Wondering if anyone else has any alternative solutions to this?
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-studentsThe stem:
Two groups: Students and not students (let's call them Professors), S
; either Veg or Non.Veg, V
.V&P+N&P=P and V&S+N&S=S
We are told that that 15 hamburger was eaten 1 by each guest
who was neither a student nor a vegetarian
and only by them. So we know the number of P which are N=N&P=15
Basically this info was given only to determine this number and to make the wording confusing. Tricky GMAT!
Half of the students V=N. --> Total=V+N=2V=2N
. So if we knew the V or N we can calculate Total number of guests.
What do we know from the stem:N&P=15Total=V+N=2V=2N V&P+N&P=V&P+15=P and V&S+N&S=SStatements:
(1) V&S/V&P=2/3 and N&S/N&P=N&S/15=2*2/3 --> N&S=20 which means that non vegetarian students
were 20, but we know that non vegetarian professors
were 15, total non vegetarians N=20+15=35. Total =2N=2*35=70. Sufficient.
NOTE: If the rate of X (some fraction) is half the rate of Y (another fraction), then the rate of Y= twice rate of X.
(2) V&P=Total*30%. We can not calculate numerical value of V&P hence insufficient.
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