If a total of 84 students are enrolled

If a total of 84 students are enrolled in two sections of a calculus course, how many of the 84 students are female? (1) 2/3 of the students in Section 1 are female. (2) 1/2 of the students in Section 2 are male. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient., EACH statement ALONE is sufficient., Statements (1) and (2) TOGETHER are not sufficient.

2 Explanations

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@FarheenAKhan, great question! You very well could approach this problem using a Venn Diagram or a matrix box, but I am not sure if it will be any faster. With this problem, you have to spend a little extra time because you are evaluating statement 1 and 2 alone, and then at the end evaluating them together. And the Venn Diagram or matrix will not make this part any shorter.

With a diagram or matrix, you will still discover that you don't have any information about how many of the 84 students are in section 1 and 2. We don't know the overlap, so we can't know how many women are in these sections.

Again, great question! It is always great to have multiple approaches ready for math questions. :)

Nov 1, 2013 • Comment

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Mike McGarry, Magoosh Tutor