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.

This is an EITHER/OR group question.
Everyone is EITHER a vegetarian OR not.
Everyone is EITHER a student OR not.
Use a GROUP GRID (also known as a matrix) to organize the data.

In the grid below, V = vegetarians, NV = non-vegetarians, S = students, NS = non-students:



Every row in the grid has to add up to the total, as does every column.
Looking at the top row, student vegetarians + student non-vegetarians = total students.
Looking at the left-most column, student vegetarians + non-student vegetarians = total vegetarians.

Now let's fill in the data step by step.

Let T = total.
Since half of the guests are vegetarians, V = (1/2)T, NV = (1/2)T.
Since the 15 hamburgers were eaten by the non-student NVs, 15 goes in the center box:



Statement 1: The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.
For VEGETARIANS, students : non-students = 2:3.
The rate for non-vegetarians was TWICE the rate for vegetarians.
Thus, for NON-VEGETARIANS, we get:
(NV students) : (NV non-students) = 2 * (2:3) = 4:3.
Thus, of every 7 NVs, 4 were students and 3 were non-students, implying that 3/7 of the NVs were non-students.
Plugging this information into the grid, we get:



Since in the center box we have (3/7)(1/2)T = 15, we can solve for T.
SUFFICIENT.

Statement 2: 30% of the guests were vegetarian non-students.
No way to determine what fraction of the NVs were non-students.
INSUFFICIENT.

The correct answer is A.