1. What is it?
Formulae questions generally are word problems where you don\’t have to provide the actual numerical results but instead just the formulae containing letters representing input variables. Normally, the question will provide input variables in letter format and you are asked to provide the answering formulae in letter format as well (e.g:it takes the process center T time to process each file. If the speed is doubled, it takes T/2 time to process each file). This is one of the easiest question types on the McKinsey PST. Let\’s make sure you don\’t miss any of this type in your exam!
2. Example of a Formulae Question
This question is written based on an official McKinsey practice PST question.
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Which of the following formulae accurately calculates the annual cement output per worker of the plant?A. (c x p) / (b + w)B. (c x p) / (b + w) x 12C. 144 x (c x p) / (b + w)D. 12 x (c x p) / (b + w)
3. Formula for Success at Formulae Questions
Formula 1: Calculate first before looking at given choices
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 much here in Formulae Questions.Reason: often the end-result formula has already incorporated simplifications (e.g: canceling out same variable on both numerator and denominator) to be in the simplest format. It gives you neither the path to get there nor any hint to solve the problem.Illustration: Look at the four given choices in the example above, does any of those give you a sense of what it represents or the path to get there? What does (c x p) represent? Taking Cement output and multiplying it by Monthly labor income to get what?
Formula 2: Divide the problem into smaller pieces (take 1 step at a time)
This is the universal tip for everybody in the consulting industry and it also works great here! Often the result can not be easily calculated straight from the provided variables. However, if you take an extra step in-between, the problem becomes a lot easier. Illustration: Let\’s solve the above example question 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
Formula 3: Get the reading-facts tools right
In some aspects, formulae questions are 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) / pStep 3: Annual cement output per worker = c / [ (b + w) / p ] = (c x p) / (b + w)
Final choice: A
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Unfortunately A is NOT the correct answer. Can you see why?Because the above calculation doesn\’t take into account the difference in units: the salary is on the 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 get into the lane. Make sure you don\’t fall into this situation!