garuhape wrote:I hate these set questions...

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, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

OA is 10 however I get 13.

#Students = #History + #Math + #English - #All Three - # Two Courses

68 = 25 + 25 + 34 - 3 - #Two Courses <=> #Two Courses = 13

Plz help

This problem is testing your knowledge of overlapping groups. Here is the formula for 3 overlapping groups in which sometimes 2 groups overlap and sometimes all 3 groups overlap:

T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)

The big idea with overlapping groups is to subtract the overlaps. When we count everyone in the 3 groups, those in 2 of the groups will be counted twice, so they need to subtracted from the total once. Those in all 3 groups will be counted 3 times, so they need to be subtracted from the total twice.

In the problem above:
T = 68
G1+G2+G3 = history + math + english = 25+25+34 = 84
Those registered for exactly 2 subjects = x
Those registered for all 3 subjects = 3

Plugging into the formula, we get:

68 = 84 - x - 2*3
68 = 78 - x
x = 10.

The correct answer is B.

GMATGuruNY wrote:
The big idea with overlapping groups is to subtract the overlaps. When we count everyone in the 3 groups, those in 2 of the groups will be counted twice, so they need to subtracted from the total once. Those in all 3 groups will be counted 3 times, so they need to be subtracted from the total twice.

Thank you very much!