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n friends donate

by crackgmat007 » Sun May 10, 2009 7:27 pm
Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n?
(1) The first n people donated 1/16 of the total amount donated.
(2) The total amount donated was $120,000.

How is statement 1 sufficient. IMO statement 2 alone is sufficient. Am I missing something?
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by bluementor » Mon May 11, 2009 1:18 am
Total number of people donated = n + n^2
Total amount donated = (n + n^2)*500 = 500n(n+1)


Statement 1:

(500n)/(500n(n + 1)) = 1/16
1/(n+1) = 1/16
n + 1 = 16
n = 15

Sufficient.

Statement 2:

(n + n^2)*500 = 120,000
n(n+1) = 240

here n can only be 15. Sufficient.

Choose D.

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Re: n friends donate

by splendentsky » Mon May 11, 2009 1:29 pm
crackgmat007 wrote:Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n?
(1) The first n people donated 1/16 of the total amount donated.
(2) The total amount donated was $120,000.

How is statement 1 sufficient. IMO statement 2 alone is sufficient. Am I missing something?
The answer is D.

Analysis:

Data 1:
(1/16) * (500n + 500n*n) = 500n
500n * (1 + n) = 500n * 16
1 + n = 16
n= 15

Data 1 is sufficient.

Data 2:
500n + 500n*n = 120,000
n^2 + n - 240 =0
n=15

Data 2 is sufficient, too.
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by crackgmat007 » Tue May 12, 2009 9:31 am
thanks guys
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by garimag » Wed May 13, 2009 5:02 pm
crackgmat007 wrote:thanks guys
i didnt understand where n + n.n came from. please explain.
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by shargaur » Wed May 13, 2009 8:09 pm
n = intial set of friends

n friends for 1 friend of her
so total friends of n friend of her = n*n

so total people donated = her friends and friends of her friends
= n + n*n
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by aj5105 » Thu May 14, 2009 4:09 am
In case of confusion, I guess it's better use numbers.
Say n = 2. Each gets 2 more, that's 4 (square of n).

garimag wrote:
crackgmat007 wrote:thanks guys
i didnt understand where n + n.n came from. please explain.
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by rahul.s » Fri Jan 08, 2010 11:14 pm
bluementor wrote:Total number of people donated = n + n^2
Total amount donated = (n + n^2)*500 = 500n(n+1)


Statement 1:

(500n)/500n(n + 1) = 1/16
1/(n+1) = 1/16
n + 1 = 16
n = 15

Sufficient.

Statement 2:

(n + n^2)*500 = 120,000
n(n+1) = 240

here n can only be 15. Sufficient.

Choose D.

-BM-
How do we get (500n)/(500n(n + 1) = 1/16 from statement 1? Could you please explain?
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by papgust » Fri Feb 26, 2010 7:40 pm
How do we get (500n)/(500n(n + 1) = 1/16 from statement 1? Could you please explain?
First n people contributed 500*n. Total amount donated is 500 n(n+1).

From I, 500*n = 1/16 * (500 n(n+1))

So, 500n / 500 n(n+1) = 1/16
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by ashua12 » Sat Sep 18, 2010 4:46 am
garimag wrote:
crackgmat007 wrote:thanks guys
i didnt understand where n + n.n came from. please explain.
hi

hope this helps


mary----
Image
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by gman.gowri » Sat Sep 25, 2010 3:03 am
I got the same equations
for the first case i got
n(n-15)=0

why cant i assume n=0
i.e. mary persuaded 0 friends who inturn persuaded 0 friends...
you may think of me as a nutcase but being completely immersed in the gmat world for the last 20 days, i have come to question everything that is put forth in anything related to gmat question. More so with Data sufficiency and Critical reasoning.

Thanks in advance
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