I think answer to this DS question is A.

It is because of fact that question tells us that "No hamburger was eaten by any guest who was a student, a vegetarian, or both".

Student and Vegetarian ate = 0

Student and Non Vegetarian ate = 0

Non student and Vegetarian ate = 0

Only people Non-Student and Non-Vegetarian ate = 1 burger each, that means there were 15 non-student and non vegetarian people were there in party.

Also given to us that half of them are vegetarian, so that also means half are non-vegetarian.

Statement 1:

Tells us the vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

Create A matrix (See the attached document).

Say there are x vegetarian student (from question that also means we have x non-vegetarian student).

As per this statement vegetarian students = 2x/5 and vegetarian non-students = 3x/5

Number of Non-vegetarian student = x - 15, as 15 were non-vegetarian non-student as calculated above.

As per this statement we have (x-15)/15 = 4/3 (Twice the rate of vegetarian students).

This will give us value of x and total number of guest = 2x.

DO NOT solve to get x and putting back the values as that is not required.

Statement 2:

Tells us that 30% of the guests were vegetarian non-students. But we don't know what is total number of guest so this alone is insufficient.

Answer A.