Register    Login    Search    Rss Feeds

 Page 1 of 1 [ 10 posts ] 



 
Author Message
 Post subject: Guests at a recent party ate a total of fifteen hamburgers.
 Post Posted: Tue Jul 24, 2007 7:17 am 
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.


The answer is A. (1) is sufficient. And here is the explanation:

For this overlapping set problem, we want to set up a two-set table to test our possibilities. Our first set is vegetarians vs. non-vegetarians; our second set is students vs. non-students.


/ VEG / NON-VEG / TOTAL
_____________/______/__________/_____
STUDENT / / /
_____________/______/__________/_____
NON-STUDENT / / 15 /
_____________/______/__________/_____
TOTAL / x / x / ?


(It is dranw in a very rudimmentary way ;-))

We are told that each non-vegetarian non-student ate exactly one of the 15 hamburgers, and that nobody else ate any of the 15 hamburgers. This means that there were exactly 15 people in the non-vegetarian non-student category. We are also told that the total number of vegetarians was equal to the total number of non-vegetarians; we represent this by putting the same variable in both boxes of the chart.


The question is asking us how many people attended the party; in other words, we are being asked for the number that belongs in the bottom-right box, where we have placed a question mark.

The second statement is easier than the first statement, so we'll start with statement (2).

(2) INSUFFICIENT: This statement gives us information only about the cell labeled "vegetarian non-student"; further it only tells us the number of these guests as a percentage of the total guests. The 30% figure does not allow us to calculate the actual number of any of the categories.

(1) SUFFICIENT: This statement provides two pieces of information. First, the vegetarians attended at the rate, or in the ratio, of 2:3 students to non-students. We're also told that this 2:3 rate is half the rate for non-vegetarians. In order to double a rate, we double the first number; the rate for non-vegetarians is 4:3 We can represent the actual numbers of non-vegetarians as 4a and 3a and add this to the chart below. Since we know that there were 15 non-vegetarian non-students, we know the missing common multiple, a, is 15/3 = 5. Therefore, there were (4)(5) = 20 non-vegetarian students and 20 + 15 = 35 total non-vegetarians (see the chart below). Since the same number of vegetarians and non-vegetarians attended the party, there were also 35 vegetarians, for a total of 70 guests.


/ VEG / NON-VEG / TOTAL
_____________/______/__________/_____
STUDENT / / 4a or 20 /
_____________/______/__________/_____
NON-STUDENT / / 3a or 15 /
_____________/______/__________/_____
TOTAL /x or 35 / x or 35 / ? or 70



The correct answer is A.


But in this explanation something does not fit, because as stated in (1) if vegetarians attended in the rate 2:3 we could similarly draw as we did for non-veg


/ VEG / NON-VEG / TOTAL
_____________/______/__________/_____
STUDENT / 2a / /
_____________/______/__________/_____
NON-STUDENT / 3a / /
_____________/______/_________/_____
TOTAL / / /

and so if we already know that 3a=15, then this will lead to 2a= 10 and 3a=15 that will give us a total of 25 and the final table will be:



/ VEG / NON-VEG / TOTAL
_____________/________/__________/_____
STUDENT / 2a or 10 / 4a or 20 /
_____________/________/__________/_____
NON-STUDENT / 3a or 15 / 3a or 15 /
_____________/________/__________/_____
TOTAL / x or 25 / x or 35 / ? or 60

But this will not be valid for the premise that half of the guest were vegetarians because here we have 25 veg and 35 non-veg.

I´m probably missing something here, but can you explain what am I missing?

Thanks


Top 
 Post subject: Tables
 Post Posted: Tue Jul 24, 2007 7:22 am 
Sorry but the tables don´t appear as I drew them.
Anyway they are the regular simple table

1st line NOTHING VEGETARIANS NON-VEGETARIANS TOTAL
2nd line STUDENTS CELL CELL CELL
3rd line NON-STUDENTS CELL CELL CELL
4th line TOTAL CELL CELL CELL

I guess everybody can imagine

Thanks


Top 
 Post subject:
 Post Posted: Tue Jul 24, 2007 11:09 am 
Quote:
But in this explanation something does not fit, because as stated in (1) if vegetarians attended in the rate 2:3 we could similarly draw as we did for non-veg


You can. But if you are plugging it for Veg, then 3a is not equal to 15. That is because 3a is for non-student, non-veg. Here, you are plugging in for veg.

