Each employee on a task force is either a manager or a director. What percentage of the task force are directors?
(1) The average manager salary is $5,000 less than the average of all employees.
(2) The average director salary is $15,000 more than the average of all employees.
Neither statement alone is sufficient.
The two statements combined constitute a MIXTURE problem.
A certain number of $5000 salaries (on average) are COMBINED with a certain number of $15,000 salaries (on average) to yield a task force that reflects the average salary of ALL of the employees.
To determine the ratio of $5000 salaries to $15,000 salaries in the task force, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Draw a number line, with the managers and directors on the ends and the average salary of all of the employees in the middle.
Managers-------------All-----------------------Directors
Step 2: Enter the distance between the MANAGERS' average and the average salary of ALL of the employees and the distance between the DIRECTORS' average and the average salary of ALL of the employees:
Managers-----
5000----All---------
15,000---------Directors
Step 3: Determine the ratio in the mixture.
The ratio of managers to directors in the mixture is equal to the RECIPROCAL of the distances in red.
Managers : Directors = 15,000:5000 = 3:1.
Thus, of every 4 employees, 3 are managers and 1 is a director, implying that 1/4 = 25% of the employees are directors.
The correct answer is
C.
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