Algebra: How many guests attended the party?

Algebra is by far the most fundamental question type appearing on GMAT, GRE, or SAT. This topic encompasses subtopics such as Algebraic Expressions, Linear Equations, Quadratic Equations, Exponents, Inequalities, Absolute Value, and Functions.
One would often find good chunk of word problems appearing from this topic. It also covers arguably the most dreaded combination on these exams – Inequality + Data Sufficiency.
Like Number Systems, Algebra forms the basis for many question types on the test and there are many smart tricks to be learnt.  One should learn how to avoid pitfalls, and be careful in dealing certain question types. This topic must be tamed with supreme authority to do well on the Maths section.

Solve the following Data Sufficiency question:

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
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