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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 03 Sep 2010, 18:34
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Difficulty:

  85% (hard)

Question Stats:

43% (07:07) correct 57% (03:35) wrong based on 7 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.

please explain your answer!! thanks~
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Joined: 31 Dec 1969
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WE: Accounting (Accounting)
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Re: burger [#permalink] New post 03 Sep 2010, 19:56
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.

Answer A
Great question! Tough to wrap your brain around within 2 minutes.
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Re: burger [#permalink] New post 04 Sep 2010, 10:54
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?
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Re: burger [#permalink] New post 05 Sep 2010, 22:01
nice question, kudos!
Re: burger   [#permalink] 05 Sep 2010, 22:01
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Guests at a recent party ate a total of fifteen hamburgers.

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