Data Sufficiency

For me this is a very easy question. Just think about it critically and the answer will jump staight at you in less than 2mins .
Statement 1 alone is sufficient.

To get this done within 2 minutes...use the matrix method...it really helps!

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.

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.

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.

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!

Stuart ,I couldn't really figure out the other two equations.

Using the ratios gives us:
non veg and student/ non veg and non student = 4/3 where non veg and non student =15

veg and student/ veg and non student = 2/3, where veg and student is indeed both in your equation above.

The terms "non veg and student" and "veg and non student' are indeed introducing new variables to the equation system.
Or I got totally confused here?

needthis wrote:
Stuart ,I couldn't really figure out the other two equations.

Using the ratios gives us:
non veg and student/ non veg and non student = 4/3 where non veg and non student =15

veg and student/ veg and non student = 2/3, where veg and student is indeed both in your equation above.

The terms "non veg and student" and "veg and non student' are indeed introducing new variables to the equation system.
Or I got totally confused here?

Hi,

it's been a while since I made that post, so forgive me if I'm a bit rusty on this one!

Remember, we an add the following equations as well:

non veg = total - veg
non student = total - student

So, if you consider those two things you mentioned "new" variables, we can solve for them using the information/variables that we already have.

For veg

S:NS = 2:3

For non veg

S:NS = (2:3)*2 , since veg is half the rate for non veg
S:NS = 4:3

Now draw the grid with the info we know ie, NV + NS = 15 (hamburgers)
Therefore, from the non veg category we have

4:3 = x:15
x = 4:3 * 15 = 20

___ | __S__ | __NS__ |
_V_ | __?__ | __?___ |
_NV_ | __20__| __15__ |

Since 15 + 20 is the total no of non vegetarians, we can say vegetarian are also 35 (since half the guests are veg)

Therefore total no of guests = 70

A alone is sufficient

Good question and i got the answer in 5 mins. I know that is quiet bad.

good Q

----V-------!V
S--2---------1-

!S-3---------3
----0.5x---0.5x--- x

thus 1:3 = s!v/15 = s!v=5
thus sv=10 thus A is sufficient.

b only gives ratio for SV/!SV. not sufficient.

A it is.

ANSWER: E

Deependra1 wrote:ANSWER: E

Nope! Its A, why is it E?

Its a clear ques of overlapping

Group 1 + group 2 +Both - neither

Statement 1 provides 3 equations..We dont really bother how to solve them but it can be solved.

Statemnt 2 insufficient.

Answer A

This was a good one...
Nice excerise and learning

not that hard in about one minute.
by a glance, stm 2 clearly is NOT sufficient.
stm 1 has everything needed to solve the problem, even without solving the problem.

NS= Non-Student
NV= Non-Veg
S= Student
V=Veg
Student No Hamburger ->
Vegeterian No hamburger -> So all hamburgers are eaten by Non Vegeterians as above no Student ate hamburgers..So all the Non-Veg who ate hamburgers were Non-student=15(NS and NV)
(S and NV)=x

A)
so 2/3=1/2*(S and NV)/(NS and NV)
or 2/3 =1/2*(x/15)
x=20
Therefore Total NV=20+15=1/2 of the Guests
(A) is sufficient

(B) Clearly Insufficient. Total No of guests unknown