Each employee in a certain task force is either a manager or a director. What percent of the employee on the task force are directors ?
1.The Average salary of the Managers on the task force is $5000 less than the avg salary of all Employees on the task force.
2.The avg salary of the directors on the task force is $15000 greater than the avg salary of all employees on the task force.
I got C
Set S = average salary of all
Sm = average salary of managers
Sd = average salary of directors
d = number of directors
m = number of managers
We are looking for:
d / (m+d) = ?
The equation of average salary is the following:
S = (m*Sm + d*Sd) / (m+d)
In (1), we know that Sm = S-5000, and plug it back in, you get no where.
In (2), same problem as (1).
If using both conditions, we have:
S = (m*(S-5000) + d*(S+15000)) / (m+d) = (m*S - 5000m + d*S + 15000d) / (m+d)
S = (S*(m+d) - 5000m + 15000d) / (m+d) = S +(15000d - 5000m)/(m+d)
0 = (15000d - 5000m)/(m+d)
15000d = 5000m
3d = m
And so, d / (m+d) = d / (3d + d) = 1/4