Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?
1) The average salary of the managers on the task force is 5,000 less than the average salary of all employees on the task force.
2) The average salary of the directors on the task force is 15,000 greater than the average salary of all employees on the task force.
Each statement is clearly insufficient on its own.
When combining the statements, we can plug in for the average salary of all the employees and use alligation.
Let:
A = average salary of all the employees.
M = average salary of the managers.
D = average salary of the directors.
Let A = 10,000.
M = 10,000 - 5000 = 5000.
D = 10,000 + 15,000 = 25,000.
This is a weighted average question: What ratio of managers (with an average salary of 5000) to directors (with an average salary of 25,000) will yield a company with an average salary of 10,000?
We can use alligation to determine the ratio:
The proportion needed of each element in the mixture is the positive difference between the average attributed to the other element and the average attributed to the final mixture.
Proportion needed of M = 25,000-10,000 = 15,000.
Proportion needed of D = 10,000-5,000 = 5000.
M : D = 15,000 : 5000 = 3:1.
Since 3+1=4, D = 1/4 = 25%.
The correct answer is
C.
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