Data Sufficiency

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.

Making two double matrices is ridiculous right? I mean - how could this possibly be a realistic question?

(A)

woah... that is difficult! I don't get it at all. where did you find this question??

doclkk 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.

Making two double matrices is ridiculous right? I mean - how could this possibly be a realistic question?

No need for a double matrix, just have to keep track of what's going on.

We have two categories of people: vegetarians and students. Like any overlapping sets question, people can be in these groups or not in these groups, so there aren't actually 4 categories to track.

We know that there are a total of 15 hamburgers; we know that anyone neither a vegetarian nor a student ate 1 hamburger each; we know that anyone who's a vegetarian, student or both ate no hamburgers.

Accordingly, we know there must be exactly 15 people (15 burgers, 1 burger per person) who are neither vegetarians nor students.

We're also told that half of the guests are vegetarians; therefore, half the guests are non-vegetarians.

Q: how many guests were at the party.

Well, we know that:

Total = veg + non veg
or
Total = 2(veg)

So, if we can figure out the number of vegetarians, we can calculate the total number of guests.

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

This sounds very complicated. Fortunately, this is data sufficiency, so we just need to understand the kind of information we have, rather than all the details of the information.

We're given the ratios of student vegetarians to non-student vegetarians and the rates for student non-vegetarians to non-student non-vegetarians.

Since we know that vegetarians = non-vegetarians, we can now use these ratios to calculate the ratios of all the different types of guests.

Accordingly, we know what portion of the guests are non-student + non-vegetarian. We also know there are 15 of these silly people. With a part-to-whole ratio and the number that goes along with the part, we can calculate the whole: sufficient.

(2) 30% of the guests were vegetarian non-students.

We know that 50% of the guests are vegetarians, so we now know that 20% of the guests were vegetarian students.

However, we still don't know what % of the guests are students, so there's no way to figure out how "15" relates to total guests: insufficient.

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

Could you show me how you would apply the ratios to figure out how many ppl were there? I'm confusing myself and think I need to see the hard numbers for clarification!

Thanks!

pathaniaus wrote:Could you show me how you would apply the ratios to figure out how many ppl were there? I'm confusing myself and think I need to see the hard numbers for clarification!

Thanks!

Sure, although this is something we pretty much never have the time to do (or need to do) during the actual exam.

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

vs = vegetarian students
vns = vegetarian non students
nvs = non vegetarian students
nvns = non vegetarian non students

vs/vns = 2/3
nvs/nvns = 2*(2/3) = 4/3

(If the rate of a is half the rate of b, then the rate of b is twice rate of a.)

So far we have 2 equations and 4 unknowns. However, we also know that:

vs + vns = nvs + nvns

and

nvns = 15

Now we have 4 equations and 4 unknowns - we can solve the entire system.

If for some unholy reason we actually needed to solve:

nvs/nvns = 4/3
nvs/15 = 4/3
nvs = (4/3)15 = 20

nvs + nvns = 20 + 15 = 35; since there are an equal number of vegetarians and non-vegetarians, there are:

2*35 = 70 guests.