours (120/60). Since the car has already traveled for 2 hours, it is impossible for it to average 60 mph over the entire trip.

Source: Former M&A analyst/IBankingFAQ

### What is the angle between the hour-hand and minute-hand of a clock at 3:15?

Source: Former M&A analyst/IBankingFAQ

### Answer: At quarter past the hour, the minute-hand is exactly at 3:00 but ...

The hour-hand has moved 1/4 of the way between 3:00 and 4:00. Therefore 1/4 times 1/12 = 1/48 of the clock. With the clock having 360 degrees, 360/48 = 7.5 degrees.

Source: Former M&A analyst/IBankingFAQ

### You are given a 3-gallon jug and a 5-gallon jug. How do you use them to get 4 gallons of liquid?

Source: Former M&A analyst/IBankingFAQ

### Answer: Fill the 5-gallon jug completely.

Pour the contents of the 5-gallon jug into the 3-gallon jug, leaving 2 gallons of liquid in the 5-gallon jug. Next, dump out the contents of the 3-gallon jug and pour the contents of the 5-gallon jug into the 3-gallon jug. At this point, there are 2 gallons in the 3-gallon jug. Fill up the 5-gallon jug and then pour the contents of the 5-gallon jug into the 3-gallon jug until the 3-gallon jug is full. You will have poured 1 gallon, leaving 4 gallons in the 5-gallon jug.

Source: Former M&A analyst/IBankingFAQ

### You are given 12 balls and a scale ...

Of the 12 balls, 11 are identical and 1 weighs slightly more. How do you find the heavier ball using the scale only three times?

Source: Former M&A analyst/IBankingFAQ

### Answer: First, weigh 5 balls against 5 balls (1st Use of Scale).

If the scale is equal, then discard those 10 balls and weigh the remaining 2 balls against each other (Second Use of Scale). The heavier ball is the one you are looking for.

If on the first weighing (5 vs 5), one group is heavier, then of the heavier group weigh 2 against 2 (2nd Use of Scale). If they are equal, then the 5th ball from the heavier group (the one not weighed) is the one you are looking for. If one of the groups of 2 balls is heaver, then take the heaver group of 2 balls and weigh them against each other (Third Use of Scale). The heavier ball is the one you are looking for.

Source: Former M&A analyst/IBankingFAQ

### You are given 12 balls and a scale ...

Of the 12 balls, 11 are identical and 1 weighs EITHER slightly more or less. How do you find the ball that is different using the scale only three times AND tell if it is heavier or lighter than the others?

Source: Former M&A analyst/IBankingFAQ