George,

Here's my solution

The question basically gives us the split which then translates to

Female: Male = 360:180
Teachers: Administrators = 405:135

Since 1/3 of the admin were male, that makes it 45, thereby making 90 of the admin female.

Since we know the total females were 360, then 270 females were teachers.

There were twice as many females as males.
Thus, F:M = 2:1.
Since 2+1 = 3, and the total number of people = 540, the multiplier for the ratio = 540/3 = 180:
F:M = 180(2:1) = 360:180.

There were 3 times as many administrators as teachers.
Thus, T:A = 3:1.
Since 3+1 = 4, and the total number of people = 540, the multiplier for the ratio = 540/4 = 135:
T:A = 135(3:1) = 405:135.

Since 1/3 of the administrators are male, the number of male administrators = (1/3)(135) = 45.

Plug all of these known values into a GROUP GRID and complete the grid so that each row/column adds up to the TOTAL for that row/column:

__________________F______M________Total

A:_______________90______45_________135

T:______________270______135________405

total:___________360______180_________540

Female teachers = 270.

The correct answer is D.