Sets for an overlapping sets problem it is best to use a double set matrix to organize the information and solve. Fill in the information in the order in which it is given

150
2P/3
TOTALS	2P/3	P/3	P

The non-boldfaced entries can be derived using simple equations that involve the numbers in one of the "total" cells. Let's look at the "Female" column as an example. Since we know the number of female students (P/6) and we know the total number of females (2P/3), we can set up an equation to find the value of female non-students:

P/6 + Female Non Students = 2P/3.
Solving this equation yields: Female Non Students = 2P/3 – P/6 = P/2.

By solving the equation derived from the "NOT FEMALE" column, we can determine a value for P.

P 6

+ 150 =

P 3

P + 900 = 2P P = 900

The correct answer is E.

5.

For an overlapping set problem we can use a double-set matrix to organize our information and solve. Because the values here are percents, we can assign a value of 100 to the total number of lights at Hotel California. The information given to us in the question is shown in the matrix in boldface. An x was assigned to the lights that were “Supposed To Be Off” since the values given in the problem reference that amount. The other values were filled in using the fact that in a double-set matrix the sum of the first two rows equals the third and the sum of the first two columns equals the third. 

	Supposed To Be On	Supposed To Be Off	TOTAL
Actually on