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.

First of all, we need to be able to find a solid number,the total number of guest, as an answer.

The only solid number we are given to work with is 15, the number of hamburgers eaten by the guests.

From the question we could see that the guests can be broken down into 4 categories.

VEGETARIAN STUDENT (V & S)
NON-VEGETARIAN STUDENT (NV & S)
VEGETARIAN NON-STUDENT (V & NS)
NON-VEGETARIAN NON-STUDENT (NV & NS)

Looking @ # of hamburgers eaten,

The question states that (NV & NS) ate exactly 1 hamburger and that
no hamburger was eaten by any guest who was a student, hamburger eaten by (V & S) = (NV & S) = 0; a vegetarian, hamburger eaten by (V & S) = (V & NS) =0; or both, hamburger eaten by (V & S) = 0.

So from this we can conclude the # of (NV & NS) = 15.

The last piece of information given is that 1/2 Total = V, which also means 1/2 Total = NV, where NV + V = Total and NS + S = Total. Drawing a table can help understand this relationship.



Statement 1:

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

I think this should be reworded to ratio instead of rate.

Anyways this just means that for every 2 (V & S) there are 3 (V & NS), which is half the ratio of S to NS for NV. Therefore for every 4 (NV & S) there are 3 (NV & NS), which means \frac{4}{3}=\frac{(NV & S)}{(NV & NS)}

Since we know that (NV & NS) = 15. We can solve for (NV & S) and Find Total because 1/2* Total = (NV & NS) + (NV & S)

Sufficient.

Statement 2:

30% of the guests were vegetarian non-students.

This give us no way to link 15 to the total number of guest. So insufficient.

This is more clear if you draw a table to help visualize things.

I'm sure someone will come up with a better explanation later, but I hope this can help till then.

This is what I drew when I read the Question stem. Half of the guests were vegetarians so Total/2 stands for the complete vegetarian circle. All outside Vegetarian circle are Total/2.


Statement 1: Veg students : Veg non students = 2:3
Let me say they are 2x and 3x in number.

Non veg students : Non veg non-students = 4:3 (Since veg's ratio is half of non veg's ratio)
Let me say they are 4y and 3y in number.
So now my diagram looks like this:


3y = 15 hence y = 5
Since 7y is half of the total, 35 is half of the total. So total number of students is 70. Sufficient.

Statement 2: We get that 30% of the guests were veg non students and we already know that 50% of the guests are veg so 20% of the guests are veg students. Essentially, we have got the 3:2 ratio of above. But we do not have the 4:3 ratio of above hence we cannot equate 15 to anything. Therefore, statement 2 is not sufficient alone.
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Good one!
Stumbled in the test. I like the MGMAT solution.

Non veg - Non Students is 15.

Since Nonveg Student to non student ratio is 4:3, therefore non veg students will be 20.
4/3=x/15
Therefore x= 20. That makes 35 NV and 35 Veg so total 70

St 1: Sufficient: Veg attended in 2:3 so the Non veg attended in ratio 4:3. We now from Question stem Non veg - Non student ate 15 burgers. therefore Non veg attended the party in 20:15 (4:3). Total no of Non Veg = 35 nos. And total guests = 2*35=70 (from Question Stem).
St 2: Not sufficient: cant calculate other group of non-veg and only %age is provided.

Hence Answer A.
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SD
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