Overlapping Sets

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Overlapping Sets

by shrey2287 » Fri Oct 07, 2011 8:05 pm
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?

a. 13
b. 10
c. 9
d. 8
e. 7

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by bhavsk9 » Fri Oct 07, 2011 8:13 pm

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by shankar.ashwin » Fri Oct 07, 2011 9:22 pm
Subtracting people who registered for all 3,

(25-3) + (25-3) + (34-3) = 75.

People registered for all 3 = 3

Therefore only 2 = (75 + 3) - 68 = 10

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