Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Jul 2014, 15:19

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A group of Republicans and Democrats was surveyed and each

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 121
Followers: 1

Kudos [?]: 182 [3] , given: 17

A group of Republicans and Democrats was surveyed and each [#permalink] New post 25 Feb 2013, 01:14
3
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

57% (03:46) correct 43% (03:08) wrong based on 87 sessions
A group of Republicans and Democrats was surveyed and each member was asked whether they liked apple pies or éclairs. 80% of the Republicans liked apple pie, 55% of the Democrats liked eclairs, and 20% of the Republicans who liked apple pie also liked eclairs. If the number of Republicans who liked both desserts is equal to the number of Democrats who liked éclairs, what is one possible value for the number of members of the group?

A. 81
B. 88
C. 160
D. 550
E. 710
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.


Last edited by Bunuel on 26 Feb 2013, 01:32, edited 1 time in total.
Edited the question.
Expert Post
2 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 626
Followers: 40

Kudos [?]: 533 [2] , given: 135

Premium Member
Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 25 Feb 2013, 05:10
2
This post received
KUDOS
Expert's post
emmak wrote:
A group of Republicans and Democrats was surveyed and each member was asked whether they liked apple pies or éclairs. 80% of the Republicans liked apple pie, 55% of the Democrats liked eclairs, and 20% of the Republicans who liked apple pie also liked eclairs. If the number of Republicans who liked both desserts is equal to the number of Democrats who liked éclairs, what is one possible value for the number of members of the group?

81

88

160

550

710


Let the number of republicans be 100x and that of the democrats be 100y. Now, we are given that 80x like apple pies. Again, 16x like both apple pie and eclairs amongst the republicans.

Also, 55y like eclairs amongst the democrats.

Also given that 16x = 55y

Thus, the total number of people in the group =100x+100y = 100(x+y) = 100*y*(\frac{55}{16}+1) = 100*y*(\frac{71}{16})

Now, the number of people has to be an integer.Also, as 71 and 16 are co-primes, thus 100y has to be a multiple of 16. Thus, 100y = 16k, where k is a non negative integer.

Thus, the total number of people = 100(x+y) = 16k*\frac{71}{16} = 71k. From the given options, for k=10, option E matches.

E.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 22 Mar 2013
Posts: 728
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 8

Kudos [?]: 132 [1] , given: 121

Premium Member CAT Tests
Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 15 Aug 2013, 12:10
1
This post received
KUDOS
As per given data 16% of the republican comes into category of both who likes eclairs and apple pie, this number is equal to 55% of democrats who likes eclairs.
Following diagram is explanatory.

Attachment:
repub.jpg
repub.jpg [ 42.15 KiB | Viewed 620 times ]

_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos :)
My Articles: WOULD: when to use?
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Intern
Intern
avatar
Joined: 26 Feb 2013
Posts: 1
Followers: 0

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

Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 26 Feb 2013, 10:55
vinaymimani wrote:
emmak wrote:
A group of Republicans and Democrats was surveyed and each member was asked whether they liked apple pies or éclairs. 80% of the Republicans liked apple pie, 55% of the Democrats liked eclairs, and 20% of the Republicans who liked apple pie also liked eclairs. If the number of Republicans who liked both desserts is equal to the number of Democrats who liked éclairs, what is one possible value for the number of members of the group?

81

88

160

550

710


Let the number of republicans be 100x and that of the democrats be 100y. Now, we are given that 80x like apple pies. Again, 16x like both apple pie and eclairs amongst the republicans.

Also, 55y like eclairs amongst the democrats.

Also given that 16x = 55y

Thus, the total number of people in the group =100x+100y = 100(x+y) = 100*y*(\frac{55}{16}+1) = 100*y*(\frac{71}{16})

Now, the number of people has to be an integer.Also, as 71 and 16 are co-primes, thus 100y has to be a multiple of 16. Thus, 100y = 16k, where k is a non negative integer.

Thus, the total number of people = 100(x+y) = 16k*\frac{71}{16} = 71k. From the given options, for k=10, option E matches.

E.


The question stated 20% of the Republicans who liked apple pie also liked eclairs, not 16% as you did. I think the question has a wrong number because the way you did is right.
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 626
Followers: 40

Kudos [?]: 533 [0], given: 135

Premium Member
Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 26 Feb 2013, 21:26
Expert's post
nnk12391 wrote:
vinaymimani wrote:
emmak wrote:
A group of Republicans and Democrats was surveyed and each member was asked whether they liked apple pies or éclairs. 80% of the Republicans liked apple pie, 55% of the Democrats liked eclairs, and 20% of the Republicans who liked apple pie also liked eclairs. If the number of Republicans who liked both desserts is equal to the number of Democrats who liked éclairs, what is one possible value for the number of members of the group?

81

88

160

550

710


The question stated 20% of the Republicans who liked apple pie also liked eclairs, not 16% as you did. I think the question has a wrong number because the way you did is right.

Suppose 100 republicans are there in total. 80% like apple pie. Thus 80 republicans include all those who like ONLY apple pie & those who like BOTH apple pie and eclairs. Now, 20% of those who like apple pie, like eclairs also. Thus, out of 80 people, 16 like both. You can see that 16 is 20% of 80. Maybe the confusion is from the fact that 80 people already include the people who like both and that number is again manifested as a percentage.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
avatar
Joined: 27 Jan 2013
Posts: 58
Location: India
Concentration: Social Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Followers: 2

Kudos [?]: 18 [0], given: 33

Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 02 Mar 2013, 01:38
vinaymimani wrote:
emmak wrote:
A group of Republicans and Democrats was surveyed and each member was asked whether they liked apple pies or éclairs. 80% of the Republicans liked apple pie, 55% of the Democrats liked eclairs, and 20% of the Republicans who liked apple pie also liked eclairs. If the number of Republicans who liked both desserts is equal to the number of Democrats who liked éclairs, what is one possible value for the number of members of the group?

