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

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

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New post 03 Sep 2010, 19:34
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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

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Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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New post 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.

Answer A
Great question! Tough to wrap your brain around within 2 minutes.
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Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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New post 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?
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Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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New post 05 Sep 2010, 23:01
nice question, kudos!
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Re: Guests at a recent party ate a total of fifteen hamburgers. Each guest  [#permalink]

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New post 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:
Image
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.
Image


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


Answer: A.

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