AIM TO CRACK GMAT wrote:How many attendees are at a convention if 150 of the attendees are neither female nor students, one-sixth of
the attendees are female students, two-thirds of the attendees are female, and one-third of the attendees are
students?
Options
a)300 b)450 c)600 d)800 e)900
ill b glad if sum1 could help me asap
An alternate approach is to use the following formula:
Total = Group 1 + Group 2 - Both + Neither.
The big idea with overlapping groups is the SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (females) and everyone in Group 2 (students), those in BOTH groups (female students) are counted TWICE.
Thus, we SUBTRACT THE OVERLAP -- the number in both groups -- so that these people are not double-counted.
Since the LCM of the denominators in the problem is 6, let the total = 6x.
Group 1 = females = (2/3)6x = 4x.
Group 2 = students = (1/3)6x = 2x.
Both = female students = (1/6)6x = x.
Neither = 150.
Plugging these values into the formula, we get:
6x = 4x + 2x - x + 150
x = 150.
Thus, the total number of attendees = 6x = 6(150) = 900.
The correct answer is
E.
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