Stuart Kovinsky 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.

Hooray for another opportunity to showcase the all-powerful data sufficiency tool, "# of equations vs # of unknowns".

There are only two groups here, so we can use the basic overlapping sets formula:

True # of objects = total # in group 1 + total # in group + total # in neither group - # in both groups

or, more simply:

Total = G1 + G2 + neither - both

Applying that formula to the question stem, we get:

# Guests = #students + #vegetarians + neither - both

and we know that

#v = 1/2(#g) and neither = 15, so:

G = S + .5G + 15 - both

So, we have 1 equation and 3 unknowns.

(1) gives us two ratios. What can we do with ratios? Turn them into equations! Now, here's the beautiful thing... we don't care what those equations are, as long as they:

- are linear;
- are distinct; and
- don't introduce any new variables.

Going through our checklist, we see that all 3 criteria are upheld. Therefore, we have 3 distinct linear equations for 3 unknowns: we can solve the entire system, sufficient!

(2) gives us one equation that still leaves some variables we don't want in the mix: insufficient.

(1) is sufficient, (2) isn't: choose (A).