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30 Mar 2015, 20:07
Bunuel wrote:
Awli wrote:
Mary persuaded n friends to donate $500 each to her election campaign, an 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 \frac{1}{16} of the total amount donated.

(2) The total amount donated was $120,000 Merging topics. Please refer to the discussion on page 1. [color=#0000ff]not sure, if my approach is right or wrong. I just took it like: 1. Mary persuaded n friends to donate$500 = n*500
2. then each of these n friends persuaded n more people.= n^(n+1) * 500

Statement 1. first n donated 1/16 of the total. remains > need total amount.
Statement 2. n^(n+1)*500 = 120,000
n*n^n = 240 .. Looks insufficient

1+2

n = 1/16 * 120000 /500 = 15

hence C

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31 Mar 2015, 04:44
Original Donations = 500n
Friends' Friends =500n^2
Total = 500n+500n^2

Statement 1 :The first n people donated \frac{1}{16} of the total amount donated.

500n = 1/16 (500n+500n^2)
16(500n) = 500n+500n^2
n = 15
stmt 1 is sufficient

Statement 2: The total amount donated was $120,000 500n+500n^2=$120,000
can solve for n
n=15
stmt 2 is sufficient

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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] ### Show Tags 10 Aug 2015, 02:55 aalriy wrote: I have understood the approach GT took to solve the problem its very similar to mine... but i cannot make out how can the first stmt give a solution for n as 0 or a -ve value. Could someone explain this? On the GMAT you ll not be asked a value based DS question if at all there is no such value.That is why n can not be zero.One more thing that U can understand that as there are n people first to donate$500 each and those n people refer n people each .So if U consider that there are 16 portions total money is donated by all then 1 portion is by the first n people.

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12 Nov 2017, 09:07
Expert's post
Top Contributor
seofah 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. Target question: What was the value of n? When I scan the two statements, it seems that statement 2 is easier, so I'll start with that one first... Statement 2: The total amount donated was$120,000
Let's summarize the given information....

First round: n friends donate 500 dollars.
This gives us a total of 500n dollars in this round

Second round: n friends persuade n friends each to donate
So, each of the n friends gets n more people to donate.
The total number of donors in this round = n²
This gives us a total of 500(n²) dollars in this round

TOTAL DONATIONS = 500n dollars + 500(n²) dollars
We can rewrite this: 500n² + 500n dollars

So, statement 2 tells us that 500n² + 500n = 120,000
This is a quadratic equation, so let's set it equal to zero to get: 500n² + 500n - 120,000 = 0
Factor out the 500 to get: 500(n² + n - 240) = 0
Factor more to get: 500(n + 16)(n - 15) = 0
So, EITHER n = -16 OR n = 15
Since n cannot be negative, it must be the case that n = 15
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Statement 1: The first n people donated 1/16 of the total amount donated.
First round donations = 500n
TOTAL donations = 500n² + 500n
So, we can write: 500n = (1/16)[500n² + 500n]
Multiply both sides by 16 to get: 8000n = 500n² + 500n
Set this quadratic equation equal to zero to get: 500n² - 7500n = 0
Factor to get: 500n(n - 15) = 0
Do, EITHER n = 0 OR n = 15
Since n cannot be zero, it must be the case that n = 15
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

[Reveal] Spoiler:
D

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

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