Brain Teasers Flashcards
- How many gallons of white house paint are sold in the U.S. every year?
THE START BIG APPROACH: If you re not sure where to begin, start with the basic assumption that there are 270 million people in the U.S. (or 25 million businesses, depending on the question). If there are 270 million people in the United States, perhaps half of them live in houses (or 135 million people). The average family size is about three people, so there would be 45 million houses in the United States. Let s add another 10 percent to that for second houses and houses used for other purposes besides residential. So there are about 50 million houses.
If houses are painted every 10 years, on average (notice how we deftly make that number easy to work with), then there are 5 million houses painted every year. Assuming that one gallon of paint covers 100 square feet of wall, and that the average house has 2,000 square feet of wall to cover, then each house needs 20 gallons of paint. So 100 million gallons of paint are sold per year (5 million houses x 20 gallons). (Note: If you want to be fancy, you can ask your interviewer whether you should include inner walls as well.) If 80 percent of all houses are white, then 80 million gallons of white house paint are sold each year. (Don t forget that last step!)
- What is the size of the market for disposable diapers in China?
Here s a good example of a market sizing. How many people live in China? A billion. Because the population of China is young, a full 600 million of those inhabitants might be of child-bearing age. Half are women, so there are about 300 million Chinese women of childbearing age. Now, the average family size in China is restricted, so it might be 1.5 children, on average, per family. Let s say two-thirds of Chinese women have children. That means that there are about 300 million children in China. How many of those kids are under the age of two? About a tenth, or 30 million. So there are at least 30 million possible consumers of disposable diapers.
- How many square feet of pizza are eaten in the United States each month?
Take your figure of 300 million people in America. How many people eat pizza? Let s say 200 million. Now let s say the average pizza-eating person eats pizza twice a month, and eats two slices at a time. That s four slices a month. If the average slice of pizza is perhaps six inches at the base and 10 inches long, then the slice is 30 square inches of pizza. So four pizza slices would be 120 square inches. Since one square foot equals 144 square inches, let s assume that each person who eat pizza eats one square foot per month. Since there are 200 million pizza-eating Americans, 200 million square feet of pizza are consumed in the US each month
- How would you estimate the weight of the Chrysler building?
This is a process guesstimate the interviewer wants to know if you know what questions to ask. First, you would find out the dimensions of the building (height, weight, depth). This will allow you to determine the volume of the building. Does it taper at the top? (Yes.) Then, you need to estimate the composition of the Chrysler building. Is it mostly steel? Concrete? How much would those components weigh per square inch? Remember the extra step find out whether you re considering the building totally empty or with office furniture, people, etc.? (If you re including the contents, you might have to add 20 percent or so to the building s weight.)
- Why are manhole covers round?
The classic brainteaser, straight to you via Microsoft (the originator). Even though this question has been around for years, interviewees still encounter it.
Here s how to solve this brainteaser. Remember to speak and reason out loud while solving this brainteaser!
Why are manhole covers round? Could there be a structural reason? Why aren t manhole covers square? It would make it harder to fit with a cover. You d have to rotate it exactly the right way. So many manhole covers are round because they don t need to be rotated. There are no corners to deal with. Also, a round manhole cover won t fall into a hole because it was rotated the wrong way, so it s safer.
Looking at this, it seems corners are a problem. You can t cut yourself on a round manhole cover. And because it s round, it can be more easily transported. One person can roll it.
- If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands?
The answer to this is not zero! The hour hand, remember, moves as well. The hour hand moves a quarter of the way between three and four, so it moves a quarter of a twelfth (1/48) of 360 degrees. So the answer is seven and a half degrees, to be
- You have a five-gallon jug and a three-gallon jug. You must obtain exactly four gallons of water. How will you do it?
You should find this brainteaser fairly simple. If you were to think out loud, you might begin by examining the ways in which combinations of five and three can come up to be four. For example: (5 - 3) + (5 - 3) = 4. This path does not actually lead to the right answer, but it is a fruitful way to begin thinking about the question. Here s the solution: fill the three-gallon jug with water and pour it into the five-gallon jug. Repeat. Because you can only put two more gallons into the five-gallon jug, one gallon will be left over in the three-gallon jug. Empty out the five-gallon jug and pour in the one gallon. Now just fill the three-gallon jug again and pour it into the five-gallon jug. (Mathematically, this can be represented 3 + 3 - 5 + 3 = 4)
ou are faced with two doors. One door leads to your job offer (that s the one you want!), and the other leads to the exit. In front of each door is a guard. One guard always tells the truth. The other always lies. You can ask one question to decide which door is the correct one. What will you ask?
he way to logically attack this question is to ask how you can construct a question that provides the same answer (either a true statement or a lie), no matter who you ask.
