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Guests at a recent party ate a total of fifteen hamburgers. [#permalink]
23 Sep 2007, 22:23
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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.
Vegeterian who attended: students/non-students = 2/3
Non-vegeterian who attended: students/non-students = 4/3
If # of people = x and # of vegeterians = v, then # of non-vegeterians = x-v
# of vegeteriansstudents = 2v/5
# of vegeterian non-students = 3v/5
# of non-vegeterian students = 4(x-v)/7
# of non-vegeterian non-student = 3(x-v)/7
We're told only non-vegeterians non-students ate hamburgers. so 3(x-v)/7 = 15
x-v = 35
But we know v = 1/2x, so x-1/2x = 35, x/2 = 35, x = 70.Sufficient.
# of guests = x
# of vegeterian non-students = 0.3x
we also know # of vegeterians = 0.5x, so # of vegeterian students = 0.2x
But we do not know how many non-vegeterians non-students, so we can't sovle. Insufficient.