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Set question from test - please provide a solution

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by nirbans » Tue Jul 05, 2011 11:52 am
I got a question like this on test. Can you please state how to solve this kind?

In a certain class of 100 students, 75 take history and 60 take chemistry. At least what number of students must study both?

1. 15, 2. 30, 3. 35, 4. 40, 5. 45 [do not exactly remember the ans choices]
Thanks, Nirban
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by ntamhane » Tue Jul 05, 2011 6:15 pm
75 take history and 60 take chemistry
hence 135-100=35 students.
hence 35 students must have taken both.
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by amit2k9 » Tue Jul 05, 2011 9:33 pm
using table method -

---C-------C!
H--35---- 40---75

H!-- ---- 0 --25

---60-----40---100

thus 35 it is.
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by abhisays » Tue Jul 05, 2011 9:42 pm
Here we can easily apply the forumula.

n(A U B) = n(A) + n(B) - n(A /\ B)

100 = 75 + 60 - n(A /\ B)

therefore, n(A /\ B) = 35
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by Anurag@Gurome » Tue Jul 05, 2011 9:55 pm
nirbans wrote:In a certain class of 100 students, 75 take history and 60 take chemistry. At least what number of students must study both?
If none of the students had studied both, number of students in the class would've been (60 + 75) = 135, i.e. 35 more than what it is now. Thus these 35 extra students must have been compensated by the students who are studying both.

Hence, number of students who studies both = 35

The correct answer is C.
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by GMATMadeEasy » Wed Jul 06, 2011 3:51 am
What would be the maximum number of people in both the courses ?
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