Therearetwosimpleanswers.Askaguard: IfIweretoaskyouifthisdoor were the correct one, what would you say? The truthful guard would answer yes (if it s the correct one), or no (if it s not). Now take the lying guard. If you asked the liar if the correct door is the right way, he would answer no. But if you ask him: If I were to ask you if this door were the correct one, what would you say, he would be forced to lie about how he would answer, and say yes. Alternately, ask a guard: If I were to ask the other guard which way is correct, what would he say? Here, the truthful guard would tell you the wrong way (because he is truthfully reporting what the liar would say), while the lying guard would also tell you the wrong way (because he is lying about what the truthful guard would say).
If you want to think of this question more mathematically, think of lying as represented by -1, and telling the truth as represented by +1. The first solution provides you with a consistently truthful answer because (-1)(-1) = 1, while (1)(1) = 1. The second solution provides you with a consistently false answer because (1)(-1) = -1, and (-1)(1) = -1.
A company has 10 machines that produce gold coins. One of the machines is producing coins that are a gram light. How do you tell which machine is making the defective coins with only one weighing?
Think this through clearly, every machine will have to produce a sample coin or coins, and you must weigh all these coins together. How can you somehow indicate which coins came from which machine? The best way to do it is to have every machine crank a different number of coins, so that machine 1 will make one coin, machine 2 will make two coins, and so on. Take all the coins, weigh them together, and consider their weight against the total theoretical weight. If you re four grams short, for example, you ll know that machine 4 is defective.
What is the decimal equivalent of 3/16 and 7/16?
A commonly-used Wall Street interview question, this one isn t just an attempt to stress you out or see how quick your mind works. This question also has practical banking applications. Stocks often are traded at prices reported in 1/16s of a dollar. If you don t know the answer off the top of your head, an easy way to start is with what you do know. You know 1⁄4 = .25, so dividing each side by 2, 1/8 = .125 and 1/16 = .0625. Just multiple that to get what you re looking for, so 3/16 = .1875 and 7/16 = .4375.
- What is the sum of the numbers from one to 50?
Another question that recent analyst hires often report receiving. This is a relatively easy one: pair up the numbers into groups of 51 (1 + 50 = 51; 2 + 49 = 51; etc.). Twenty-five pairs of 51 equals 1275.
- You have a painting that was $320 which is now selling for 20 percent off. How much is the discounted price?
Calculate quickly: What s 80 percent of $320? The answer is $256. Even in a question like this, if you are good with numbers and use shortcuts, don t be afraid to talk aloud. For example: 80 percent of $320 can be broken down to a calculation like 80 percent of $80 x $4, or $256.
- How many Delta Airlines planes will take off in the next hour in United States?
There are several ways to attack this question. One way is to start by figuring out the number of airports in the United States. Most states have one or two large airports from which a major carrier departs. So on average, you can assume that there are 1.2 large airports per state. Finally, if you say that one Delta plane departs every 10 minutes, you can see that there 6 take off per hour from each airport, so you can estimate that there are
1.2 x 50 x 6, or 360 Delta planes taking off this hou
- If you have seven white socks and nine black socks in a drawer, how many do you have to pull out blindly in order to ensure that you have a matching pair?
Three. Let s see if the first one is one color, and the second one is the other color, the third one, no matter what the color, will make a matching pair. Sometimes you re not supposed to think that hard.
- Say you are driving two miles on a one-mile track. You do one lap at 30 miles an hour. How fast do you have to go to average 60 miles an hour?
This is something of a trick question, and was recently received by a Goldman candidate. The first thought of many people is to say 90 miles an hour, but consider: If you have done a lap at 30 miles an hour, you have already taken two minutes. Two minutes is the total amount of time you would have to take in order to average 60 miles an hour. Therefore, you can not average 60 miles an hour over the two laps.
