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## Case Interview Fundamental

**Case Interview Question**

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## Consulting Math

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## McKinsey Problem Solving Test Formulae Question

## 1. What is it?

Formulae questions are generally like word problems in PST where you don’t have to provide the actual numerical results, just the formulae containing letters representing input variables. Normally, the question will provide input variables in letter format and you will be asked to provide the right formulae in letter format (e.g. it takes the process center T hours to process each file. If the speed is doubled, it takes T/2 hours to process each file). This is one of the easiest PST question types on the McKinsey PST. Let’s make sure you don’t lose points on any question of this type in your exam!

## 2. Example of a Formulae Question

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

**Which of the following formulae accurately calculates the annual cement output per worker?**

- (c x p) / (b + w)
- (c x p) / [(b + w) x 12]
- 144 x (c x p) / (b + w)
- 12 x (c x p) / (b + w)

## 3. Formula for Success at Formulae Questions

A popular technique for multiple-choice questions is to read the answers first before coming back to the facts. However, that technique would not help you with Formulae Questions. The reason for this is that, often, the end-result formula has already been simplified (e.g. canceling out the same variable on both numerator and denominator) as much as possible. It gives you neither the path to get there nor any hints on how to solve the problem. For instance, when you look at the four options in the example above, does any of them give you a sense of what it represents or how to get there? What does (c x p) represent? What do you get by multiplying Cement output by Monthly labor income?

This is the universal tip for everybody in the consulting industry, and it also works great here! Often, the result cannot be directly calculated from the provided variables. However, if you take an extra step in-between, the problem becomes a lot easier. Let’s solve the sample question above together to illustrate this point. I broke the problem into smaller steps as below:

**Step 1**: Annual cement output per worker = Total annual cement output / Total number of workers**Step 2**: Since we already have Total annual cement output of (c), the next step is to calculate the total number of workers.- Total number of workers = Total labor cost / Salary of 1 worker
- Both Total labor cost and salary are provided. Bingo!

**Step 3**: Simplify the final formulae

In some aspects, formulae question is also a tweaked version of reading-facts questions. You still need to read some facts and perform some calculations (with letters instead of real numbers). Therefore, it is important to master those reading-facts tools and apply them here.

** Illustration of a usual mistake: **Now come back to Step 2 above and explicitly solve it.

Step 2**:** Total number of workers = Total labor cost / Salary of 1 worker = (b + w) / p

Step 3: Annual cement output per worker = c / [(b + w) / p] = (c x p) / (b + w)]

Chosen choice: A

Unfortunately, A is **NOT** the correct answer, because the above calculation doesn’t take into account the *difference in units* – the salary is on a *monthly* basis whereas the total labor cost is on the *annual* basis. If you convert the unit, the final choice should be** D**.

No matter how beautifully you have tackled the problem, you will not get any credit if small mistakes like this slip through the crack. Make sure you don’t get blindsided by this kind of pitfall!

**BACK TO THE PST MASTER STUDY PLAN**

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