09. Consulting Flashcards
How many people are there in the world, US, and China?
US = 300 million China = 1.5 billion World = 7.0 billion
How many people are there in New York City, Shanghai, Los Angeles and London?
NYC = 8 million
Shanghai = 25 million
Los Angeles = 4 million
London = 8 million
How many households are there in the US?
100 million
How many people are online in the US?
75% of the US population = 225 million people
How many web users are there in the world?
2.5 billion
How many businesses are there in the United States?
30 million
How much pizza is sold in New York City every year?
This is a strict consulting case question; you’ll encounter fewer of these in your interviews. HF/PE consulting questions focus more on business scenarios, but you can get asked this type of question as a brainteaser. These “guestimations” can be solved either “top down” or “bottom up.” Top down approach: Assume that 10 million people live in New York City and that 80 percent of them, or eight million people, eat pizza. Let’s say that the average New Yorker eats pizza twice a month, and will eat two slices each time. If a slice of pizza costs $2, then that’s $4 spent at each sitting and $8 spent each month. That equates to $96 (round to $100 for simplicity) every year. Multiply that by eight million pizza eaters, and the market size for pizza in New York is approximately $800 million. Bottom-up approach: A slice of pizza in New York costs approximately $2 per slice. If the average person has two slices with his meal, then the average ticket (not including drinks) is $4. If the average person eats pizza twice a month, then that’s $8 a month or $96 a year (round to $100 for simplicity). Let’s assume that 80 percent of the 10 million people in New York City eat pizza. That means that the eight million pizza eaters in New York spend approximately $100 each every year on pizza, for a total of $800 million.
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!)
(more of this guesstimate on the next page)
THE “START SMALL” APPROACH: You could also start small, and take a town of 27,000 (about 1/10,000 of the population). If you use the same assumption that half the town lives in houses in groups of three, then there are 4,500 houses, plus another 10 percent, then there are really 5,000 houses to worry about. Painted every 10 years, 500 houses are being painted in any given year. If each house has 2,000 square feet of wall, and each gallon of paint covers 100 square feet, then each house needs 20 gallons - and so 10,000 gallons of house paint are sold each year in your typical town. Perhaps 8,000 of those are white. Multiply by 10,000 - you have 80 million gallons.
Your interviewer may then ask you how you would actually get that number, on the job, if necessary. Use your creativity - contacting major paint producers would be smart, putting in a call to HUD’s statistics arm could help, or even conducting a small sample of the second calculation in a few representative towns is possible.
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 200 million children in China. How many of those kids are under the age of two? About a tenth, or 20 million. So there are at least 20 million possible consumers of disposable diapers.
To summarize:
1 billion people x 60% childbearing age = 600,000,000 people
600,000,000 people x 1/2 are women = 300,000,000 women of childbearing age
300,000,000 women x 2/3 have children = 200,000,000 women with children
200,000,000 women x 1.5 children each = 300,000,000 children
300,000,000 children x 1/10 under age 2 = 30 million
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. Therefore, there are a billion square feet of pizza eaten every month.
To summarize:
300 million people in America
200 million eat pizza
Average slice of pizza is six inches at the base and 10 inches long = 30 square inches (height x half the base)
Average American eats four slices of pizza a month
Four pieces x 30 square inches = 120 square inches (one square foot is 144 inches), so let’s assume one square foot per person
200 million square feet a 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.)
What is the annual US market for chewing gum (in total number of customers)?
- Estimate the total US population (~300 million)
- Segment the population based on some metric (age is usually a good metric)
- Estimate the number of people in each population segment
- Make a guess at the percentage of each segment that chews gum
- Complete the math and arrive at a final answer
How many ping-pong balls fit in a 747?
Let’s assume that the volume of a ping-pong ball is three cubic inches. Now let’s assume that all the seats in the plane are removed. We’ll say the average person is six feet high, one foot wide and one foot deep. That’s 6 cubic feet, or 10,368 cubic inches. (One cubic foot is 12x12x12 inches, or 1,728 cubic inches.)
