Data Sufficiency

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.

IMO A.

from stmt 1 it is given the among the vegetarians, Students / Not Students = 2 /3 which is half the rate of students / non students who are non vegetarians.

==> 2/3 = 1/2 * x / 15(where x is the number of students who eat non vegetarian and 15 is given in the question stem who are not students and not vegetarian. )

On solving the eq, we get x = 20. Once we know this rest of the information can be filled. This is sifficient.

Stmt 2 - it just states that vegetarians who are not students is 30% but no other information is given. Hence insufficient.

Well I solved it in 6 min app.

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.

I could solve in in 3 minutes.

I used matrix method..

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.

From statement 1, we can conclude that for Non-Vegetarians, the ratio of students and non-students is 4 :3

In the question it is given that Non-Veg Non-Students = 15.

So Non-Veg Students = 4/3 (15) = 20.

So total Non-Vegetarians = 35.

Since half of the quests are vegetarians, obviously Non-Vegetarians also will be half of the guest which is 35.

Hence total number of guests = 70.

Clearly statement 2 is not sufficient.

Hence A.

2 min 10 sec

Hey guys,

Thanks for the great insight i tried my luck too and here is how i solved this problem (matrix method as well)


Students Non Students
Vegetarian 2 3
Non Veg. (stmnt 2) 1 3

the question stem states that people who are non veg and non students ate the burgers i.e. 15 burgers = 15 people or in other words the 3 in the second row corresponds to 15 ppl. Using this info u can come up with the number of non Veg. and students:

1/3 = x/15
x= 5
this tells us that total non veg. (Students and non students) are 20 (5+15); and since veg. (both students and non students) represent 50% of the entire guests the total number of guests should be 40.
Hence, statement 1 is sufficient. (Took me 10 mins); hopefully i'll be able to do it quicker next week when i give the actual exam. Thanks.

There are two non overlapping groups vegetarians and non- vegetarians

With in each group there are students and non-students

Lets look at the givens .............


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,


Total number of hamburgers = 15

Who ate hamburgers ------> Non veg Non students

so non-veg Non students = 15

By A we get for the non veg group ------> students / non students = 4/3

hence for this group students = 20 ( 4/3 = x/15)

So the total number of non-veg people = 20+15 =35 = total number of veg people

The total number of guests = 35*2 = 70


B is insufficient

B gives the number of veg non students but doesn't give any relationships between the two main groups

This might be very easy if you can mentally imagine ---the Venn diagrams for the problem

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).

Try to determine what you need to know:

What fraction of the people are non-student non-vegetarians?

or, with the knowledge that half are vegetarians, it is enough to know

"What fraction of the non-vegetarians are not students ? "

(1) gives us the ratio of students to non-students among non-vegetarians and if we know the ratio, we can find the fraction. SUFF

(2) We don't care about vegetarians, but about non-vegetarians NOT SUFF

Stuart would you mind writing how out we can turn the 2 ratios from statement A into 2 additional equations? Thank you!

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).

it certainly took me 4 min but this is how I did it:

Make a Venn diagram except that there is no overlap between the two. Given that you can either be Veg or Non-Veg, sizes are same. Assume veg count = non-veg count = X
Now draw arc thru both to represent Students and highlight the area of Non-V circle outside of the student arc. This are represents those who ate ham burgers which is 15
Now to equations. First equation tell you that the Student portion of Veg circle / non-student portion = 2/3 * X
It also tells you that student portion of Non-Veg circle / non-student portion = 2*2/3 * X
You also know that the non-studnt portion of Non-veg circle = 15
So total non-veg = 35 = Veg. Hence TOTAL = 70

Bingo

I am sorry but I did'nt get how the ratio in statement 1 helped you get 4/3???

What was the equation that was set up?I got everything else - what we need to find but I just dnt understand how 2.3 became 4/3
Thanks!!!

Hi ashblog02:

The 1st possible solution statement says "The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarian" - so the rate for vegetarian student/non-student was half that for non-vegetarians. Hence ratio of 2*2/3 for non-veg circle

Option A.

Expln:

From Ques:

Student Non Student
Veg x y
Non Veg z 15

eq 1 : x+y = z+15

from opt A:

eq 2 : x/y = 2/3
eq 3 : z/15 = 4/3

3 equations, 3 variables -> option A is enough

from opt B

eq 2' : 30(x+y+z+15)/100 = y

2 equations, 3 variables -> option B is not enough

Real challenging and confusing!

Can some one show how to solve this using tables/matrix?


What kind of topic does these kind of questions come under?

anirudhbhalotia wrote: Can some one show how to solve this using tables/matrix?

Sure! Have a look here (read till the LAST post, very instructive):

https://www.manhattangmat.com/forums/gue ... -t756.html

anirudhbhalotia wrote: What kind of topic does these kind of questions come under?

I consider this kind of question as a "grid" one. (I use the name "grid" for what you called "tables/matrix".)