Your answer, however, is what I got too. (A).


Top 
 Post subject: MGMAT. EX5. Quest 2
 Post Posted: Tue Jul 24, 2007 11:43 am 
Dear Luci

Since, you've already calculated that the no. of Non-veg guests are 35, and we know from statement 1 that the no. of veg. guests = non veg. guests,

35 in the ratio of 2:3 (Ratio mentioned for veg students v/s non- students) means 14 veg. students and 21 veg non-students.

Veg. Non-Veg

Students 14 20
Non Students 21 15

Hope this helps!!


Top 
 Post subject: You are right
 Post Posted: Tue Jul 24, 2007 11:49 am 
You are absolutely right, I dunno what I was thinking about, :-)

Thanks


Top 
 Post subject: Re: Guests at a recent party ate a total of fifteen hamburgers.
 Post Posted: Wed Aug 15, 2012 9:08 am 
Offline
Students


Posts: 203
Hi - I understand the complete sol, but What i don't get is the significance of this statement "No hamburger was eaten by any guest who was a student, a vegetarian, or both"

where does this statement fit in the matrix? please help?

Cheers


Top 
 Post subject: Re: Guests at a recent party ate a total of fifteen hamburgers.
 Post Posted: Fri Aug 17, 2012 2:04 pm 
Offline
Forum Guests


Posts: 125
I think this statement fits into the explanation that all the 15 hamburgers are eaten by the non vegetarian non-students and none were eaten by any other groups. That fact is what gives us 3a=15. If not for this fact, 3a could be any value less than 15


Top 
 Post subject: Re: Guests at a recent party ate a total of fifteen hamburgers.
 Post Posted: Tue Aug 21, 2012 1:13 pm 
Offline
ManhattanGMAT Staff


Posts: 5074
Location: Southwest Airlines, seat 21C
thanks; let us know if there are any further questions on this one..

_________________
Tim Sanders
Manhattan GMAT Instructor


Top 
 Post subject: Re: Guests at a recent party ate a total of fifteen hamburgers.
 Post Posted: Sat Nov 03, 2012 7:51 pm 
Offline
Course Students


Posts: 23
I have the same question as the poster. I got this wrong as I am getting 25 veg and 35 non-veg.Does the fact that the # of veg = # of non-veg take precedence over ratio??

Image

Is the "a" after the 2 different than the a after the 4?
2a + 3a = 4a + 3a

If a = 5, then 2a = 10 and 3a = 15, and # of veg = 25
But with the other method, we know
2a + 3a = 4a + 3a
2a + 3a = 35
3a = 15
so 2a = 20
Now, a is 10...? I am confused why a changes to be something else.

4a + 3a = 35


Top 
 Post subject: Re: Guests at a recent party ate a total of fifteen hamburgers.
 Post Posted: Mon Nov 05, 2012 11:20 pm 
Offline
ManhattanGMAT Staff


Posts: 13509
asharma8080, the two ratios given in the problem (the ratios 2:3 and 4:3) are separate ratios, so you can't use the same coefficient letter "a" for both of them.
if you write the things in the 2:3 ratio as 2a and 3a, and you also write the things in the 4:3 ratio as 4a and 3a, then you are assuming -- incorrectly, as it turns out -- that all four quantities are in a fixed ratio of 2:3:4:3.
this is why you seem to be finding a contradiction here: the relationship that you've (accidentally) assumed, here, is impossible given that there are equal numbers of vegetarians and non-vegetarians.

instead, if you denote the things in the 2:3 ratio as 2a and 3a, then you should use a different letter for the things in the other ratio, e.g., 4b and 3b.

_________________
Pueden hacerle preguntas a Ron en castellano
Potete fare domande a Ron in italiano
On peut poser des questions ã Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

Un bon vêtement, c'est un passeport pour le bonheur.
– Yves Saint-Laurent


Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 10 posts ] 





Who is online

Users browsing this forum: No registered users and 0 guests

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron