Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 27 May 2017, 03:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Guests at a recent party ate a total of fifteen hamburgers.

Author Message
TAGS:

### Hide Tags

Manager
Joined: 11 Aug 2009
Posts: 122
Followers: 1

Kudos [?]: 155 [3] , given: 3

Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

18 Nov 2009, 21:47
3
KUDOS
34
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

52% (02:26) correct 48% (01:37) wrong based on 481 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA
Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 112

Kudos [?]: 1421 [3] , given: 18

Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

19 Nov 2009, 05:46
3
KUDOS
2
This post was
BOOKMARKED
kairoshan 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.

Good question.

Question Stem :
Total number of people attending the party , x = students + vegetarians + neither - both
Also, vegetarians = x/2 (this implies that non vegetarians also = x/2)
And, NVnonstudents = 15

St. (1) : Vstudents/ Vnonstudents = 2/3 ; NVstudents/NVnonstudents = 4/3
The second ratio gives us NVstudents = 20
Therefore total Non Vegetarians = 20 + 15 = 35
This accounts for half the number of people at the party.
This total number of people = 70
Hence, Sufficient.

St. (2) : 30% were Vnonstudents.
By itself, this statement gives us nothing.
Hence, Insufficient.

_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html

Intern
Joined: 18 Aug 2009
Posts: 41
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 740 Q49 V42
GPA: 3.29
WE: Engineering (Consulting)
Followers: 0

Kudos [?]: 14 [0], given: 4

### Show Tags

09 Nov 2010, 12:15
First of all, we need to be able to find a solid number,the total number of guest, as an answer.

The only solid number we are given to work with is 15, the number of hamburgers eaten by the guests.

From the question we could see that the guests can be broken down into 4 categories.

VEGETARIAN STUDENT (V & S)
NON-VEGETARIAN STUDENT (NV & S)
VEGETARIAN NON-STUDENT (V & NS)
NON-VEGETARIAN NON-STUDENT (NV & NS)

Looking @ # of hamburgers eaten,

The question states that (NV & NS) ate exactly 1 hamburger and that
no hamburger was eaten by any guest who was a student, hamburger eaten by (V & S) = (NV & S) = 0; a vegetarian, hamburger eaten by (V & S) = (V & NS) =0; or both, hamburger eaten by (V & S) = 0.

So from this we can conclude the # of (NV & NS) = 15.

The last piece of information given is that 1/2 Total = V, which also means 1/2 Total = NV, where NV + V = Total and NS + S = Total. Drawing a table can help understand this relationship.

Statement 1:

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

I think this should be reworded to ratio instead of rate.

Anyways this just means that for every 2 (V & S) there are 3 (V & NS), which is half the ratio of S to NS for NV. Therefore for every 4 (NV & S) there are 3 (NV & NS), which means $$\frac{4}{3}=\frac{(NV & S)}{(NV & NS)}$$

Since we know that (NV & NS) = 15. We can solve for (NV & S) and Find Total because 1/2* Total = (NV & NS) + (NV & S)

Sufficient.

Statement 2:

30% of the guests were vegetarian non-students.

This give us no way to link 15 to the total number of guest. So insufficient.

This is more clear if you draw a table to help visualize things.

I'm sure someone will come up with a better explanation later, but I hope this can help till then.

Last edited by chaoswithin on 09 Nov 2010, 12:24, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38910
Followers: 7741

Kudos [?]: 106290 [13] , given: 11620

### Show Tags

09 Nov 2010, 12:19
13
KUDOS
Expert's post
5
This post was
BOOKMARKED
mrinal2100 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.

can someone explain in detail

We have 4 groups of guests:
1. Vegetarian students;
2. Vegetarian non-students;
3. Non-vegetarian students;
4. Non-vegetarian non-students.

Now, as guests ate a total of 15 hamburgers and each guest who was neither a student nor a vegetarian (group #4) ate exactly one hamburger and also as no hamburger was eaten by any guest who was a student, a vegetarian, or both (groups #1, #2 and #3) then this simply tells us that there were 15 non-vegetarian non-students at the party (group #4 = 15).

Make a matrix:
Attachment:

Stem.PNG [ 2.33 KiB | Viewed 17956 times ]
Note that we denoted total # of guests by $$x$$ so both vegetarians and non-vegetarians equal to $$\frac{x}{2}$$.

