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

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Guests at a recent party ate a total of fifteen hamburgers. [#permalink] New post 02 Nov 2009, 03:00
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Difficulty:

  85% (hard)

Question Stats:

57% (02:20) correct 43% (01:35) wrong based on 48 sessions
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: guests-at-a-recent-party-ate-a-total-of-fifteen-hamburgers-104547.html
[Reveal] Spoiler: OA
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Re: Venn Diagram [#permalink] New post 02 Nov 2009, 05:23
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This Q should use spaghetti not ^$% hamburgers... it is so twisted, represents the examiners mind ;)

I'd go with A.
Here's how...

50% veg, 50% non veg
VEG{Students:Non-students}=2:3=2xNON-VEG{Students:Non-students}=4:3
(3/7 Non-Veg, are non-students who ate burgers)=15
=>Non-Veg = 35; total attendees = 70
Sufficient.

B.
Either not sufficient (disconnected sets) or I'm too tired to look at it anymore :evil:
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Re: Venn Diagram [#permalink] New post 11 Nov 2009, 02:51
Wondering if anyone else has any alternative solutions to this?
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Re: Venn Diagram [#permalink] New post 11 Nov 2009, 05:53
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yangsta8 wrote:
Wondering if anyone else has any alternative solutions to this?


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

The stem:
Two groups: Students and not students (let's call them Professors), S and P; either Veg or Non.Veg, V and N.
V&P+N&P=P and V&S+N&S=S

We are told that that 15 hamburger was eaten 1 by each guest who was neither a student nor a vegetarian and only by them. So we know the number of P which are N=N&P=15.

Basically this info was given only to determine this number and to make the wording confusing. Tricky GMAT!

Half of the students V=N. --> Total=V+N=2V=2N. So if we knew the V or N we can calculate Total number of guests.

What do we know from the stem:
N&P=15
Total=V+N=2V=2N
V&P+N&P=V&P+15=P and V&S+N&S=S

Statements:
(1) V&S/V&P=2/3 and N&S/N&P=N&S/15=2*2/3 --> N&S=20 which means that non vegetarian students were 20, but we know that non vegetarian professors were 15, total non vegetarians N=20+15=35. Total =2N=2*35=70. Sufficient.

NOTE: If the rate of X (some fraction) is half the rate of Y (another fraction), then the rate of Y= twice rate of X.

(2) V&P=Total*30%. We can not calculate numerical value of V&P hence insufficient.

Answer: A.
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Re: Venn Diagram [#permalink] New post 11 Nov 2009, 08:14
gmattokyo wrote:
This Q should use spaghetti not ^$% hamburgers... it is so twisted, represents the examiners mind ;)

I'd go with A.
Here's how...

50% veg, 50% non veg
VEG{Students:Non-students}=2:3=2xNON-VEG{Students:Non-students}=4:3
(3/7 Non-Veg, are non-students who ate burgers)=15
=>Non-Veg = 35; total attendees = 70
Sufficient.

B.
Either not sufficient (disconnected sets) or I'm too tired to look at it anymore :evil:


kudos..exactly right..spaghetti..
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Re: Venn Diagram [#permalink] New post 11 Nov 2009, 18:01
that's a 600 level question?
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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink] New post 25 Apr 2013, 21:23
Can any one help me solving this using 2*2 matrix

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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink] New post 25 Apr 2013, 23:59
Expert's post
Re: Guests at a recent party ate a total of fifteen hamburgers.   [#permalink] 25 Apr 2013, 23:59
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Guests at a recent party ate a total of fifteen hamburgers.

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