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07 Apr 2009, 14:51
8
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54
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Difficulty:

65% (hard)

Question Stats:

63% (01:31) correct 37% (01:31) wrong based on 1865 sessions

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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. [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 43849 Re: Need Solution for some DS problems from SET1 [#permalink] ### Show Tags 23 Jun 2010, 14:04 21 This post received KUDOS Expert's post 25 This post was BOOKMARKED 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? # of people donated at the firs stage - $$n$$, amount - $$500n$$; # of people donated at the second - $$n^2$$, amount - $$500n^2$$; Total amount donated - $$500n+500n^2$$ Little assumption here: $$n>0$$. (1) The first n people donated 1/16 of the total amount donated --> $$16(500n)=500n+500n^2$$ --> $$n=15$$. Sufficient. (2) The total amount donated was$120,000 --> $$500n+500n^2=120,000$$ --> $$n=15$$. Sufficient.

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14 Nov 2010, 11:59
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?
Math Expert
Joined: 02 Sep 2009
Posts: 43849
Mary persuaded n friends to donate $500 each to her election [#permalink] ### Show Tags 14 Nov 2010, 12:21 Expert's post 2 This post was BOOKMARKED 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? It cannot give negative solution for $$n$$, though it can give $$n=0$$ as a solution. See below: 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? # of people donated at the firs stage - $$n$$, amount donated - $$500n$$; # of people donated at the second - $$n^2$$, amount donated - $$500n^2$$; Total amount donated - $$500n+500n^2$$ Little assumption here: $$n>0$$. (1) The first n people donated 1/16 of the total amount donated --> $$500n=\frac{1}{16}(500n+500n^2)$$ --> $$n=15$$ (we can rule out $$n=0$$, which is also a solution of this equation). Sufficient. (2) The total amount donated was$120,000 --> $$500n+500n^2=120,000$$ --> $$n=15$$. Sufficient.

Hope it's clear.
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12 Mar 2011, 17:50

1. sufficient

500n = x/16 = (500n+500n^2)/16
sufficient enough to find n.

2. 500n+500n^2 = 120,000

sufficient enough to find n.

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13 Mar 2011, 04:52
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.

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03 Mar 2012, 21:54
3
KUDOS
Man this question makes me mad that i got it wrong initially and it took me a while to figure it out..

OK so (1)

n/(n + n^2) = 1/16
16n = n^2 + n
n^2 -15n = 0
n(n-15) = 0
But n cant really be zero
Sufficient

(2)
(n + n ^2)* 500 = 120,000
n + n^2 = 240
n^2 + n -240=0
(n +16) (n-15) = 0
But n cant really be -16
Sufficient

I couldnt figure out the way to factor n^2 +n -240 = 0 for a long time
I guess my real issue was trying to solve it.. once i constructed the quadratic i shouldve just moved on with life!!!
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08 Apr 2012, 04:49
fluke wrote:
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. *********************************************************** Susie can buy apples from two stores: a supermarket that sells apples only in bundles of 4, and a convenience store that sells single, unbundled apples. If Susie wants to ensure that the total number of apples she buys is a multiple of 5, what is the minimum number of apples she must buy from the convenience store? A. 0 B. 1 C. 2 D. 3 E. 4 ******************************** If Susie can buy '0' apples, why can't Mary persuade '0' friends? Absurd!!! Can someone please answer the above mentioned fluke's query ? I have the same confusion "If Susie can buy '0' apples, why can't Mary persuade '0' friends?" In that case, Condition I will not be sufficient. Intern Joined: 04 Jan 2012 Posts: 17 Re: Mary persuaded n friends [#permalink] ### Show Tags 13 Apr 2012, 22:13 Bunuel wrote: 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? It can not give negative solution for $$n$$, though it can give $$n=0$$ as a solution. See below: 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? # of people donated at the firs stage - $$n$$, amount donated - $$500n$$; # of people donated at the second - $$n^2$$, amount donated - $$500n^2$$; Total amount donated - $$500n+500n^2$$ Little assumption here: $$n>0$$. (1) The first n people donated 1/16 of the total amount donated --> $$500n=\frac{1}{16}(500n+500n^2)$$ --> $$n=15$$ (we can rule out $$n=0$$, which is also a solution of this equation). Sufficient. (2) The total amount donated was$120,000 --> $$500n+500n^2=120,000$$ --> $$n=15$$. Sufficient.

Hope it's clear.

How to solve equation like 500n^2 + 500n = 120,000

This translates to quadratic equation n^2 + n = 240

Should one use formula of \sqrt{b^2 - 4ac}
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Posts: 43849

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14 Apr 2012, 02:01
Expert's post
1
This post was
BOOKMARKED
ps25 wrote:
Bunuel wrote:
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?

It can not give negative solution for $$n$$, though it can give $$n=0$$ as a solution. See below:

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?