Okay, so a 747 has about 400 seats in it, excluding the galleys, lavatories, and aisles on the lower deck and about 25 seats on the upper deck. Let’s assume there are three galleys, 14 lavatories, and three aisles (two on the lower deck and one on the upper deck), and that the space occupied by the galleys is a six-person equivalent, by the lavatories is a two-person equivalent, and the aisles is a 50-person equivalent on the lower deck and a 20-person equivalent on the upper deck. That’s an additional 18, 28, and 120 person-volumes for the remaining space. We won’t include the cockpit since someone has to fly the plane. So there are about 600 person-equivalents available. (You would be rounding a bit to make your life easier, since the actual number is 591 person equivalents.)
In addition to the human volume, we have to take into account all the cargo and extra space – the belly holds, the overhead luggage compartments, and the space over the passengers’ head. Let’s assume the plane holds four times the amount of extra space as it does people, so that would mean extra space is 2,400 person-equivalents in volume. (Obviously, this assumption is the most important factor in this guesstimate. Remember that it’s not important that this assumption be correct, just that you know the assumption should be made.)
Therefore, in total we have 3,000 (or 600 + 2,400) person-equivalents in volume available. Three thousand x 10,368 cubic inches means we have 31,104,000 cubic inches of space available. At three cubic inches per ball, a 747 could hold 10,368,000 balls. However, spheres do not fit perfectly together. Eliminate a certain percentage – spheres cover only about 70 percent of a cube when packed – and cut your answer to 7,257,600 balls.
How many pay phones are there on the island of Manhattan?
There are two ways to handle this problem. First of all, you could estimate how many blocks there are in Manhattan, and assume that 75 percent of all blocks have a pay phone. (Remember, the interviewer didn’t say they had to work.) If there are about 15 avenues across Manhattan, and if the island is 300 streets long, then there are about 4,500 intersections. If every intersection indicates a block, then there are 4,500 blocks in the city. That means 3,000 pay phones. Now add the extra step and subtract the size of Central Park. Say that Central Park is 50 streets by six avenues – that mean you lose 300 blocks, or 200 pay phones. You have the figure of 2,800 pay phones. Now estimate how many pay phones exist in bars, restaurants, schools, etc. There may be a total of 3,500 pay phones in Manhattan. (This question is also sometimes used with estimating the number of manhole covers in Manhattan.)
How many weddings are performed each day in Japan?
Try a ground-up approach. In a city of 1 million (Kyoto), how many people are of marriageable age? Let’s say 750,000. How many get married in a given year? Maybe 2 percent? That’s 15,000. Now, the population of Japan is about 150 million, so multiply 15,000 by 150 – and you get 2.25 million weddings every year. Divide that by 365 and you get 6,164 weddings per day (on the average, though clearly some days are more popular than others).
To summarize:
There are 1 million people in Kyoto.
750,000 are of marriageable age.
2 percent get married in the average year.
750,000 x 0.02 = 15,000 marriages every year in Kyoto.
There are 150 million people in Japan.
150 x 15,000 = 2.25 million weddings per year.
2,250,000/365 = 6,164 weddings per day.
How many children are born every day in the United States?
The population of the United States is 300 million (approximately). Half are women (150 million). Perhaps half of those are of childbearing age. How do you determine how many women are pregnant at any given time? Well:
Let’s say the average span of childbearing for a woman is 40 years.
The average woman has two children.
So a woman is pregnant one year in 20, or 5 percent of the time.
3.75 million women are pregnant every year.
Divide by 365 – you get about 10,000 babies a day (actually, 10,273).
Do the extra step – round up for multiple births, so perhaps 12,000.
How much change would you find on the floor of an average mall?
This seemingly silly guesstimate was received by a job seeker at McKinsey. It’s an example of a guesstimate that is also a way to test candidate’s “out-ofthe- box” thinking. First, estimate how many stores there are in the average mall – say, 50. Now, how many people enter the average store on the average day? A thousand? So if there are 50,000 visitors to a mall daily, how many lose change? If one in 50, say, drops money (1,000 people a day), how much is the average loss of change? Most amounts are probably small. People carry fewer quarters, for example, and are more likely to retrieve them. So let’s say that if a person is equally likely to drop a penny, nickel, or dime, then the average person who loses change loses a nickel. That means there would be $500 worth of change on the average floor. If half of that change has been picked up immediately, that would be $250 worth of change.
