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Population living in Town A

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by gmattesttaker2 » Sat Nov 02, 2013 6:59 pm
Hello,

Can you please assist with this:

What fraction of the combined populations
of Towns A and B live in Town A?

(1) The average income of the population of
Town A is $3,000 higher than the average
income of the populations of both towns
combined.

(2) The average income of the population of
Town B is $2,000 lower than the average
income of the populations of both towns
combined.

OA: C

Thanks a lot for your help - Sri
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Source: — Data Sufficiency |
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by theCodeToGMAT » Sat Nov 02, 2013 11:29 pm
N1 = TOwn A
N2 = Town B

To find: N1/(N1+N2)

Weighted Average formula = N1/N2 = (M2-M)/(M-M1)

Statement 1:
M1 = M + 3000
M1 - M = 3000
We don't have info about M2
INSUFFICIENT

Statement 2:
M2 = M - 2000
M2 - M = -2000
We don't have info about M1 for the weighted average formula.
INSUFFICIENT

Combining...
we have all info needed
SUFFICIENT

Answer [spoiler]{C}[/spoiler]
R A H U L
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by Matt@VeritasPrep » Sat Nov 02, 2013 11:38 pm
Let's call p the average income of the two towns together, a the number of residents in Town A and b the number of residents in Town B. We want to find a/(a+b).

Alone each statement isn't sufficient, as it doesn't tell us about the other town, but together we have this equation:

Total Income A + Total Income B = Total Income A+B
or
(p + 3000)a + (p - 2000)b = p(a+b)
or
ap + 3000a + bp - 2000b = ap + bp
or
3000a = 2000b
or
b = (3/2)a

So a/(a+b) = a/(a+(3/2)a) = a/(5/2)a = 2/5, and Town A has 40% of the combined population.
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