Data Sufficiency

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

If the first n friends each donate $500, they'll have donated a total of $500n.

If each of those n friends persuades n more friends to donate $500, we'll have another n*n = n^2 friends, and 500*n^2 more dollars.

So the total donation will be 500n^2 + 500n.

1) We're told that 500n represents 1/16 of the total amount.
500n = (1/16) * 500n^2 + 500n
500n *16 = n(500n + 500)
Divide both sides by n: 500*16 = 500n + 500; can solve for n, so sufficient.

2) Total is 120,000;
500n^2 + 500n = 120,000
Divide both sides by 500
n^2 + n = 240
n^2 + n - 240 = 0
(n - 15)(n+16) = 0
n = 15 or n = -16. Clearly n must be positive. Sufficient. (And note we didn't have to finish solving. As soon as you see that there is one negative and one positive result, there can only be one workable solution to this question.)

Answer is D

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.