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Mental Math is extremely important for any Management, Bank, Law or Other Related Entrance Exam, where Quantitative Aptitude is tested.
Most of these entrance exams are time bound. You have to attempt a certain number of questions within a certain time limit. If your mental math skills are very good, then it becomes easier for you to attempt more number of questions in that time limit, get them correct and maximize your scores.
Mental math at times tends to be the deciding factor, that differentiates a top ranker from an average scorer. It is not that the person who has performed average does not know the concepts or their application. Even he can, if given the requisite time, can solve all the questions. However, it is because that he takes more time, he is able to attempt less number of questions and thereby, score less than someone whose mental math skills are good and is able to attempt more number of questions in the same time.
In addition, all the questions of the Quantitative Aptitude Section may differ conceptually i.e. one can be from the topic Time, Speed and Distance, one can be from Percentage, one can be from Probability, etc... however; one thing that remains fairly common in all the questions is the Calculation part. Every Quant question will have something or the other to calculate. Therefore, if your mental math is good, it helps you not just for one question but for the entire Quantitative Aptitude and especially Data Interpretation / Integrated Reasoning Section.
There are some entrance exams, where the usage of an on-screen calculator is allowed. However, using it is still time-consuming because of the inherent nature of an on-screen calculator, so using it is not advisable.
To conclude, Mental Math is INEVITABLE for all Management, Bank, Law and Other Related Entrance Exams, where Quantitative Aptitude is a section on which you are tested.