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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