(1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians --> $$\frac{vegetarian \ students}{vegetarian \ non-students}=\frac{2}{3}$$ --> if the rate X (some fraction) is half of the rate Y (another fraction), then Y = 2*X --> $$\frac{non-vegetarian \ students}{non-vegetarian \ non-students}=2*\frac{2}{3}=\frac{4}{3}$$ --> so, non-vegetarian non-students compose 3/7 of all non vegetarians: $$non-vegetarian \ non-students = 15 = \frac{3}{7}*\frac{x}{2}$$ --> $$x=70$$. Sufficient.
Attachment:

1.PNG [ 2.59 KiB | Viewed 18140 times ]

(2) 30% of the guests were vegetarian non-students --> just says that # of $$vegetarian non-students$$ equal to $$0.3x$$ --> insufficeint, to calculate $$x$$.
Attachment:

2.PNG [ 2.38 KiB | Viewed 17946 times ]

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7377
Location: Pune, India
Followers: 2288

Kudos [?]: 15130 [4] , given: 224

### Show Tags

10 Nov 2010, 19:16
4
KUDOS
Expert's post
mrinal2100 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.

can someone explain in detail

This is what I drew when I read the Question stem. Half of the guests were vegetarians so Total/2 stands for the complete vegetarian circle. All outside Vegetarian circle are Total/2.
Attachment:

Ques.jpg [ 17.29 KiB | Viewed 17847 times ]

Statement 1: Veg students : Veg non students = 2:3
Let me say they are 2x and 3x in number.

Non veg students : Non veg non-students = 4:3 (Since veg's ratio is half of non veg's ratio)
Let me say they are 4y and 3y in number.
So now my diagram looks like this:
Attachment:

Ques1.jpg [ 18.33 KiB | Viewed 17848 times ]

3y = 15 hence y = 5
Since 7y is half of the total, 35 is half of the total. So total number of students is 70. Sufficient.

Statement 2: We get that 30% of the guests were veg non students and we already know that 50% of the guests are veg so 20% of the guests are veg students. Essentially, we have got the 3:2 ratio of above. But we do not have the 4:3 ratio of above hence we cannot equate 15 to anything. Therefore, statement 2 is not sufficient alone.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Senior Manager
Joined: 21 Mar 2010
Posts: 312
Followers: 5

Kudos [?]: 30 [0], given: 33

### Show Tags

25 Feb 2011, 23:19
I got this on the mgmat test and boy was this hard! is there a thread for similar questions?
Senior Manager
Joined: 21 Mar 2010
Posts: 312
Followers: 5

Kudos [?]: 30 [0], given: 33

Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

27 Feb 2011, 19:24
Good one!
Stumbled in the test. I like the MGMAT solution.

Non veg - Non Students is 15.

Since Nonveg Student to non student ratio is 4:3, therefore non veg students will be 20.
4/3=x/15
Therefore x= 20. That makes 35 NV and 35 Veg so total 70
Senior Manager
Joined: 15 Jun 2010
Posts: 361
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 11

Kudos [?]: 399 [0], given: 50

Re: Guests at a recent party ate a totaal of [#permalink]

### Show Tags

20 Oct 2012, 23:59
nitzz 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.

St 1: Sufficient: Veg attended in 2:3 so the Non veg attended in ratio 4:3. We now from Question stem Non veg - Non student ate 15 burgers. therefore Non veg attended the party in 20:15 (4:3). Total no of Non Veg = 35 nos. And total guests = 2*35=70 (from Question Stem).
St 2: Not sufficient: cant calculate other group of non-veg and only %age is provided.

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Last edited by SOURH7WK on 21 Oct 2012, 09:36, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38910
Followers: 7741

Kudos [?]: 106290 [0], given: 11620

Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

23 Jul 2013, 00:17
From 100 hardest questions.

Bumping for review and further discussion.
_________________
Intern
Joined: 20 Aug 2013
Posts: 1
Location: India
Concentration: Finance, Technology
Followers: 0

Kudos [?]: 5 [0], given: 0

Guests at a recent party ate a total of fifteen hamburgers.. [#permalink]

### Show Tags

05 Sep 2013, 09:52
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 other guests ate hamburgers. 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.

Can anyone please elaborate any method for solving the problem?
Unable to find an easy approach.
Math Expert
Joined: 02 Sep 2009
Posts: 38910
Followers: 7741

Kudos [?]: 106290 [0], given: 11620

Re: Guests at a recent party ate a total of fifteen hamburgers.. [#permalink]

### Show Tags

05 Sep 2013, 09:55
sapto123 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 other guests ate hamburgers. 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.

