Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionA 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.
We are given that of the 20,000 residents in Town T, 20,000 x 0.6 = 12,000 are female, and thus 8,000 are male. We need to determine the percentage of residents who were born in Town T.
Statement One Alone:
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.
We can let the number of male residents born in Town T = m, and the number of female residents born in Town T = f. Thus, (8,000 - m) males and (12,000 - f) females were not born in Town T.
From the statement, we see that f = 2(8,000 - m). However, we still cannot determine the percentage of residents who were born in Town T. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
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.
We can let the number of female residents born in town T = f. Thus, (12,000 - f) females were not born in Town T.
From the statement, we see that (12,000 - f) = 2f. Solving for f, we have:
3f = 12,000
f = 4,000
However, we still cannot determine the percentage of residents who were born in Town T, since we don’t know the number of males who were born in Town T. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Using both statements, we see that f = 2(8,000 - m) and f = 4,000. Thus:
4,000 = 2(8,000 - m)
4,000 = 16,000 - 2m
2m = 12,000
m = 6,000
So, 4,000 females and 6,000 males were born in Town T, which is 10,000 people.
Thus, 10,000/20,000 = 50% of the residents were born in Town T.
Answer: C
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