Data Sufficiency

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.

Mjkourtis wrote: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 $5000 average salary is being combined with a $15,000 average salary to yield a COMBINED average salary for ALL of the employees.

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 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.

For another alligation problem, check here:

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