This article is the third article in the product interview series. The product interview series aims to solve the problems you encounter in the interview through structured thinking and specific cases.

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This article is the third article in the product interview series. The product interview series aims to solve the problems you encounter in the interview through structured thinking and specific cases.

In the interview process of product managers, in addition to product design and product improvement issues, the most common questions also include estimation issues, such as:

  • Please estimate how many gas stations there are in Shanghai
  • Please estimate how many mooncakes can be sold in the Mid-Autumn Festival
  • Please estimate how many table tennis balls can be installed in a room

The interviewer asked the estimated questions to evaluate your ability to quantify and solve problems. They want to know whether you can quickly use mathematical operations and calculate the size of the opportunity, the potential impact of the project, the project cost and other reasonable estimates.

To answer the estimated interview questions, you must make some assumptions in the process. To make sure you clearly convey your assumptions. You can also ask the interviewer whether your assumptions meet the requirements and modify them based on feedback provided by the interviewer. Here are the steps to answer your estimation interview questions.

1. Steps to answer estimation questions

1. Clarify the scope of the question

First of all, you must make sure that you understand the question and understand the key points of the other party’s question. If there are no clear questions, please discuss and clarify with the interviewer.

For example, if you are asked to estimate the bandwidth of QQ mailbox , then make sure that the time period for the estimated bandwidth (e.g., one day vs one month vs one year) is clear. Suppose we are estimating the daily bandwidth of the QQ mailbox.

2. Create the main equation

You need to list the equations that solve this problem. Doing so will speed up your process of solving this problem and will also allow the interviewer to see that you have the ability to face difficulties. This equation will be the basis for your estimation.

There are different solutions to any problem, but some of them will be more efficient and simple. However, based on the knowledge and background you have, there is generally no "best method".

For example, for example, we can apply the following formula:

If you want to calculate the total revenue of QQ mailbox in China in a year, then you can use the following formula:

3. List what you (think)

You have already understood what the problem is, and you can have a general idea of ​​the knowledge you have mastered and the content you need to calculate. In some interviews, you can seek some key materials from the interviewer. Suppose you are estimating the total income of QQ mailboxes in China every year, the knowledge you may have is as follows:

  • The total population of China
  • The proportion of the number of people with computers in China
  • The click-through rate of advertising
  • The number of QQ mailbox ads

Maybe you can ask the interviewer some of these situations, and if you have any questions, you can take some "friendly" methods to ask questions.

4. Consider the edge situation

Think carefully about the potential obstacles of your method and show the interviewer your focus and courage to challenge yourself.

For example, if you want to calculate how many gas stations there are in Shanghai, have you considered the suburbs? Or, if you were to calculate how much it would cost to clean all windows in your city, did you consider the broken glass, and did you consider the glass of cars and buses? Are there still some resources for

that you didn't consider? Think carefully and see what else does not match the ideas you created in the previous step.

5. Decompose unknown numbers in formula into simpler formula

When there is unknown input in the equation, you need to demonstrate how to find unknown numbers. guessing is not enough, the way to find unknown numbers is to create a new reasonable equation.

In the example above, the unknown number is the number of QQ mailbox accounts and the average bandwidth of each QQ mailbox account. To find the number of QQ mailbox accounts, we need a new formula:

You can use a similar approach to develop a new formula for the bandwidth of each QQ mailbox account:

You have to continue to decompose unknowns into simpler equations until you can replace unknowns with reasonable assumptions.I considered the population of Chinese people who have access to the internet (800 million), and we can assume that there are 100 million QQ mail users in total in China, when you consider that many people aged 0 to 16 and older don’t have email accounts, while some have other email services (such as NetEase Mail, Hotmail and Sina Mail ).

You can also estimate the probability that people of a specific age group have a QQ mailbox here and multiply that percentage by the population of that age group to get a more accurate estimate. Add the number of QQ mailbox users for each age group and you will get the total number of QQ mailbox users in China.

We can also assume that the total number of QQ mailbox accounts per user is 1.5 to illustrate the fact that some users have multiple accounts and company accounts using QQ mailbox. We can assume that a person viewed or sent 5 emails a day. Finally, let's say that each email averages about 1MB. Prepare to explain your reasons after any number you choose (e.g., how many % of the emails are with attachments? How big is the attachment?) By stepping down the equations, you can finally come up with an equation that can be calculated by a hypothetical design.

6. Calculate the number

After explaining the unknown and how to calculate the unknown, replace the unknown with the assumption and the calculated number until a number is derived is the estimated number you are looking for.