81

88

160

550

710


Let the number of republicans be 100x and that of the democrats be 100y. Now, we are given that 80x like apple pies. Again, 16x like both apple pie and eclairs amongst the republicans.

Also, 55y like eclairs amongst the democrats.

Also given that 16x = 55y

Thus, the total number of people in the group =100x+100y = 100(x+y) = 100*y*(\frac{55}{16}+1) = 100*y*(\frac{71}{16})

Now, the number of people has to be an integer.Also, as 71 and 16 are co-primes, thus 100y has to be a multiple of 16. Thus, 100y = 16k, where k is a non negative integer.

Thus, the total number of people = 100(x+y) = 16k*\frac{71}{16} = 71k. From the given options, for k=10, option E matches.

E.


My approach was as follows:
0.16 R = 0.55 D (initial method same as yours where R= Republicans and D=Democrats)
\frac{4R}{25} = \frac{11D}{10}
R can be = 25*11 and D = 25*4
which means R= 275 and D= 100
Alas the answer comes out to be 375 and none of the options match :oops:
could u harp on the fault in my approach??
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 626
Followers: 40

Kudos [?]: 533 [0], given: 135

Premium Member
Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 02 Mar 2013, 01:55
Expert's post
Quote:

My approach was as follows:
0.16 R = 0.55 D (initial method same as yours where R= Republicans and D=Democrats)
\frac{4R}{25} = \frac{11D}{10}
R can be = 25*11 and D = 25*4
which means R= 275 and D= 100
Alas the answer comes out to be 375 and none of the options match :oops:
could u harp on the fault in my approach??


0.16 R = 0.55 D

or 16/100 R = 55/100 D

or 4/25 R = 11/20 D

Further, when you take R = 25*11, you get D as 80 . This adds upto 275+80 = 355. As yo can see that this is 710/2 , thus you can choose R = 25*11*2. This will give D as 160. The sum is 550+160 = 710.

Thanks.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
avatar
Joined: 27 Jan 2013
Posts: 58
Location: India
Concentration: Social Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Followers: 2

Kudos [?]: 18 [0], given: 33

Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 02 Mar 2013, 02:22
vinaymimani wrote:
Quote:

My approach was as follows:
0.16 R = 0.55 D (initial method same as yours where R= Republicans and D=Democrats)
\frac{4R}{25} = \frac{11D}{10}
R can be = 25*11 and D = 25*4
which means R= 275 and D= 100
Alas the answer comes out to be 375 and none of the options match :oops:
could u harp on the fault in my approach??


0.16 R = 0.55 D

or 16/100 R = 55/100 D

or 4/25 R = 11/20 D

Further, when you take R = 25*11, you get D as 80 . This adds upto 275+80 = 355. As yo can see that this is 710/2 , thus you can choose R = 25*11*2. This will give D as 160. The sum is 550+160 = 710.

Thanks.


Thanx....Silly mistake YET AGAIN :evil:
Senior Manager
Senior Manager
User avatar
Joined: 23 Mar 2011
Posts: 474
Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Followers: 11

Kudos [?]: 92 [0], given: 59

GMAT Tests User
Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 02 Mar 2013, 04:28
I gave up half way through till 100Y (55/16 + 1) :assumed I was going the wrong way and lost it....damn it pays to complete our thought process!

Just to check quickly, though sum does not mention, are we not taking into considerations people who liked neither?
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++



-----------------------------
Quant Notes consolidated: consolodited-quant-guides-of-forum-most-helpful-in-preps-151067.html#p1217652

My GMAT journey begins: my-gmat-journey-begins-122251.html

All about Richard Ivey: all-about-richard-ivey-148594.html#p1190518

Intern
Intern
avatar
Joined: 08 Dec 2012
Posts: 7
Followers: 0

Kudos [?]: 6 [0], given: 10

Re: A group of Republicans and Democrats was surveyed and each [#permalink] New post 02 Mar 2013, 13:05
80% R --> like a
55% D --> like e
20% R --> like a + e
80% x 20% R = 55% D --> No. of R like a + e = No. of D like e
=> R = 55/16 D
However, R + D should be one of the above answers => R + D = 71/16 D = B (the answers) B must divisible by 15/4, D is an integer and positive
--> Answer is E
Re: A group of Republicans and Democrats was surveyed and each   [#permalink] 02 Mar 2013, 13:05
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic A line of people is divided into groups. Each group consists Chembeti 3 25 Feb 2012, 23:59
4 Experts publish their posts in the topic How many different committees each composed of 2 Republicans elinka 13 11 Nov 2009, 07:33
Of a group of people surveyed in a political poll, 60 aliensoybean 2 27 Nov 2007, 22:54
A survey of a group of people between the ages of 75 and 80 vineetgupta 13 06 Apr 2007, 01:56
The Democrats have accused the Republicans of resorting to Marina 17 22 Feb 2005, 20:38
Display posts from previous: Sort by

A group of Republicans and Democrats was surveyed and each

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.