# of people donated at the firs stage - $$n$$, amount donated - $$500n$$;
# of people donated at the second - $$n^2$$, amount donated - $$500n^2$$;
Total amount donated - $$500n+500n^2$$
Little assumption here: $$n>0$$.

(1) The first n people donated 1/16 of the total amount donated --> $$500n=\frac{1}{16}(500n+500n^2)$$ --> $$n=15$$ (we can rule out $$n=0$$, which is also a solution of this equation). Sufficient.

(2) The total amount donated was $120,000 --> $$500n+500n^2=120,000$$ --> $$n=15$$. Sufficient. Answer: D. Hope it's clear. How to solve equation like 500n^2 + 500n = 120,000 This translates to quadratic equation n^2 + n = 240 Should one use formula of \sqrt{b^2 - 4ac} You can solve it using the formula for quadratics, though it's better to use another approach: $$500n+500n^2=120,000$$ --> $$n+n^2=240$$ --> $$n(n+1)=240$$. Since $$n$$ is an integer then we have that the product of two consecutive integers is 240, now it's easy to find that $$n=15$$. Hope it's clear. _________________ Current Student Joined: 26 Jul 2012 Posts: 63 Re: Mary persuaded n friends to donate$500 each to her election [#permalink]

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24 Aug 2013, 17:49
I am just wondering if there is another way to solve this problem without the quadratics solution.
Fundraising run 1 = 500n
Fundraising run 2 = 500n^2

500n + 500n^2 = total amount donated.

Goal of our DS question, find n, and to find "n", we need to know:
1) Total amount donated
OR
2) The RATIO of the two fundraising runs. If we have the ratio, we can set them against each other and get rid of "n"s.

Each given statement meets the criteria above, thus D.
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] ### Show Tags 10 Jan 2014, 08:08 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.

My problem with this question was that I foolishly assumed that there were two different n's, n1 and n2, and thus we had two variables (n1,n2) plus the total amount donated.

1 gave us the relation between n1,n2 and 2 gives us total donated so we can solve for the unknowns, that's why I picked C.

It just simply couldnt comprehend how we could get n^2, hopefully I will not make the same mistake on the actual test in a couple of days.
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13 Mar 2014, 07:57
3
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Expert's post
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unceldolan wrote:
Hey all,

I think I don't get the wording: If EACH of the n friends persuaded n people, wouldn't it be n^n??

Wouldn't really change the outcome, but I'd like to know it exactly....

Thanks!

No. Say n=3, then at the second stage the number of people who donated would be 3*3=9, not 3^3=27:
Attachment:

Untitled.png [ 888 Bytes | Viewed 24501 times ]

Hope it's clear.
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19 Apr 2014, 08:41
2
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Expert's post
hhakud wrote:
I still am confused with the phrase...
"then each of these n friends persuaded n more people"
How could this be $$n*n$$ why not $$n+n$$

If 3 people persuade 3 more people then the total would become 3+3=6 right.??
Pls clarify

Bunuel wrote:
unceldolan wrote:
Hey all,

I think I don't get the wording: If EACH of the n friends persuaded n people, wouldn't it be n^n??

Wouldn't really change the outcome, but I'd like to know it exactly....

Thanks!

No. Say n=3, then at the second stage the number of people who donated would be 3*3=9, not 3^3=27:
Attachment:
Untitled.png

Hope it's clear.

Each of these n friends persuaded n more people, not that n people together persuaded n more people.

Hope it's clear.
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09 Nov 2014, 07:34
Can someone please explain the logic in putting the equation in part (1) = 500n? In my own working i came up with the RHS, but in my mind that should be put equal to the total amount donated. I am not sure how this is equal to 500n (which in turn is equal to the total number of 1st tier friends who donated).
I am sure its simple and I am just missing a logical step. The rest of Brunels/OG's solution is crystal clear.
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Posts: 43849
Re: Mary persuaded n friends to donate $500 each to her election [#permalink] ### Show Tags 10 Nov 2014, 01:35 1 This post received KUDOS Expert's post Madrigal wrote: Can someone please explain the logic in putting the equation in part (1) = 500n? In my own working i came up with the RHS, but in my mind that should be put equal to the total amount donated. I am not sure how this is equal to 500n (which in turn is equal to the total number of 1st tier friends who donated). I am sure its simple and I am just missing a logical step. The rest of Brunels/OG's solution is crystal clear. Amount donated by the first n people = $$500n$$; Total amount donated = $$500n+500n^2$$. (1) says that the first n people donated 1/16 of the total amount donated, thus $$500n=\frac{1}{16}(500n+500n^2)$$ --> $$16(500n)=500n+500n^2$$. Hope it's clear. _________________ Re: Mary persuaded n friends to donate$500 each to her election   [#permalink] 10 Nov 2014, 01:35

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