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

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Manager
Joined: 21 Feb 2010
Posts: 207
Followers: 2

Kudos [?]: 34 [1] , given: 1

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

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03 Sep 2010, 19:34
1
KUDOS
00:00

Difficulty:

85% (hard)

Question Stats:

38% (07:07) correct 63% (03:21) wrong based on 8 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.

[Reveal] Spoiler: OA
Joined: 31 Dec 1969
Location: Russian Federation
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)
Followers: 0

Kudos [?]: 233 [0], given: 104586

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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: 207
Followers: 2

Kudos [?]: 34 [0], given: 1

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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: 181
Location: United States (MI)
Concentration: Marketing, General Management
Followers: 6

Kudos [?]: 69 [0], given: 40

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05 Sep 2010, 23:01
nice question, kudos!
Re: burger   [#permalink] 05 Sep 2010, 23:01
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