Math case practice?

One of the basic skills a candidate requires is good mental math abilities. Your interviewer will test this skill either directly by asking a math question such as "What is the square root of 759?" or in an indirect manner while solving a business case problem.Interviewers can differentiate between hard and soft mistakes. Calculation errors are considered hard mistakes because there is no partial answer in math. Therefore, you must improve or refresh your mental math skills before interviews. Remember, it is alright to use scratch paper for most calculations, but it is expected that you are able to mentally perform easy calculations. Try the following tool to improve your mental math skills.*box-open*Train your brain! Improve your math skills using our Mental Math tool!*box-close*Impress the interviewer with outstanding mental math skillsPossessing excellent mental math skills is crucial during a case interview because you will need these skills as a consultant. In general, there are two main reasons why consultants should possess excellent math skills:As a consultant, you will come across several occasions in which you will need mental math skills. Estimation skills can save a lot of time and, in some cases, help figure out unnecessary analysis that can waste a lot of time if a quick estimation is not done (see 80/20 or pareto principle). Without excellent math skills, you could end up spending the entire night using Excel.You can easily impress your client by demonstrating to them that you are a potential math genius. Clients often pay a lot of money to you (or your employer) and expect real wisdom and cleverness. Quick math solutions can be an effective way to convince clients of your recommendations.Math or "quant" skills account for 20-25% of overall performance evaluationQuant's skills are only one of the skills assessed in case interviews. As a candidate, you are evaluated on your overall combination of skills and your perceived potential. Generally, a candidate’s quantitative assessment consists of 20-25% of the overall interview evaluation weight. The goal of Management Consulting firms is to find the set of candidates with what they perceive is the best set of skills overall.Most firms have a “minimum bar” for quant skills for their candidates, which means you are unlikely to receive an offer if you do not exceed this bar—unless you are otherwise a highly exceptional candidate (such as being a Rhodes Scholar). At some firms, dramatically exceeding this “bar” does not strengthen your candidacy—that is, the quantitative evaluation is binary: you either pass the quant assessment or you don’t. At other firms, such as McKinsey, if you can demonstrate very strong quantitative skills, it will differentiate you from other candidates. The quant problems from these firms can be more complex, which allows candidates with strong quant skills to fully demonstrate their ability. The corollary is that, for some very complex quant problems, you don’t need to correctly solve all the components to receive an offer.The relative importance of quantitative skills in the case interview varies by firm, office, and individual interviewer. As an example, if you are interviewing with a consulting firm partner who has a Ph.D. in a very quantitative field like Applied Mathematics or Physics, they may ask more challenging quant questions and place a greater emphasis on quant skills in their interviews. McKinsey, in particular, places more emphasis on quant skills than other firms, and, as mentioned previously, demonstrating exceptional quant skills can significantly strengthen your candidacy at McKinsey.Given the large weighting of 20-25% that quant skills have in consulting interviews - and the quant “minimum bar” at most consulting firms - you can certainly sink your chances of receiving an offer if you perform poorly in the quant portion of the interview.*box-open*For extra practice, check out our Quizzes on Logical Reasoning and Math Assignments for Case Interviews!*box-close*SummaryA quant's skills are needed to be an effective Management Consultant; hence, they are assessed in Management Consulting interviews. Quant's skills are one of the skills consulting firms consider in their interviewsAt most firms, if you do not exceed a “minimum bar” for quant skills, it is unlikely you will receive an offerYou cannot use calculators or spreadsheets in Management Consulting interviews, and the assessment of your quant skills usually contributes about 20-25% of the overall interview evaluation weight.

Correlation and causality are two important terms in statistics that are often confused with each other. In this text, the difference between the two is explained with understandable examples and related to the business consulting industry. Keep in mind that math is an important aspect of the case interview.The Principle of CorrelationCorrelation describes the degree of relationship between two variables. When two variables correlate, it means that changes in one variable are accompanied by changes in the other variable. A positive correlation occurs when the values of both variables increase or decrease together. An example of a positive correlation is the relationship between the number of hours spent preparing for an exam and the score achieved. As a rule, the more time one invests, the better the exam score.A negative correlation occurs when the values behave in opposite ways, that is, when the value of one variable increases, the value of the other variable decreases, and vice versa. As an example, there may be a negative correlation between the number of hours one spends watching TV and physical fitness. The more time one spends in front of the TV, the less time one has for physical activities, which can lead to lower fitness.However, it is important to understand that correlation alone is not sufficient to conclude causality.The Principle of CausalityCausality means that a change in one variable is a direct cause of a change in another variable. In other words, one variable causes a change in another variable. An example often used to explain the difference between correlation and causality is the relationship between the number of ice cream sales and the number of sunburns. There is a positive correlation between these two variables because more ice cream is sold on sunny days and more people also get sunburned. However, it would be wrong to assume that ice cream consumption causes sunburns. In reality, the common cause of both is sun exposure. On sunny days, people buy more ice cream and are also at higher risk of sunburn. This example illustrates that correlation does not automatically indicate causation.Correlation and Causality in Management ConsultingIn consulting, understanding correlation and causality can play a critical role. When consultants analyze data to help companies or organizations, it is important that they draw the right conclusions and not make false assumptions. Usually it is important to decide which factors should be qualitative and/or quantitative analyzed.Let's say a company finds that there is a strong correlation between the use of a particular marketing strategy and sales growth. The company might be tempted to assume that the marketing strategy is directly responsible for sales growth and therefore continue to invest heavily in that strategy. However, it could be that the correlation only indicates that both variables are influenced by another, as yet unknown, cause. To confirm causality, further research would be required, such as experiments or bigger control groups to test the direct impact of marketing strategy on sales. Possible causes could also be pricing, a change in the product portfolio or the changing size of the market.Overall, it is important to understand that correlation and causality are different concepts. Correlation simply describes the relationship between two variables, while causality implies a cause-and-effect relationship. Just because two variables correlate does not automatically mean that one variable is the cause of the change in the other variable. Further investigation and evidence is needed to conclude causality.