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DS overlapping sets

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by kris610 » Mon May 26, 2008 1:36 pm
In a certain school, out of a total of 65 students, 80% are enrolled in a history course or literature course or both.
How many of the students are currently enrolled in a history course.

A) 10 of the students are currently enrolled in both a history course and a literature course.

B) 33 of the students are currently enrolled in a literature course.
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by VP_Tatiana » Mon May 26, 2008 4:34 pm
The answer here would be C.

The formula for overlapping sets is:

# in set A + # in set B - both = total members of both sets

The reason for this is that # in set A = # only in A + # in both

and # in set B = # only in B + # in both

As you can see, when we add these together, # in both gets counted twice, so we have to subtract one of them to avoid double counting.

For this particular problem, we'd have:

# history + # literature - both = 80% * 65

# history + # literature - both = 52

To solve for the number of history students, we need both the number of literature students AND the number of students enrolled in both. Thus, we need both statement (1) and statement (2), so the answer is C.
Tatiana Becker | GMAT Instructor | Veritas Prep
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