Data Sufficiency

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.

OA is A

We've got four groups:

Vegetarian Students (my favorite )
Non-Vegetarian Students
Vegetarian Non-Students
Non-Vegetarian Non-Students

Let's call these groups A, B, C, and D, respectively.

We know A, B, and C ate a total of 0 hamburgers. So D ate all 15, meaning that we have 15 Non-Vegetarian Non-Students.

We also know that half the guests were vegetarians, so A + C = B + D, or A + C = B + 15.

S1 tells us that A/C = 2/3, or 3A = 2C, or A = (2/3)C. If this is half the rate for non-veggies, the non-veggie rate is B/D = 4/3, or 3B = 4D. D = 15, so 3B = 4*15, or B = 20.

Putting it all together, we have

A + C = B + 15, or
(2/3)C + C = 20 + 15, or
(5/3)C = 35, or
C = 21

So A = 14, C = 21, B = 20, and D = 15. SUFFICIENT.

S2 tells us 30% of (A+B+C+15) = C. We still have a few unknowns here, so this INSUFFICIENT.