Also ask: Is there a fountain in the mall? If a fountain is considered to be the “floor” of the mall, the amount of change would obviously increase.
Estimate the annual revenue of Tropicana Orange Juice in the United States.
Assume the average American orange juice drinker consumes two glasses of OJ per week, which means 104 glasses per year. Further assume that each glass of OJ produces $0.50 of revenue. This means $52 of revenue per orange juice drinker per year.
There are approximately 300 million people in the United States. Assume that 2/3 of them are orange juice drinkers. This means 2/3(300,000,000)(52) = $10.4 billion
Now assume that Tropicana has a 75% market share. This means that the annual revenue of Tropicana Orange Juice in the United States is 0.75(10.4) = $7.6 billion.
How many gas stations are there in the United States?
My town has approximately 30,000 people and it has five gas stations serving in that area. The United States has approximately 300 million people, which means there should be approximately 10,000 “towns” in the United States and 50,000 gas stations.
However, there are certain adjustments that must be made. Assume ¼ of the population lives in larger cities with only one gas station per 30,000 people. This means that there are 7,500 towns with five gas stations and 2,500 towns with one gas station, or 40,000 gas stations in total.
How many bottles of wine are consumed in the United States each week?
Determine:
1. The number of people in the United States.
2. The number of adults.
3. The number of wine drinkers.
4. Average number of glasses of wine consumed per week.
5. Number of glasses of wine in an average bottle.
(Extra step: You may wish to estimate how much wine is used for nondrinking purposes – cooking, for example. Also clarify whether the interviewer is speaking of standard-sized bottles of wine.)
You could reasonably make the following assumptions:
There are about 300 million people in the United States.
250 million are adults.
Perhaps 220 million drink alcohol.
200 million drink wine.
The average wine drinker drinks two glasses of wine a week.
400 million glasses of wine consumers per week.
About five glasses of wine in the average bottle.
80 million bottles of wine consumed in America each week.
Estimate how many bottles of wine are used for cooking – perhaps another five million.
This brings your total to 85 million bottles of wine consumed per week.
How many men’s suits were sold in the United States last year?
Determine:
- Estimate the population of the United States.
- Cut that in half to get the number of men.
- Determine how many men are employed in occupations which require business attire.
- Determine how many suits the average business attire employee would have purchased (due to weather, fashion changes, cleanings, wear, and so on).
- Assume (or ask) a number of suits that those men not employed in business attire jobs purchased for religious, social, or other reasons.
- Sum up the number and present your answer.
To summarize:
The population of the United States: 270 million (or 300 million, to round up).
Half are men – so 150 million.
Let’s say two-thirds are employed.
150 million x 2/3 = 100 million.
Assume every employed man owns one suit = 100 million suits.
Estimate that about a quarter of men are in a field where they must own more than one suit.
If each of those men has an additional two suits, 25 million men x 2 additional suits = 50 million suits.
150 million suits in the United States.
How often does the average suit-owner replace a suit? Perhaps once every three years.
There are 50 million suits sold every year in the United States.
How many tennis balls fit in a swimming pool?
Determine:
- What is the shape and depth of the swimming pool?
- What is the volume of a tennis ball?
- Estimate the volume of the swimming pool based on the depth, length, and width of the pool.
- Calculate the number of balls by dividing the volume of the pool by the volume of the tennis ball.
- You may wish to subtract balls due to steps in the pool and the gradual upslope of the pool due to the varying depth (but ask first).
How many gas stations are there in Los Angeles?
Determine:
- What is the population of Los Angeles?
- What is the number of cars in Los Angeles? What is the average number of cars per person (including commuters)?
- How many gas stations are needed per car?
What is the annual size of the golf ball market in the United States?
Determine:
- What is the population of the United States?
- What percentage of the population golfs?
- How often does the average golfer golf?
- What is the number of balls used in an average golf game (and number that are lost)?
What factors drive demand?
- How many golf courses are being built in the United States?
- How many are planned?
- Is the population of golfers (due to Tiger Woods and his ilk) expanding?
