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### Show Tags

30 Mar 2015, 19:07
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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### Show Tags

31 Mar 2015, 03:44
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, 01:55 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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### Show Tags

12 Nov 2017, 08:07
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

Cheers,
Brent
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### Show Tags

22 Jun 2018, 22:23
gmatcrash wrote:
Within context of GMAT DS question, the moment I manage to set up such relationship n(n+1) = 240, will it be safe to say there is 1 solution for n without trying to find a pair of factors that fit? This would save some time. Whenever I get to this point, I always try to find a pair just to make sure it will not be the case of a) having no solution for n or b) having 2 solutions for n.

n(n + 1) = (positive number) will always have two solutions, one negative and one positive but not always these solutions will be integers.

For example:

n(n + 1) = 2 --> n = -2 or n = 1;

n(n + 1) = 2 --> $$n = -\frac{1}{2}-\frac{\sqrt{13}}{2}$$ or $$n = -\frac{1}{2}+\frac{\sqrt{13}}{2}$$
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] ### Show Tags 04 Nov 2018, 11:47 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.

$${\rm{Total}}\,\, = \,\,500 \cdot n + 500 \cdot n \cdot n\,\,\,\,\,\,\left[ \ \right]$$

$$? = n$$

$$\left( 1 \right)\,\,\,500 \cdot n = {1 \over {16}} \cdot 500 \cdot n \cdot \left( {1 + n} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\,\left( {500\,n} \right)\,\,\,\left[ {\,n\, \ne \,0\,} \right]} \,\,\,1 = {1 \over {16}} \cdot \left( {1 + n} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,n\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

$$\left( 2 \right)\,\,\,500 \cdot n\left( {1 + n} \right) = 120000\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,500} \,\,\,\,n\left( {1 + n} \right) = 240\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,n\,\, > 0\,\,\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

$$\left( * \right)\,\,15 \cdot 16 = 240\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ \,n\left( {n + 1} \right) < 240\,\,{\rm{for}}\,\,0 < n < 15 \hfill \cr \,n\left( {n + 1} \right) > 240\,\,{\rm{for}}\,\,n \ge 16 \hfill \cr} \right.\,\,\,\,\,\,\left( {{\rm{Now}}\,\,{\rm{rethink}}\,\,{\rm{without}}\,\,{\rm{knowing}}\,\,{\rm{that}}\,\,n = 15...} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Mary persuaded n friends to donate $500 each to her election &nbs [#permalink] 04 Nov 2018, 11:47 Go to page Previous 1 2 [ 29 posts ] Display posts from previous: Sort by # Mary persuaded n friends to donate$500 each to her election

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