Ok, Lets make a grid for Hamburgers as that's the information we have.

--------Student--------------Non Student-------------Total

Veg. ----------0------------------------0-----------------------0

Non-Veg-------0-----------------------15----------------------15


Total-----------0------------------------15---------------------15


Explanation for the 0's
No hamburger was eaten by any guest who was a student, a vegetarian, or both

Moving on:
Let the total number of guests = x

therefore, vegetarian guests = 1/2x (If half of the guests were vegetarians, how many guests attended the party)
Non-vegetarian guests = 1/2x

From statement 1:

Number of students - vegetarians = 2y (ratio is 2:3)
Number of non-students vegetarians = 3y

Now,

Number of students - non-vegetarians = 4y (ratio is double that of student vegetarians to non-student vegetarians i.e. 2*2/3 = 4/3)
Number of non-students - non-vegetarians = 3y

Number of hamburgers eaten by non-students - non-vegetarians = 15 (from the grid we made)

Therefore - as each non-student - non-vegetarian student ate only 1 hamburger

number of non-student - non-vegetarians = 3y = 15

or y = 5

Total number of guests (x) = 2y + 3y + 4+ 3y = 12y

x = 12y
x = 12(5)
x = 60

SUFFICIENT

Statement II

Number of guests = x
Number of Vegetarians = 0.3x
Non-vegetarians = 0.7x

Students??? - no idea - NOT SUFFICIENT

imo A

Heres my reasoning.

From the question we know that:

No hamburger was eaten by any guest who was a student, a vegetarian, or both.

And the guests ate a total of 15 hamburgers. Also half of the guests were vegetarian and the other half non vegetarian.

So the hamburgers were eaten only by non-veg non students.
Hence number of non-veg non students = 15

St 1 veg students to veg non students = 2:3
non veg students to non veg non students = 4:3

4/3 = non veg students/15
non veg students = 20
Total number of non veg guests = 20 + 15 = 35
Total number of veg guests = 35
Total number of guests = 70 ---SUFF

St 2: 30% of the guests were vegetarian non-students.
We have no information about the remaining 70% whether how many of them were veg students and non-veg guests. INSUFF.