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# Guests at a recent party ate a total of fifteen hamburgers.

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Senior Manager
Joined: 30 Nov 2008
Posts: 493
Schools: Fuqua
Followers: 10

Kudos [?]: 154 [0], given: 15

Guests at a recent party ate a total of fifteen hamburgers. [#permalink]  29 Aug 2009, 21:33
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Guests at a recent party ate a total of fifteen hamburgers. Each guest who was neither a student nor a vegetarian ate exactly one hamburger. No hamburger was eaten by any guest who was a student, a vegetarian, or both. If half of the guests were vegetarians, how many guests attended the party?

(1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

(2) 30% of the guests were vegetarian non-students.
Senior Manager
Joined: 21 Jul 2009
Posts: 366
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Followers: 15

Kudos [?]: 110 [0], given: 22

Re: Sets - DS [#permalink]  31 Aug 2009, 06:38
Blindly we can go with a E. There are four entities, students and non-students and vegetarians and non-vegetarians and then there are over-laps and we last end up with just one thing, all non-students and non-vegetarians only ate one hamburger each and total hamburgers eaten were 15. With the given two statements, nothing makes sense in a Venn Diagram as well. I think, it is a straight-forward E.
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Senior Manager
Joined: 30 Nov 2008
Posts: 493
Schools: Fuqua
Followers: 10

Kudos [?]: 154 [0], given: 15

Re: Sets - DS [#permalink]  02 Sep 2009, 10:54
Hum....I didn't see much of the responses. Anyhow here is my take -

consider the following matrix format - where S(Student), ~S (Non Student) V (Vegetarian) and ~V(Non Vegetarian). It is given that exctly 15 people had hamburger and no body else ate the hamburger(Student, Vegetarian or either of them). Also given that Vegetarian : Non Vegetrian = 1:1. Based on this, the matrix can be filled as follows - where a,b,c and x are unknowns. Need to find 2x = ? (The picture dipicted might not be as readable as I expected.

| S ~S Total
V | a b x
~V | c 15 x
-----------------------
| 2x - ???

From Clue 2, it is given that b= 30 % or 2x ==> From this we cannot find the exact value of x So options B and D are ruled out.

From clue 1, it is given that Vegetarian Students : Vegetarian non-students = 1 /2 (NonVegetarian students : NonVegetrain Non Students) Also Vegetarian students : Vegetarian non-students = 2: 3

==> 2/3 = (1/2)*(C/15) ==> 2/3 = c/30

==> c = 20 ==> x = 35

So total no of guests = 2x = 70.

My take is A(which is also OA)

Initially I was confused with the wording of clue 1. Could not represent it as a mathematical notation.
Re: Sets - DS   [#permalink] 02 Sep 2009, 10:54
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# Guests at a recent party ate a total of fifteen hamburgers.

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