MGMAT CAT1 question

[kris610]

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.

If in the overlapping set matrix, we represent the students with 'S', non-students with 'NS' and non-vegetarians with 'NV',
don't the 2nd and 3rd statements in the question indicate that the intersection of S&NV equal 0?
Or should I assume that the students who are non-vegetarians (S&NV) had some other non-vegetarian burger option?A

[navami]

IMO C

What is OA?

[GMATGuruNY]

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.

If in the overlapping set matrix, we represent the students with 'S', non-students with 'NS' and non-vegetarians with 'NV',
don't the 2nd and 3rd statements in the question indicate that the intersection of S&NV equal 0?
Or should I assume that the students who are non-vegetarians (S&NV) had some other non-vegetarian burger option?A

Whenever we have groups (in this case, vegetarians and non-vegetarians) that are being divided into smaller groups (in this case, students and non-students), we can use a group grid to organize the data.

Here's what the grid looks like (V = vegetarians, NV = non-vegetarians, S = students, NS = non-students):



In the grid above, every row has to add up to the total, as does every column. Looking at the top row, student vegetarians + student non-vegetarians = total students. Looking at the left-most column, student vegetarians + non-student vegetarians = total vegetarians.

Now let's fill in the data step by step.

Let T = total.
Since half the guests are vegetarians, V = (1/2)T, NV = (1/2)T.
Since the 15 hamburgers were eaten by the non-student NVs, 15 goes in the center box:



The only fixed value in the problem is the 15 hamburgers. All of these hamburgers were eaten by the non-student NVs. Thus, to determine the value of T, we're looking for information about the non-student NVs.

Statement 1: The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.
Thus, for the NVs, students : non-students = 4:3. This means that 3/7 of the NVs were non-students. Here is what the grid now looks like:



Since in the center box we have (3/7)(1/2)T = 15, we can solve for T.
Sufficient.

Statement 2: 30% of the guests were vegetarian non-students.
No information about the non-student NVs.
Insufficient.

The correct answer is A.

[sureng]

Mitch:
I am little confused at the way you arrived at 3/7.

"Thus, for the NVs, students : non-students = 4:3. This means that 3/7 of the NVs were non-students. "
Can you pls clarify?

[sureng]

and also

"(3/7)(1/2)T = 15" ?