Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 13:54

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

### Show Tags

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
Intern
Joined: 04 Mar 2015
Posts: 4

### Show Tags

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

Intern
Joined: 30 Jul 2014
Posts: 1
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.
Intern
Joined: 16 May 2017
Posts: 17

### Show Tags

12 Nov 2017, 09:07
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
_________________
Test confidently with gmatprepnow.com
Intern
Joined: 16 Jan 2011
Posts: 4
Location: Singapore
Concentration: Finance
Schools: HKUST (S)
GMAT 1: 690 Q49 V34
GPA: 3.62

### Show Tags

22 Jun 2018, 23:23
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 $$n = -\frac{1}{2}+\frac{\sqrt{13}}{2}$$
_________________
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: Mary persuaded n friends to donate $500 each to her election [#permalink] ### Show Tags 04 Nov 2018, 12:47 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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net