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Mary persuaded n friends to donate $500 ...

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Mary persuaded n friends to donate $500 ...

by factor26 » Wed Dec 07, 2011 6:05 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.

OG answer is D ... can someone please breake the question down step by step? I'm having trouble understanding statement 1 in particular ... any help would be really appreciated ... thanks all!
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by Anurag@Gurome » Wed Dec 07, 2011 6:36 pm
factor26 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.

OG answer is D ... can someone please breake the question down step by step? I'm having trouble understanding statement 1 in particular ... any help would be really appreciated ... thanks all!
Donation by n friends = 500n
Then each of these n friends persuaded n more people to donate $500 each to Mary's campaign implies Donation = 500n²
Total donation = 500n + 500n² = 500n(n + 1)
We have to find n.

(1)(1/16){500n(n + 1)} = 500n, which can be solved for n.
So, (1) is SUFFICIENT.

(2) 500n(n + 1) = 120000, which can again be solved for n.
So, (2) is SUFFICIENT.

The correct answer is D.
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by factor26 » Sat Dec 10, 2011 11:14 am
@ anurag ... i'm a little confused with the formula you provided

"Total donation = 500n + 500n² = 500n(n + 1)"

shouldn't it be 500n + 500n = 1000n .... the first n people contributed $500 ($500n) ... each of these friends convinced n more friends to contribute $500 as well ... also represented by ($500n).

each of these n friends convinced n more people to donate $500 each to marys campaign

i think i see it now n * n * $500 = amount generated from the second batch of people

can you please explain you reasonin g in statement 1. again when you have a moment?

since the first n people represent 1/16 of the total amount donated --- $500n = 1/16 --- i'm confused can you please go into further detail here?
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