## 1. What is it?

**Word Problems** are quantitative questions where the answer cannot be calculated purely based on given numbers. Usually we have to set up 1 (or more) equations in order to solve it. **Word Problems** in the **McKinsey PST** and **case interviews** are just the usual word problems we have seen in schools, GMAT… but put into business contexts. The methodology therefore to solve them is the same.

All of us have been solving word problems for years; and yet, word problems are still one of the hardest **question types** in **the McKinsey PST** and **case interview**. Now let’s buckle up and strengthen this area!

**2. Example of a Word Problem in the McKinsey PST (and in case interview)**

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

***

**Table 1**

Suppose the restaurant opens 350 days a year, 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 visits per day 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

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

## 4. Illustration of Methodology

Let’s solve the above example question 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 write these converted number on the table provided as follows:

**Table 2**

Notice that I have just converted all possible 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 gets by 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 asked variable. The asked variable here is: how much percent of 530 customers/day does Jean Valjean need to add?

As mentioned above, it is **NOT** necessary to put the asked question as the variable 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 *(notice that there is more than 1 way to set up equation). Let Y be the “break even size” (measured by people). I can easily calculate the asked percentage after having 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 properly doing 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 times 530, we can quickly convert Y into the asked variable: how much percent of 530 customers/day Jean Valjean does need to add?

**Final answer is C.**

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