• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: GMAT Overlapping Sets
PostPosted: Mon Jul 27, 2009 9:14 am 
Offline

Joined: Sun Apr 19, 2009 6:56 pm
Posts: 32
In a survey of potential presidential candidates A and B, 30 percent liked A and 48 percent liked B. If the percentage of people who liked only one candidate is twice the percentage who liked both candidates, then what is the percentage of people that liked neither candidate?

I dont understand 78-x=3x, if the percentage of people who liked at least one candidate is twice the percentage of people who liked both candidates, isn't it 78-x=2x?


Top
 Profile  
 
 Post subject: Re: Test 3, question 18
PostPosted: Mon Jul 27, 2009 9:49 am 
Offline
User avatar

Joined: Mon Apr 06, 2009 5:44 pm
Posts: 81
Image

Perhaps it will help to visualize the problem with a Venn diagram. We see that x + y = 30, y + z = 48, and that x + y + z + U = 100.

percentage that liked only one candidate is x + z
percentage that liked both candidates is y
percentage that liked neither candidate is U

We have 3 equations to work with (listed above). So lets translate the word problem into symbols:

% liked one candidate = 2 (% liked both) means x + z = 2 ( y )

We want to solve for U, so we have U = 100 - y - (x + z). So we make the substitution U = 100 - 3y, so 3y = 100 - U = 78- y. So 3y = 78 - y. We can now solve for y and substitute to determine the value for U.


Top
 Profile  
 
 Post subject: Re: Test 3, question 18
PostPosted: Mon Apr 19, 2010 12:54 pm 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 457
Please, be very concentrated when reading question statement. It says “If the percentage of public who liked only one candidate is twice the percentage who liked both candidates”.
In the terms of denotation we used it is:
(30 – x) + (48 – x) = 2x

For better comprehension, take a look at this Venn diagram:
Image

Let's denote by x the percentage of people that liked both candidates. Then the percentage of people that liked candidate A only is (30 – x). The percentage of people that liked candidate B only is (48 – x). The total percentage of people that liked only one candidate is (30 – x) + (48 – x). We know that it is twice the percentage of people that like, both candidates. Therefore we get equation:
(30 – x) + (48 – x) = 2x
78 = 4x
x = 19,5

We can find percentage of people that like neither candidate if we deduct from 100% those that like only one candidate as also those who like both candidates.

100 – x – (30 – x) – (48 – x) = (100 – 78) + x = 22 + 19,5 = 41,5
The percent of people that liked neither candidate is 41,5%
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: Yahoo [Bot] and 2 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
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.