kris610 wrote: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.
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