Case math question

Question

Hi, I come from a social science background and so am practising case calculation to help with my interview with McKinsey. Would anyone be able to help explain how I can solve the following 2 problems quickly? Thank you!

1. A shoe factory has a maximum capacity of 12,000 workers. It started off with 1200 workers and recruited 280 new workers every month. After 6 months, the factory directors decided to hire 375 new workers every month. After another 6 months, they decided to hire 460 new workers every month. How many months will it take (from the very beginning) the factory to reach its maximum capacity? Round up your answer to the nearest whole number.

2. On average, a Frenchman consumes 560,000 liters of water each year. That number for a German is 430,000 liters and 120,000 liters for a Dane. The average price of water at these three countries is $1.6 per liter. Calculate the ratio of water consumption between France, Germany and Denmark in term of $ value, i.e.: amount paid for consuming water.

Answer 1

Hi! Let me try to help you. In general, both exercises will require several calculations, so I don't see many shortcuts here you can take.

Problem 1. I would say there are almost no shortcuts here, the key in solving this quickly is being well-structured and follow each calculation step without getting lost. Quickest way of solving it is: 1) Calculate workers in 6m with recruitment at 280, 2) Calculate workers in 6m with recruitment at 375, 3) Add up initial workers (1200), plus the ones recruited so far in 12m (total of 5130), 4) Divide the remaining capacity gap by 460 to understand how much it will take to reach the limit (final answer 27m).

Problem 2. The main shortcut here is that you can disregard the price of water (since it's the same for every country). You can just directly compare the quantities consumed in each country and come up with the ratios (F:G 1.3 F:D 4.7 G:D 3.6).

I hope this helps!

Answer 2

You just need to know how to turn that prompt into math. The process is always the same, so there are no useful tips here.

12000 = 1200 + 280 * 6 + 375 * 6 + 460X

460X = (12000 - 1200 - 1680 - 2250) / 460

X = 5870 / 460 = 13

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Total number of months: 6 + 6 + X = 6 + 6 + 13 = 25 months

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To be honest, I don't think one would be asked to do this kind of math in a case, but practicing this doesn't hurt.