In a group of 68 students, each student is . . . . . .

Hi MY7MBA,

We're told that in a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, thirty-four students are registered for English and only three students are registered for all three classes. We're asked for the number of students who are registered for EXACTLY TWO classes.

A three-group Overlapping Sets question can be solved in a coupe of ways: with a 3-circle Venn Diagram or with a Formula:

Total = (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)

With the data in the prompt, we can fill in most of the formula:

Total = (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)
68 = (25) + (25) + (34) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(3)
68 = 84 - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 6
(Gp 1&2) + (Gp1&3) + (Gp2&3) = 10

While we don't know exactly how many students were in each individual "pair" of classes, we DO know that a total of 10 students were enrolled in 2 classes.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich