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Cosma
on Apr 14, 2020
Global
Question about
Case Interview Basics Article
I want to receive updates regarding this question via email.

Can you please show me how you solved the equation (x/6 + x/12 + x/7 + 5 + x/2 + 4 = x)

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Coach
on Apr 14, 2020
Digital entrepreneur turned BCG consultant // Coach with focus on PEI

Hi Cosma,

Here is one way (not saying it's the only one :)

First step: get all multiples of 2 to the same high denominator:

x/6 + x/12 + x/7 + 5 + x/2 + 4 = x <=> 2x/12 + x/12 + x/7 + 5 + 6x/12 + 4 = x

Then you add them up:

2x/12 + x/12 + x/7 + 5 + 6x/12 + 4 = x <=> 9x/12 + x/7 + 9 = x

And actually your equation is equivalent to 3x/4 + x/7 + 9 = x

Then you bring it all to the same denominator which gives you 21x/28 + 4x/28 + 9 = x

And finally you have 9 = 3x/28 which is equivalent to x = 28*3 = 84

Hope this helps :)

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Clara
Coach
on Apr 15, 2020
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

I would find the common denominator for ALL numbers together: 

  • 12= 2 x 2 x 3
  • 6 > included in the 12
  • 2 > included in the 12
  • 7 = prime

Common denominator: 12 x 7

If you are more or less good with math you should have no issue, since it´s multiplications of one single digit. 

Hope it helps!

Cheers,

Clara

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Emily
Coach
on Apr 15, 2020
9 years in MBB Southeast Asia & China| 8 years as MBB interviewer | Free intro call

Agree with Hugo. That's how I would do it too. :)

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1 comment
Katya
on Mar 13, 2023
No need to solve it, you need to find a common denominator which will be the age (just check if it makes sense if there is more than one)
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Question on the Case Interview Basics Article
Brainteaser
Brainteasers are a type of problem that focuses on a single issue rather than complex business cases. They require out-of-the-box thinking, logic or math skills and can take the form of riddles, word problems or visual puzzles. These tasks are designed to test your problem-solving skills, analytical thinking and ability to remain calm under pressure.Typical problems cover everyday life's topics and might even include unrealistic assumptions. All necessary information is usually included in the question so that further assumptions are not necessary. This article explains in more detail why brainteasers are useful in case interview preparation and how to solve them. Why Are Brainteasers Used in Case Interviews?First, in consulting case interviews, brainteasers are rarely used. Regular cases are considered more suitable as they allow the interviewer to better test key skills needed in a consultant (structured, analytical and conceptual thinking). However, brainteasers add significant value to the preparation process of several reasons:Enhancing Creative Thinking: Brainteasers demand unconventional solutions that go beyond the standard approaches used in typical business cases. This hones the ability to think outside the box and encourages flexibility in developing and applying different problem-solving frameworks.Building Stress Resilience and Speed: Brainteasers often place candidates under time pressure, mimicking the stressful situations commonly encountered in consulting. Regular practice with these challenges helps candidates remain calm and think clearly, even when the solution is not immediately apparent.Strengthening Mathematical and Logical Skills: Many brainteasers involve numbers or require logical deductions. Regular practice with these tasks improves the ability to quickly translate problems into mathematical or logical equations, a skill that is also valuable in complex business analyses.Avoiding Standard Solutions: By working on brainteasers, candidates reduce the risk of becoming too dependent on standard frameworks. This practice sharpens their ability to consider alternative solutions, which can be crucial in unpredictable business situations. How to Solve BrainteasersWhen approaching brainteasers, the method you use to tackle the problem is often more critical than arriving at the correct answer. Brainteasers test not only your creativity and logic but also your ability to structure your thoughts and communicate your reasoning clearly. By following a systematic approach, you can effectively break down complex puzzles and demonstrate your problem-solving skills: Structure Before Solution: The approach to solving a brainteaser is often more important than the final answer. Write down all the information provided, listen carefully, and make sure you haven’t missed or added anything. A structured approach demonstrates your ability to systematically analyze and tackle a problem.Brute Force: When a problem requires a specific number and the possible solutions are limited, a trial-and-error approach can be effective.Example: Replace 'x' with the digits 1, 2, 3, 4, 5, and 6 to make the equation xx * x = xxx true. Solution: 54 * 3 = 162.Logic: Many brainteasers can be solved by logically interpreting the information given and drawing the correct conclusions.Example: Five friends have 10 cookies. They vote on how to split them in alphabetical order. Anyone who doesn’t get at least 50% of the votes is out. Anton votes first. The maximum number of cookies he can demand is 8. Key Takeaways - What Brainteasers Are Useful ForBrainteasers are not common in case interviews but are highly useful for preparing for unconventional problem-solving situations.They enhance creative and structured thinking, build stress resilience, and improve mathematical and logical skills. Brush up on your mental math skills. Being quick and accurate with numbers is crucial!Focus on the problem-solving process and structure rather than just finding the correct answer. 
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