gmat preparation courses

It is currently Fri Jun 22, 2018 5:13 am

All times are UTC - 5 hours [ DST ]




Post new topic Reply to topic  [ 7 posts ] 
Author Message
 Post subject: GMAT Overlapping Sets
PostPosted: Sat Jun 12, 2010 11:36 am 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
In a survey of potential presidential candidates A and B, 30 percent of the public liked A and 48 percent of the public liked B. If the percentage of public who liked only one candidate is twice the percentage who liked both candidates, then what is the percentage of public that liked neither candidate?

A. 27.5%
B. 35.5%
C. 41.5%
D. 58.5%
E. 64.5%

We denote percent of people who liked both candidates A and B by x. Then the percent of people who liked only one candidate is 2x. The sum of these numbers is the percent of people who liked at least one candidate, 3x. The percent of people that liked at least one candidate can also be calculated as the percent of people that liked candidate A, plus the percent of people that liked candidate B, minus the percent of people that liked both (set as x). So the percent that liked at least one candidate is: 30% + 48% – x = 78% – x.

Setting these expressions equal:
78% – x = 3x
78% = 4x
x = 19.5%.

So the percent that liked at least 1 candidate is:
78% – 19.5% = 58.5%.

The percent of people that liked neither candidate is:
100% – percentage that liked at least one = 100% – 58.5% = 41.5%.

The correct answer is choice (C).
-------------

How do you get 78% - x = 3x?


Last edited by questioner on Fri Jan 28, 2011 2:57 pm, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: math (test3, question 18): percentages
PostPosted: Mon Jun 14, 2010 1:11 pm 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Let us draw a Venn diagram for this question:
Image

We denote percentage of people who liked both candidates A and B by x. Then the percentage of people who liked only one candidate is 2x. The sum of these numbers is the percentage of people who liked at least one candidate. 3x.

On the other hand, the percentage of people who liked at least one candidate can be calculated as
30% + 48% – x = 78% – x.

Therefore we get equation:
78% – x = 3x


We can also construct an equation in a different way

If we denote percentage of people who liked both candidates A and B by x then we can calculate percentages of people who liked only A or only B. The sum of these numbers is
(30% – x) + (48% – x) = 78% – 2x

It must be equal to 2x. Therefore we get an equation:
78% – 2x = 2x

We can see that it is the equivalent equation to the one that is in the explanation.


Attachments:
perc_venn_1.gif [16.16 KiB]
Downloaded 6 times
Top
 Profile  
 
 Post subject: Re: math (test3, question 18): percentages
PostPosted: Mon Dec 06, 2010 12:47 pm 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
I like the question, but I feel a mistake here (perhaps it will be my mistake).

When we add 30% + 48% logically:
A + (A & B ) + B + ( A & B )
this will happen so that will result in (2N + (N) + 2N + (N))
6N = 78%; N = 13%
78% – 13% = 65% who like only one candidate.

So the rest will be 35%, right?


Top
 Profile  
 
 Post subject: Re: math (test3, question 18): percentages
PostPosted: Mon Dec 06, 2010 1:11 pm 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
What do you denote by N?
If your denotations are following:
A - percentage of public who liked candidate A only
B - percentage of public who liked candidate B only
(A & B) - percentage of public who liked the both candidates
N - percentage of public who liked the both candidates
THEN:
A = 48% – N
B = 30% – N
(A & B) = N
Let's plug it in:
A + (A & B ) + B + ( A & B ) = A + B + 2(A & B) = A + B + 2N = (48% – N) + (30% – N) + 2N = 78%.

In your reasoning, you mistakingly think that A = 2N and B = 2N, which is clearly NOT true.


Top
 Profile  
 
 Post subject: Re: math (test3, question 18): percentages
PostPosted: Wed Jan 12, 2011 5:40 pm 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Thanks a lot sir , you have cleared my confusion.


Top
 Profile  
 
 Post subject: Re: math (test3, question 18): percentages
PostPosted: Fri Jan 28, 2011 3:04 pm 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Solution is incorrect if x + 2x is the number of people who liked at least one candidate but 30 + 48 – x is the number of people who liked exactly one candidate so we cannot say 30 + 48 – x = x + 2x it should be 30 + 48 = x + 2x or 30 + 48 – x = 2x.


Top
 Profile  
 
 Post subject: Re: math (test3, question 18): percentages
PostPosted: Fri Jan 28, 2011 3:15 pm 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
(30 + 48 – x) is NOT the number of people who like exactly one candidate. It is the number of people who like at least one candidate. While the number of people who like only (exactly) one candidate is (30 + 48 – 2x).

Take a look at the Venn diagram provided above. Also, note, that there is the explanation of how the main equation can be constructed differently.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 7 posts ] 

All times are UTC - 5 hours [ DST ]


Who is online

Users browsing this forum: No registered users 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