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MGmat wrong answer in Practice test

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satishchandra.aily
 Post subject: MGmat wrong answer in Practice test
 Post Posted: Sat May 14, 2011 2:59 am 
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Students


Posts: 2
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

Mgmat has wrongly given the answer as 10.

Its a simple problem. My method of solving is as follows. Instead of suggesting a different method of solving the problem, find out the flaw in my method.
H-History, M-Math, E-English; Not Mutually exclusive



(H U M U E) = H + M + E – H^M – M^E – E^H + H^M^E

68 = 25+25+24-(H^M + M^E + E^H) + 3

(H^M + M^E + E^H) = 9

My answer is 9.
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rocsid.g91
 Post subject: Re: MGmat wrong answer in Practice test
 Post Posted: Sat May 14, 2011 12:55 pm 
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Students


Posts: 6
Ummm actually there's a flaw in your reasoning and your substitution.
(H U M U E) = H + M + E – H^M – M^E – E^H + H^M^E

Man this formula after tons of practice still makes no sense to me, so i don't use it. :-)
Either ways you've substituted 24 for 34. So that's an error.

This is the reasoning I used.
68 people out of which 3 members are in all three = 65 ( 1 class plus 2 classes)
25 members out of which 3 members are in all three = 22 ( 1 class plus 2 classes)
25 members out of which 3 members are in all three = 22 ( 1 class plus 2 classes)
34 members out of which 3 members are in all three = 31 ( 1 class plus 2 classes)

22 + 22 + 31 = 75 ( 1 class plus 2 classes)
75-65 = 10.

I believe manhattan's right.
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jnelson0612
 Post subject: Re: MGmat wrong answer in Practice test
 Post Posted: Sat May 14, 2011 9:42 pm 
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ManhattanGMAT Staff


Posts: 1857
Thank you rocsid. The answer is indeed 10. This thread may shed more light on it: overlapping-sets-t1960.html

_________________
Jamie Nelson
ManhattanGMAT Instructor
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