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## OG QR 2nd Ed. DS #63

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tofubeans Just gettin' started!
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OG QR 2nd Ed. DS #63 Fri Apr 27, 2012 12:37 pm
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• Lap #[LAPCOUNT] ([LAPTIME])
63) A 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.

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neelgandham Community Manager
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Fri Apr 27, 2012 3:58 pm
Total number of residents = 20000
Total number of female residents = 12000
Total number of male residents = 8000

Let the number of females born in town T = x
Then the number of females not born in T = 12000-x
Let the number of males born in town T = y
Then the number of males not born in T = 8000-y
The question can now be rephrased to 'What is the value of ((x+y)/20000)*100 ?

Quote:
(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.
x=2*y. So, ((x+y)/20000)*100 = (3y)/200. Since we don't know the value of y, statement I is not sufficient to answer the question
Quote:
(2) The number of female residents who were not born n Town T is twice the number of female residents who were born in Town T.
12000-x = 2x
3x = 12000
x = 4000
So, ((x+y)/20000)*100 = (4000+y)/200. Since we don't know the value of y, statement II is not sufficient to answer the question
Quote:
From I and II
x = 2y = 4000, implies y = 2000.So, ((x+y)/20000)*100 = (4000+2000)/200 = 30%. So, Statement I + Statement II combined works great. IMO C

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jrakhe Just gettin' started!
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Fri Apr 27, 2012 5:07 pm
I think each statement is enough.

shantanu86 Rising GMAT Star
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Fri Apr 27, 2012 6:40 pm
jrakhe wrote:
I think each statement is enough.
Hi jrakhe,

Total population of T = 20,000
Total males = 8,000.
Total females = 12,000

Let number of males born in town T = M
Let number of females born in town T = F

Now, for two variables we will need two *distinct* equations.

Lets examine..

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.

=> F = 2*(8000 -M)

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.

=> (12000 -F) = 2*F

Thus, since 1.) and 2.) are distinct they will give unique value of M and F, from which the required % will be (M+f)/20000*100

Hope it helps!!

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fyllmax Just gettin' started!
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Sat Apr 28, 2012 4:54 am
IMO:C

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