3 sets prob

Expert replies

mavesum: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Sun Aug 31, 2008 11:20 pm

by mavesum » Mon Apr 20, 2009 5:52 am

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

[spoiler]Ans : 10 [/spoiler]

My approach :

We need to find HM+HE+ME

68 = H+M+E-(HM+HE+ME) + HME
68 = 25+25+34 - (HM+HE+ME) + 3

68 = 84 - (HM+HE+ME) + 3

HM+HE+ME = 19

What am i missing ??

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Source: Beat The GMAT — Problem Solving | Mon Apr 20, 2009 5:52 am

rossmj: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Feb 26, 2009 12:50 pm; Location: Chicago; Thanked: 3 times

by rossmj » Mon Apr 20, 2009 7:20 am

We know that 3 students are in all 3 courses so that means we are only looking at 65 students. Subtracting these students leads to 22 History, 22 Math, and 31 English. The sum of these groups is 75, thus 10 people is the overlap.

In your approach you are double counting people by adding 3 additional students to the ones that are registered.

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dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

by dumb.doofus » Mon Apr 20, 2009 4:26 pm

If you simply draw a venn diagram, things become very simple..

Look at the figure below..

Now just write the equation as you see it in the diagram..

i.e.

(25 -x - z - 3) + (25 -x -y -3) + (34 -y -z -3) + x + y + z + 3 = 68

=> x + y + z = 10

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mavesum: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Sun Aug 31, 2008 11:20 pm

by mavesum » Tue Apr 21, 2009 12:10 am

thanx DD n Ross , venn diagram makes it clear

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