An easy way to solve the problem is to set up a double set matrix. In our matrix we have two main categories: gender and drama club status. More specifically our table will be labeled with:
1) Percent of males (Males)
2) Percent of females (Females)
3) Percent of people enrolled in the drama club (Drama)
4) Percent of people not enrolled in the drama club (No Drama)
(To save room on our table headings we will use the abbreviations for the categories.)
Since we are asked “what percent” of the drama club members enrolled at a certain school are female students, we can use the convenient number 100 as the total number of people in the school.
Thus, we know:
Total people = 100
Let’s fill all the information into a table.
Now we can move on to the statements.
Statement One Alone:Of the female students enrolled at the school, 40 percent are members of the drama club.
Since we do not know the number of female students, we can let the number of females equal f. We can thus express the number of female students in the drama club as 0.4f.
Let’s fill the information into the table.
The information provided is not enough to determine what percent of the drama club members enrolled at a certain school are female students. Statement one alone is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:Of the male students enrolled at the school, 25 percent are members of the drama club.
Since we do not know the number of male students, we can let the number of males in the school equal m. Thus, we can express the number of male students in the drama club as 0.25m.
Let’s fill the information into the table.
The information provided is not enough to determine what percent of the drama club members enrolled at a certain school are male students. Eliminate answer choice B.
Statements One and Two Together:We know the following:
We see that from the information in the table we do not have the ability to determine the value of f or m; thus, we can’t determine the percentage of the students in the drama club who are female students.
The answer is E.