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nirbans: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Thu Feb 03, 2011 9:39 pm; Location: Canada

Set question from test - please provide a solution

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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Source: Beat The GMAT — Problem Solving | Tue Jul 05, 2011 11:52 am

ntamhane: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Thu Jun 30, 2011 4:15 am; Thanked: 1 times; Followed by:1 members

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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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 am; Location: pune; Thanked: 36 times; Followed by:3 members

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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abhisays: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Sun Nov 29, 2009 7:11 pm; Location: Bangalore; Thanked: 4 times

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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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