Data Sufficiency

GMATGuruNY wrote:

meng wrote:Hi everybody, this is actually a 700 level question ! I hope that you can solve it within 2 min ! if you did .. I can say that your score gonna be around 700

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.

Whenever we have groups (in this case, vegatarians 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:



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 way to determine what fraction of the NVs were non-students.
Insufficient.

The correct answer is A.