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A Town T has 20,000 residents, 60 percent of whom are fem al

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A Town T has 20,000 residents, 60 percent of whom are fem al [#permalink] New post 29 Jan 2014, 01:16
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 63
Category: Arithmetic Percents
Page: 157
Difficulty: 600


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Re: A Town T has 20,000 residents, 60 percent of whom are fem al [#permalink] New post 29 Jan 2014, 01:16
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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.
Attachment:
1.png
1.png [ 4.51 KiB | Viewed 792 times ]
Not sufficient.

(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.
Attachment:
2.png
2.png [ 5.19 KiB | Viewed 780 times ]
Not sufficient.

(1)+(2)
Attachment:
3.png
3.png [ 5.81 KiB | Viewed 779 times ]
Sufficient.

Answer: C.
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Re: A Town T has 20,000 residents, 60 percent of whom are fem al [#permalink] New post 29 Jan 2014, 02:00
From ques stimulus:no. of females=60% of 20000=12,000
no. of males=8000
From S1:Let no. of females born in town be 2x
Therefore no. of females not born=12000-2x
And no. of males not born=x
Also.no. of males born=8000-x
But this doesn't give us value of x.Insufficient.

From S2:No. of females not born=2x
Therefore,no. of females born=x
And 2x+x=12000
x=4000
But we still don't know the no. of males born and not born in town.Insufficient.

Combining the two statments we can find the no. of residents born in town T.
Ans.C
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Re: A Town T has 20,000 residents, 60 percent of whom are fem al [#permalink] New post 29 Jan 2014, 02:27
Attachment:
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untitled.PNG [ 11.92 KiB | Viewed 851 times ]


We are given no. of Female is 60% of Total Population so 12000 and no. of Male =8000

No From St 1 we get Only No Information (Refer Table 1)
From St 2, we can find no. of Female born and not born in the city so not enough cause we don't know about men.

Combined we No. of Male born in the city is half of female born in the city so a=x/2=2000
So Total Refer table 3, We can find the no. of people born in the city.

Ans C
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Re: A Town T has 20,000 residents, 60 percent of whom are fem al [#permalink] New post 29 Jan 2014, 23:29
The no. of residents in town T is 20,000. We, need to find the % of residents born in town T.

As 60% of them are female, the no. of female residents = 60% or (3/5) * 20,000 = 12,000;
So, the no. of male residents = 20,000 - 12,000 = 8,000;

We can assign the no. of Male and Female born in town T as MB and FB respecitively.
Similary, we can assign the no. of Male and Female not born in town T as MNB and FNB respectively.

Statement (1):
FB = 2 * MNB; Insufficient as we do not know the ratio of Born and Not Born.

Statement (2):
FNB = 2 * FB;
Since, we know the total no. of female residents in town T as 12,000, they can be classified as either Born or Not Born in town T.
Therefore, FB + FNB = 12,000;
FB + 2FB = 12,000;
3FB = 12,000;
FB = 4,000 and therefore FNB = 8,000;
Since we do not know the male strength born in town T, this statement is Insufficient too.

Combining, MNB = FB/2 = 4,000/2 = 2,000;
Therefore, MB = 8,000 - 2,000 = 6,000;

% of residents born in town T = (FB + MB)/Total = 4,000 + 6,000 = 10,000/20,000 = 50%;

Ans is (C).

Note: Most of the calculation done here is not required as it is a DS question. Press kudos if you think my explanation makes sense.
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Re: A Town T has 20,000 residents, 60 percent of whom are fem al [#permalink] New post 01 Feb 2014, 09:00
Expert's post
SOLUTION

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.
Image
Not sufficient.

(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.
Image
Not sufficient.

(1)+(2)
Image
Sufficient.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A Town T has 20,000 residents, 60 percent of whom are fem al   [#permalink] 01 Feb 2014, 09:00
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