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Marys campaign

by rkav » Sat Mar 16, 2013 4:09 pm
OG 13 edition number 72 page 281

Mary persuaded 'n' friends to donate 500 dollars each to her election campaign and then each of these n friends persuaded n more people to donate 500 dollars each to Marys campaign. If no one donated more than once 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.



Quick question bout the formula you set up to answer the question

why is the amount contributed to the campaign set up as total= 500(n^2 +n) as opposed to 500 (2n)

Thanks!
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by neha24 » Sat Mar 16, 2013 6:05 pm
interesting !!!
N friends to donate 500 dollars each to her election campaign--- --> money collected 500N
each of these n friends persuaded n more people----->that means u have each lot of N people and how many lots are there? there r N such lots so total number of people = N^2
money collected by these N^2 people =500N^2
so total money =500n^2 + 500n

i feel the answer sud be D
just a side note: had this series increased further the next lot wud have been N^3
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by rkav » Sat Mar 16, 2013 6:16 pm
ahhh thank you.

I overlooked "each of these n friends convinced n people"


Thank you!
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by GMATGuruNY » Sun Mar 17, 2013 4:41 am
rkav wrote:OG 13 edition number 72 page 281

Mary persuaded 'n' friends to donate 500 dollars each to her election campaign and then each of these n friends persuaded n more people to donate 500 dollars each to Marys campaign. If no one donated more than once 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.
If n=2, and each of these 2 people invite 2 other people, then the total number of ADDITIONAL people invited = 2*2 = 2² = n².
If n=3, and each of these 3 people invite 3 other people, then the total number of ADDITIONAL people invited = 3*3 = 3² = n².
Thus, the total number of ADDITIONAL people invited = n².

Since each person donates $500:
Total donated by the first n people = 500n.
Total donated by the n² additional people = 500n².

Statement 1: The first n people donated 1/16 of the total amount donated.
Thus, of every $16 donated, $1 was donated by the first n people, while $15 was donated by the n² additional people.
Thus:
500n / 500n² = 1/15
1/n = 1/15
n=15.
SUFFICIENT.

Statement 2: The total amount donated was 120,000.
Since each person donates $500, the total number of people = 120,000/500 = 240.
Since n=15 in statement 1, let's see whether this value also satisfies statement 2:
If n=15, the total number of people = n + n² = 15 + 225 = 240.
Clearly, no other value of n will yield the required total of 240 people.
Thus, n=15.
SUFFICIENT.

The correct answer is D.
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