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

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Manager
Joined: 21 Feb 2010
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Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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03 Sep 2010, 19:34
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Difficulty:

95% (hard)

Question Stats:

50% (03:16) correct 50% (03:07) wrong based on 12 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/guests-at-a-r ... 04547.html

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Joined: 31 Dec 1969
Location: Russian Federation
WE: Supply Chain Management (Energy and Utilities)
Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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03 Sep 2010, 20:56
There are four categories of people
-vegetarian student - no hamburgers eaten
-vegetarian non-student - no hamburgers eaten
-non-vegetarian student - no hamburgers eaten
-non-vegetarian non-student - 1 hamburger eaten per person, thus 15 people in this category

If you can determine what proportion of guests were non-veg non-students, you can find the total number of guests.

Statement (1)
From the question stem, half the guests are vegetarian, thus half are non-vegetarian. Statement (1) says that the ratio of non-veg students to non-veg non-students is 4:3. The number of non-veg non-students must be = (4/7)*0.5N where N is the total number of guests.
15 guests are non-veg non-students, so 3/4*(0.5N)=15. Now you can solve for N.
Statement (1) is SUFFICIENT

Statement (2) allows us to determine the proportion of guests who are vegetarian students and vegetarian non-students, but it does not tell us anything about the proportion of guests who are non-veg non-students, thus statement (2) is NOT sufficient.

Great question! Tough to wrap your brain around within 2 minutes.
Manager
Joined: 21 Feb 2010
Posts: 177
Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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04 Sep 2010, 11:54
if i have such question on the actual test, does anyone think that you can solve it in 2 mins? if not, should we guess the answer and go forward, instead wasting time on this kind of question?
Manager
Joined: 03 Jun 2010
Posts: 144
Location: United States (MI)
Concentration: Marketing, General Management
Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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05 Sep 2010, 23:01
nice question, kudos!
Math Expert
Joined: 02 Sep 2009
Posts: 55277
Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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14 Aug 2017, 08:57
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?

We have 4 groups of guests:
1. Vegetarian students;
2. Vegetarian non-students;
3. Non-vegetarian students;
4. Non-vegetarian non-students.

Now, as guests ate a total of 15 hamburgers and each guest who was neither a student nor a vegetarian (group #4) ate exactly one hamburger and also as no hamburger was eaten by any guest who was a student, a vegetarian, or both (groups #1, #2 and #3) then this simply tells us that there were 15 non-vegetarian non-students at the party (group #4 = 15).

Make a matrix:

Note that we denoted total # of guests by $$x$$ so both vegetarians and non-vegetarians equal to $$\frac{x}{2}$$.

(1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians --> $$\frac{vegetarian \ students}{vegetarian \ non-students}=\frac{2}{3}$$ --> if the rate X (some fraction) is half of the rate Y (another fraction), then Y = 2*X --> $$\frac{non-vegetarian \ students}{non-vegetarian \ non-students}=2*\frac{2}{3}=\frac{4}{3}$$ --> so, non-vegetarian non-students compose 3/7 of all non vegetarians: $$non-vegetarian \ non-students = 15 = \frac{3}{7}*\frac{x}{2}$$ --> $$x=70$$. Sufficient.

(2) 30% of the guests were vegetarian non-students --> just says that # of $$vegetarian non-students$$ equal to $$0.3x$$ --> insufficeint, to calculate $$x$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/guests-at-a-r ... 04547.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest   [#permalink] 14 Aug 2017, 08:57
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