It is currently 14 Dec 2017, 05:21

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1


Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Manager
Manager
avatar
Joined: 11 Aug 2009
Posts: 121

Kudos [?]: 195 [3], given: 3

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

Show Tags

New post 18 Nov 2009, 20:47
3
This post received
KUDOS
40
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

51% (01:28) correct 49% (01:22) wrong based on 548 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

Kudos [?]: 195 [3], given: 3

5 KUDOS received
Manager
Manager
User avatar
Joined: 29 Oct 2009
Posts: 209

Kudos [?]: 1672 [5], given: 18

GMAT 1: 750 Q50 V42
Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

Show Tags

New post 19 Nov 2009, 04:46
5
This post received
KUDOS
3
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.

Answer : A

_________________

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

Word Problems Made Easy!
1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Kudos [?]: 1672 [5], given: 18

Intern
Intern
avatar
Joined: 17 Aug 2009
Posts: 36

Kudos [?]: 15 [0], given: 4

Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 740 Q49 V42
GPA: 3.29
WE: Engineering (Consulting)
Re: data suffeciency [#permalink]

Show Tags

New post 09 Nov 2010, 11:15
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, 11:24, edited 2 times in total.

Kudos [?]: 15 [0], given: 4

Expert Post
13 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135613 [13], given: 12705

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

Show Tags

New post 09 Nov 2010, 11:19
13
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
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?

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:
Image
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.
Image


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


Answer: A.


[Reveal] Spoiler:
Attachment:
Stem.PNG
Stem.PNG [ 2.33 KiB | Viewed 21207 times ]

Attachment:
2.PNG
2.PNG [ 2.38 KiB | Viewed 21192 times ]
Attachment:
1.PNG
1.PNG [ 2.59 KiB | Viewed 21386 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135613 [13], given: 12705

Expert Post
5 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7796

Kudos [?]: 18128 [5], given: 236

Location: Pune, India
Re: data suffeciency [#permalink]

Show Tags

New post 10 Nov 2010, 18:16
5
This post received
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
Ques.jpg [ 17.29 KiB | Viewed 20546 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
Ques1.jpg [ 18.33 KiB | Viewed 20538 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

Kudos [?]: 18128 [5], given: 236

Senior Manager
Senior Manager
avatar
Joined: 21 Mar 2010
Posts: 306

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

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

Show Tags

New post 27 Feb 2011, 18:24
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

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

Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 356

Kudos [?]: 467 [0], given: 50

Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Reviews Badge
Re: Guests at a recent party ate a totaal of [#permalink]

Show Tags

New post 20 Oct 2012, 22:59
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.

Hence Answer A.
_________________

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, 08:36, edited 1 time in total.

Kudos [?]: 467 [0], given: 50

Current Student
User avatar
Joined: 11 May 2013
Posts: 80

Kudos [?]: 16 [0], given: 43

Concentration: Finance, Strategy
GMAT 1: 710 Q48 V39
GPA: 3.94
WE: Accounting (Accounting)
Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

Show Tags

New post 01 Dec 2014, 04:54
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, 06:34, edited 1 time in total.

Kudos [?]: 16 [0], given: 43

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135613 [0], given: 12705

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

Show Tags

New post 01 Dec 2014, 05:14
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135613 [0], given: 12705

Current Student
User avatar
Joined: 11 May 2013
Posts: 80

Kudos [?]: 16 [0], given: 43

Concentration: Finance, Strategy
GMAT 1: 710 Q48 V39
GPA: 3.94
WE: Accounting (Accounting)
Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

Show Tags

New post 01 Dec 2014, 08:35
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.

Kudos [?]: 16 [0], given: 43

1 KUDOS received
Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 589

Kudos [?]: 493 [1], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

Show Tags

New post 12 Dec 2015, 03:51
1
This post received
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.

Share some Kudos, if my posts help you. Thank you !

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

Kudos [?]: 493 [1], given: 200

1 KUDOS received
Intern
Intern
avatar
B
Joined: 26 May 2016
Posts: 22

Kudos [?]: 5 [1], given: 5

GMAT 1: 640 Q49 V30
Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

Show Tags

New post 30 Apr 2017, 03:01
1
This post received
KUDOS
I have outlined my approach in the attached file. Please share your thoughts about this approach. Thanks.
Attachments

vegnonveg.png
vegnonveg.png [ 49.54 KiB | Viewed 3409 times ]

Kudos [?]: 5 [1], given: 5

Manager
Manager
avatar
B
Joined: 23 Dec 2013
Posts: 235

Kudos [?]: 16 [0], given: 21

Location: United States (CA)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

Show Tags

New post 28 May 2017, 18:23
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.


The first step is to set up an overlapping sets table and insert the one known value: 15 non-vegetarian non-students. It's worded in a confusing way, but clearly the stimulus states that each relevant student at 1 hamburger each and only 15 hamburgers were eaten.

1) The ratio of vegetarian students to vegetarian non-students is 2:3, or half the ratio of non-vegetarians. So we know that non-vegetarians are in the ratio 4:3. 3x = 15, since we already know the number of non-vegetarian non-students, so x = 5. If x = 5, then the total number of vegetarians is 7(5) = 35. Since vegetarians are half of the guests, the total number of guests is 70. Sufficient.

2) This provides the relationship of the vegetarian non-student number to the total number of guests, but we don't know any other values. Not sufficient.

Kudos [?]: 16 [0], given: 21

Senior Manager
Senior Manager
User avatar
G
Joined: 29 Jun 2017
Posts: 392

Kudos [?]: 80 [0], given: 71

GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User
Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

Show Tags

New post 25 Oct 2017, 06:31
main catch is 1 statement rate

Veg
2 student ---> 3 non student
1 s-------1.5 ns

half of it is for Non veg
1s-------1.5/2 ns

1s---------3/4 ns
4s => 3ns
4:3 ratio

=> 3x/7 = 15
x= 35
2x is total members => 70 is answer A.
since 2x are members x are veg and x are non veg
so took 4:3 s:ns for nonveg and since total number is x
so 3x/7 => x= 35 and 2x =70

and clearly 2 is insufficient
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 80 [0], given: 71

Re: Guests at a recent party ate a total of fifteen hamburgers.   [#permalink] 25 Oct 2017, 06:31
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.