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 other guests ate hamburgers. 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.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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 other guests ate hamburgers. 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 a common '2by2' type of question
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We have 3 variables (a,b,c), one equation (a+b+c=14) in the original condition, 2 equations in the given conditions.
a:b=2:3, a+b=(c+1)/2 --> c=9, a=2, b=3. This is sufficient, and the answer becomes (A).[/img]