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Each of these questions consists of a problem followed by two statements numbered as I and II. Decide whether the data in the statements are sufficient to answer the question. Mark answer as
If a total of 84 students are enrolled in two sections of a calculus course, how many of the 84 students are female?
I. $$\frac{2}{3}$$ of the students in Section 1 are female.
II. $$\frac{1}{2}$$ of the students in Section 2 are female.
We are given that both sections have 84 students each. We are not given if both sections have the same number of students or the ratio in which they have the students.
Looking at the statements, each statement gives what fraction of students in one section are female. Still, without calculating the number of students in the sections individually, we cannot determine what fraction of the total number of students would be female.
Let's take the students into sections A and B, respectively.
Taking both the statements together, we would get the total number of students as: $$\frac{2}{3}A+\frac{1}{2}B$$
Hence, both statements together are insufficient to find the total number of female students.
Therefore, Option D is the correct answer.