Note: Explain the reason for your assumptions to the interviewer. Your inferences and ideas are more important than giving accurate values ​​.

7. Perform a rationality review

rationality is the best way to ensure your results make sense. Ask yourself, is this ultimately logical? For example, if your estimate of QQ mailbox bandwidth is 100GB, it may be wrong and you will need to double-check the calculation results and assumptions.

2. Case analysis

1. Estimate how much money does the Chinese shampoo industry make every year?

(1) Clarify the scope of the problem

First, clarify the scope of the problem, how much money is made refers to total income or profit? Should I only consider shampoo or count conditioner along with other products? Consider the distributor's revenue?

Assume that we need to calculate the amount: the total revenue of the shampoo industry company, and only consider shampoo.

(2) Create the main equation

Total income = Total number of people in China X Per capita shampoo bottle book X The income of each bottle of shampoo sold

In addition, considering that the amount of shampoo is not the same for everyone, and the amount of use is different from gender and age. So we also have to segment the market and split this method to calculate. For example, women spend more money on shampoos than men because they have longer hair than men and they buy more expensive shampoos. Therefore, our calculation method needs to be adjusted, separate men and women and calculate them separately.

for women, we use the following scheme:

income of female users = number of Chinese women X average annual shampoo bottles X income per bottle of shampoo sold

for men, we use the following scheme:

income of male users = number of Chinese men X average annual shampoo bottles of males X The income of each bottle of shampoo sold

(3) List what you want to know

  • The total number of people in China is 1.4 billion
  • The average life span is 80 years old
  • The amount of shampoo used for shampoos per person per person
  • The average premium of a product in the store accounts for its selling price

(4) Considering the edge situation

Does the number of shampoos and the amount of shampoos used in the shampoos? Are you considering the amount of pet shampoo? We do not consider these edge cases in this issue. But you can illustrate that some edge situations are always good.

(5) Decompose the unknowns in the formula into a simpler formula

Formula for women, we split the formula as follows:

Number of women in China = 50% X Total Chinese population Average number of shampoo bottles used in women = Average number of hair shampoos per bottle X Number of times per bottle of shampoo available

Income per bottle of shampoo sold = Average price of shampoos per bottle X (1-Store premium ratio)

Formula for men, we split the formula as follows:

Number of men in China = 50% X Total Chinese population Average number of shampoos used in men = Average number of shampoo bottles used by women in a year X (the amount of shampoo used by men/the amount of shampoo used by women)

The income per bottle of shampoo sold = the average price of shampoo per bottle of women X (1-store premium ratio)

Make reasonable assumptions on the data used in the above formula:

  • Average shampoo used by shampoo for one shampoo: 3ml.
  • shampoo dosage ratio between men and women: 50%.
  • average shampoo capacity per bottle: 340 grams.
  • average capacity per 340 grams: 300ml.
  • average shampoo (male or female) unit price: 40.
  • store premium: 50%.

(6) Calculate the number

For female users:

shampoo companies earn an average of about 80 yuan per woman, so the result of this part is 56 billion yuan. Men have shorter hair, so they should use less shampoo. Suppose that men use shampoo half as much as women. This means that men contribute about 28 billion yuan to the shampoo income every year.

(7) Re-check

In addition, you can use how many bottles of shampoo you use each year to test the results.

Recall that I, we, should have made an inappropriate assumption before. I assume that the amount of shampoo used per person matches a typical adult (male or female, respectively), but I'm not sure about this. I did not consider young children, the elderly, the disabled, and the bald. In this regard, that is, I did not consider people who do not wash their hair every day. We need to adjust the amount of shampoo used here.

html Children, elderly people under the age of 110 and people with disabilities account for 10% of the total population of China. Because of short hair or fewer shampoos, they use much less shampoo than ordinary adults; it may be assumed that the amount used is 0. This reduces shampoo usage by 10%. For example, 5% of adult men in China have baldness, which reduces shampoo usage by 5%. So, what about those people who don’t wash their hair every day? Let’s assume that 20% of people do not wash their hair every major, but wash their hair once every two days. This reduces usage by 10%.

Add these numbers together and we have to reduce the amount of shampoo usage by 25%. Therefore, 84 billion yuan is not accurate, and the final annual income is about 60 billion yuan.

2. How many tennis balls can be installed in a two-bedroom apartment?

This is very similar to a classic Google interview question: How many golf balls can a Boeing 747 aircraft carry?

(1) Clear the scope of the problem

This problem is like many problems, and there are some ambiguity or not clearly stated, for example.