Can anyone please elaborate any method for solving the problem?
Unable to find an easy approach.

Merging similar topics. Please refer to the solutions above.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15477
Followers: 651

Kudos [?]: 209 [0], given: 0

Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

14 Sep 2014, 15:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Current Student
Joined: 11 May 2013
Posts: 80
Concentration: Finance, Strategy
GMAT 1: 710 Q48 V39
GPA: 3.94
WE: Accounting (Accounting)
Followers: 1

Kudos [?]: 14 [0], given: 43

Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

01 Dec 2014, 05:54
Bunuel, could you explain this statement: " --> so, non-vegetarian non-students compose 3/7 of all non vegetarians." Don't see how you get there. Thanks!

Last edited by Krage17 on 01 Dec 2014, 07:34, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38910
Followers: 7741

Kudos [?]: 106290 [0], given: 11620

Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

01 Dec 2014, 06:14
Krage17 wrote:
Bunuel, could you explain this statement: " --> so, non-vegetarian non-students compose 3/7 of all non vegetarians." Don't see how you there. Thanks!

Since non-vegetarian students plus non-vegetarian non-students equals all non-vegetarians, then (non-vegetarian non-students/(total) = 3/(4 + 3) = 3/7.

Hope it's clear.
_________________
Current Student
Joined: 11 May 2013
Posts: 80
Concentration: Finance, Strategy
GMAT 1: 710 Q48 V39
GPA: 3.94
WE: Accounting (Accounting)
Followers: 1

Kudos [?]: 14 [0], given: 43

Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

01 Dec 2014, 09:35
It is. Took me a while to grasp it.

Bunuel wrote:
Krage17 wrote:
Bunuel, could you explain this statement: " --> so, non-vegetarian non-students compose 3/7 of all non vegetarians." Don't see how you there. Thanks!

Since non-vegetarian students plus non-vegetarian non-students equals all non-vegetarians, then (non-vegetarian non-students/(total) = 3/(4 + 3) = 3/7.

Hope it's clear.
Intern
Status: available
Joined: 11 Jun 2015
Posts: 12
Location: United States
Concentration: Strategy, Marketing
GMAT 1: 650 Q50 V29
Followers: 3

Kudos [?]: 8 [2] , given: 9

### Show Tags

28 Jun 2015, 22:00
2
KUDOS
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 vegetarian, a student, 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.
Math Forum Moderator
Joined: 06 Jul 2014
Posts: 1271
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Followers: 174

Kudos [?]: 2015 [0], given: 178

### Show Tags

28 Jun 2015, 23:33
campus1995 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 vegetarian, a student, 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.

Hello campus1995

This topic is discussed here
guests-at-a-recent-party-ate-a-total-of-fifteen-hamburgers-104547.html

_________________
Director
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 17

Kudos [?]: 356 [1] , given: 200

Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

12 Dec 2015, 04:51
1
KUDOS
Hi Math Experts, I have one question regarding my approach for this question:

This is a rule From MGMAT

If a Data Sufficiency question asks for the concrete value of one element of a ratio, you will need
BOTH the concrete value of another element of the ratio AND the relative value of two elements
of the ratio

So, after reading Statement 1, I've marked Answer A, because Statement 1 gives us the relationship among all the groups + we have a concrete value from the question stem, hence, one can find the required value --> I've just pretty much followed the rule from MGMAT....
Do you think it's a valid approach for such kind of questions ?
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15477
Followers: 651

Kudos [?]: 209 [0], given: 0

Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

07 Feb 2017, 15:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 26 May 2016
Posts: 21
Followers: 0

Kudos [?]: 3 [0], given: 4

Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

### Show Tags

30 Apr 2017, 04:01
Attachments

vegnonveg.png [ 49.54 KiB | Viewed 323 times ]

Re: Guests at a recent party ate a total of fifteen hamburgers.   [#permalink] 30 Apr 2017, 04:01
Similar topics Replies Last post
Similar
Topics:
The king set a big party. Each guest had to wear either a red tunic or 2 21 Nov 2016, 12:37
14 30 people in total attended an office party for a 15 29 Nov 2016, 16:44
1 Guests at a recent party ate a total of fifteen hamburgers. 3 05 Sep 2010, 23:01
At a certain restaurant, the total price for one hamburger a 2 14 Jun 2010, 18:37
8 Guests at a recent party ate a total of fifteen hamburgers. 7 26 Apr 2013, 00:59
Display posts from previous: Sort by