I got this wrong in the GMATPrep. Can you believe I spent 8 mins on this Q and yet got it wrong eventhough I managed to make-up after this mess & recovered to get 760 in GMATPrep test. But I cannot afford to waste time like this in the actual exam. Not being able to let go is my biggest enemy and that problem is not allowing me to finish the Quant section in time.
Hence I am trying to ensure that I understand the concept behind solving this one once and for all. Actually the problem is not at all difficult once one understands the concept behind it. While I did setup the equations correctly in the test, where I went wrong was that I over-simplified the equation from the beginning. eg. Avg=Sum/No. There is no need for this simplification. Here is how it should have been solved. Don't mind the extra no. of steps. That's just for my own understanding. The actual solution should not take more than 2 mins.
Let M=No of managers, D=No. of Directors. Therefore, M+D=All employees.
Let AM=Avg Sal of Managers, AD=Avg Sal of Directors & A(M+D)=Avg sal of all employees.
St1: AM=A(M+D) - 5000
Sum of Sal of all Managers = M*AM = M*(A(M+D) - 5000)=M*A(M+D) - 5000M
St2: AD=A(M+D) + 15000
Sum of Sal of all Directors = D*AD = D*(A(M+D) + 15000)=D*A(M+D) + 15000D
St1 & St2 when combined yields the equation.
Sum of Sal of all Employees = A(M+D)*(M+D)
Also Sum of Sal of all Employees = Sum of Sal of all Managers + Sum of Sal of all Directors
Therefore, A(M+D)*(M+D) = M*A(M+D) - 5000M + D*A(M+D) + 15000D
i.e. 5000M = 15000 D
i.e. D/M = 1/3
i.e. D/(M+D) = 1/4 = 25%