  • The two-bedroom apartment mentioned here specifically refers to a certain apartment (maybe of any size), or any typical two-bedroom apartment? (Suppose it is a typical two-bedroom apartment.)
  • Understand what a "typical" two-bedroom apartment means, first we need to know where it is located. (Suppose it is a typical two-bedroom apartment in the commercial district of Shanghai.) The question
  • is, how many tennis balls can a typical two-bedroom apartment be installed at most, or how many tennis balls can we throw in at any time? (Suppose you are asking about the maximum number of tennis balls that can be installed.) Is there furniture in this two-bedroom apartment in
  • ? How much furniture is there? Is there anyone in the apartment? (Suppose there is a normal amount of furniture in the apartment, but no one.)
  • Can we stuff tennis balls into the cabinet? (Assuming it doesn't work.All tennis must be placed "within the sight". )

(2) Creating the main equation

The basic equation is very simple and direct: the number of tennis balls = (the space size of the apartment - the specific product of the home - the volume of the other use - the volume of personal items)/The unit volume of the tennis ball.

(3) List what you want to know

The information we know or want to know at present includes the following:

  • According to my personal experience, a typical two-bedroom apartment is about 75 square meters.
  • A typical two-bedroom apartment usually has 2 bedrooms, a living room, a kitchen and a bathroom.
  • furniture generally includes: 2 double beds, 2 dressing tables, 4 bedside tables, 1 sofa, 1 double sofa, 1 dining table and 4 dining chairs, 1 coffee table and a TV.
  • How much space does kitchen utensils occupy? Where are the bathroom utensils?

(4) Consider the edge situation

whether the owner is sloppy, the discharge location of the item, etc. We will not consider the edge situation.

(5) Decompose the unknowns in the formula into a simpler formula

  • size of the apartment : size of the apartment space = ceiling height x floor area.
  • specific items: We assume that furniture is simply listed as follows: 4 double mattresses (the volume of the bed frame itself is negligible), 1 sofa, 1 double sofa and 2 dressing tables. The size of the space occupied by furniture = 4× medium-sized mattress volume + 1× sofa volume + 1× double sofa volume + 2× dressing table volume.
  • The volume of personal items: The volume of personal items = % The proportion of personal items in the wardrobe × the volume of all personal items.
  • Unit volume of tennis: You need to calculate the volume of the tennis ball, so that the volume of the cube is meaningful. Note that there are gaps between the tennis balls. We assume that the effective volume of a tennis ball: the effective unit volume of a tennis ball = tennis length × width × height = the diameter of a tennis ball × the diameter of a tennis ball × the height of the stack adapted to the stack.

(6) Calculate the number

  • The space size of the apartment = ceiling height x floor area = 3.6 meters × 75 square meters = 270 cubic meters.
  • specific storage =4×Double mattress volume +1xCouch volume +1×Double sofa volume +2×Double sofa volume =4×1.8m×0.3m×1.8m+1×1.8m×1m×0.6m+1×1.2m×1m×0.6m+2×1m×0.6m×1.2m=7.1 cubic meters.
  • volume of daily necessities = sink and cabinet volume + kitchen storage cabinet volume = 1 meter × 0.6 meter × 1.2 meter + 2 × 3 meter × 0.6 meter × 1 meter = 4.3 cubic meters.
  • Personal items volume =%The proportion of personal items in the wardrobe × the volume of all items = 58% × 2 people × 10 boxes per person × 0.22 cubic meters = 2.2 cubic meters.
  • The effective unit volume of a tennis ball = the diameter of the tennis ball × the diameter of the tennis ball × the height of the adapted stack = 6.5 cm × 6.5 cm × 5 cm = 211.25 cubic centimeters = 0.000211% cubic meters.
  • Available space in apartment =The size of the apartment space-the specific volume of home-the volume of daily necessities-the volume of personal items=270 cubic meters-7.1 cubic meters-4.3 cubic meters-2.2 cubic meters=256.4 cubic meters.

Number of tennis balls = 256.4 cubic meters/0.000211 cubic meters = 1.22 million

(7) Reasonable review

A 75 square meters, 3.6 meters high apartment, the size is 270 cubic meters. If this apartment can accommodate 1.22 million tennis balls, then 1 cubic meter should accommodate 4,500 tennis balls. If 15 tennis balls can be placed in a length of 1 meter, then 1 cubic meter can accommodate 4,500 tennis balls. The calculation check has been checked, no problem.

Author: haoxinguo, official account: Kris Product Growth Road

This article was originally published by @haoxinguo on Everyone is a Product Manager. Reproduction of

is prohibited without permission from

. The title image is from Unsplash, based on CC0 protocol

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