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What percent of the residents were born in Town T?

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What percent of the residents were born in Town T?

by uououououo » Mon Sep 01, 2014 5:50 pm
"Town T has 20,000 residents, 60 percent of whom are female. What percent of the residents were born in Town T?
(1) The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.
(2) The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T."



Please help, thanks!
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by Uva@90 » Mon Sep 01, 2014 11:07 pm
uououououo wrote:"Town T has 20,000 residents, 60 percent of whom are female. What percent of the residents were born in Town T?
(1) The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.
(2) The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T."



Please help, thanks!
Hi,
Let, T = Total Number of Population
F = Total number of Female Population
M = Total Number of Male population
FB = Total Number Female population born in Town T
MB = Total Number of Male population born in Town T
FNB = Total Number of population not born in Town T
MNB = Total Number of population not born in Town T

From question we can infer below details,

T = 20000
F = 12000(FB+FNB)
M = 8000(MB+MNB)
T = MB+FB+MNB+FNB

To Find ,
MB +FB ?

Sentence 1: FB = 2MNB
Not enough to find MB+FB

Sentence 2: FNB = 2FB
=> 3X = 12000 => FB = 4000 & FNB = 8000
12000=MB+4000 +MNB+8000
we have two unknown in single equation, not sufficient.

1+2: MNB = 1/2(FB) => 2000

MB = 8000-2000 = 6000

We need MB+FB => 6000+4000 = 10,000.

Hence Sufficient.

OA is C

Regards,
Uva.
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by GMATGuruNY » Tue Sep 02, 2014 3:20 am
uououououo wrote:"Town T has 20,000 residents, 60 percent of whom are female. What percent of the residents were born in Town T?
(1) The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.
(2) The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T."
This is an EITHER/OR group problem.
Every resident is EITHER male OR female.
Every resident is EITHER born in Town T OR not born in Town T.
To organize the data, use a GROUP GRID (also known as a double-matrix).

Let M=male, F=female, B=born in Town T, NB=not born in Town T.
Since the question stem asks for a PERCENTAGE, let the total number of residents = 100.
Since 60% of the residents are female, the following grid is yielded:
Image

In a group grid, the values in any row or column must add up to the TOTAL of that row or column, as illustrated by the values in the bottom row.
The question asks for the value in the upper right corner: the total percentage born in Town T.

Statement 1: The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.
The following gird is yielded:
Image
No way to determine the value in the upper right corner.
INSUFFICIENT.

Statement 2: The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T.
The following grid is yielded:
Image
No way to determine the value in the upper right corner.

Statements combined:
The following grid is yielded:
Image
According to the grid, the total percentage born in Town T = 50%.

The correct answer is C.
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by Brent@GMATPrepNow » Tue Sep 02, 2014 7:10 am
Mitch's "group grid" approach (aka Double Matrix Method). can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of residents, and the two characteristics are:
- born in Town T and NOT born in Town T
- males or female

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

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Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
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- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
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- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATinsight » Tue Sep 02, 2014 10:40 pm
uououououo wrote:"Town T has 20,000 residents, 60 percent of whom are female. What percent of the residents were born in Town T?
(1) The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.
(2) The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T."



Please help, thanks!
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