## Word Problem

### 1. What is it?

Word Problem is a quantitative question where the answer cannot be calculated directly from the data provided. Usually, we have to set up one or more equations in order to solve this kind of question. Word Problem questions in the McKinsey PST and Case Interviews are just the word problems we usually see in schools, GMAT… but put into business contexts. The method to solve them, therefore, is the same.

All of us have been solving word problems for years; and yet, they are still one of the hardest PST question type__s__ in the McKinsey PST and Case Interviews. Now let’s buckle up learn how to take them on!

### 2. **Example of a Word Problem in the McKinsey PST (and in Case Interviews)**

*This question is written based on an official McKinsey practice PST*

***

**Table 1**

Suppose the restaurant opens 350 days a year. There are 3 meal shifts per day, 1 shift lasts 3 hours, 1 customer uses an average of 5 dishes per visit, and currently the restaurant hosts 530 customers on average daily.

What percentage of increase in the number of daily visits would be required in order to make purchasing the machines financially beneficial?

A. 25%

B. 50%

C. 100%

D. 200%

### 3. Methodology

**Step 1:** Convert data/facts into manageable and standardized format and units (only needed for complex questions)

**Step 2:** Set up an equation with one (or more) unknown variables, i.e. X, Y, Z, etc.

*Tips: Don’t worry about having to make the variable as the question asked. Just set up the equation in a way that makes the most sense to you as long as the variables can be easily converted to the asked variable. It will save time much more time and helps you avoid silly mistakes.*

**Step 3:** Solve the equation and get the answer

### 4. Illustration of Methodology

Let’s solve the sample question above together.

**Step 1: **

This is a very complex question with many non-standardized and not ready-to-use data. If I am going to tackle this question on my PST, I would convert the provided figures and write them out on a table as follows.

**Table 2**

Notice that I have converted all the necessary data points into the same unit of “Franc per day”. The only data point not fully converted is the Labor cost in Manual Process (measured by the “per dish” variable), yet I want to make sure that I go as far as I can.

See how simple the problem is now!

**Step 2: **

Now that we have very manageable data, let’s go ahead and set up an equation that will help us find the answer. The asked variable here is: what percent increase in current daily visits does Jean Valjean need?

As mentioned above, it is **NOT** necessary to put the variable question is looking for in the equation. In this case, doing so will result in a very awkward and complicated equation.

Instead, I set up the equation that *makes the most sense to me *(do note that there is more than one way to set up equations). Let Y be the “break-even size” (measured by people). I can easily calculate the percentage asked for after getting the break-even size.

Cost per day of Manual Process = Cost per day of Machine Process

Washing cost + Set up cost = Washing cost + Set up cost + other cost

Y x 5 dishes x 0.1 Franc + 30 Franc = 270 Franc + 90 Franc + 200 Franc

**Step 3:**

After executing step 1 and step 2, the problem becomes a lot easier. Now we have:

0.5 Y = 530

Y = 2 x 530

Once we have Y (the new “break-even” visit volume) of 2 * 530, we can quickly convert Y into the asked variable: What percent increase of 530 customers/day does Jean Valjean need?