It is currently Sun Oct 21, 2018 8:29 pm

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 7 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT Overlapping SetsPosted: Sat Jun 12, 2010 11:36 am

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

 Post subject: Re: math (test3, question 18): percentagesPosted: Mon Jun 14, 2010 1:11 pm

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

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.

Top

 Post subject: Re: math (test3, question 18): percentagesPosted: Mon Dec 06, 2010 12:47 pm

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

 Post subject: Re: math (test3, question 18): percentagesPosted: Mon Dec 06, 2010 1:11 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
What do you denote by N?
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

 Post subject: Re: math (test3, question 18): percentagesPosted: Wed Jan 12, 2011 5:40 pm

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

Top

 Post subject: Re: math (test3, question 18): percentagesPosted: Fri Jan 28, 2011 3:04 pm

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

 Post subject: Re: math (test3, question 18): percentagesPosted: Fri Jan 28, 2011 3:15 pm

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

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 7 posts ]

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 3 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions