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07 Apr 2009, 15:51
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Question Stats:

56% (02:36) correct 44% (01:38) wrong based on 1236 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: 33547 Followers: 5942 Kudos [?]: 73722 [14] , given: 9903 Re: Need Solution for some DS problems from SET1 [#permalink] ### Show Tags 23 Jun 2010, 15:04 14 This post received KUDOS Expert's post 11 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, 12:59
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?
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14 Nov 2010, 13:21
Expert's post
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. _________________ Director Joined: 01 Feb 2011 Posts: 757 Followers: 14 Kudos [?]: 95 [0], given: 42 Re: Mary persuaded n friends [#permalink] ### Show Tags 12 Mar 2011, 18:50 My answer is D. 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. Answer D. Math Forum Moderator Joined: 20 Dec 2010 Posts: 2021 Followers: 155 Kudos [?]: 1483 [0], given: 376 Re: Mary persuaded n friends [#permalink] ### Show Tags 13 Mar 2011, 05:52 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. (2) The total amount donated was$120,000.

***********************************************************
Minor detour:
apples-and-apples-word-problem-85741.html

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!!!
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13 Mar 2011, 08:38
Same approach from every body and same from me. Basically it is OG approach.
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DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] ### Show Tags 03 Mar 2012, 22:54 1 This post received 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 Answer is D 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!!! Intern Joined: 14 Mar 2012 Posts: 13 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Mary persuaded n friends [#permalink] ### Show Tags 08 Apr 2012, 05:49 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.
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13 Apr 2012, 23:13
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. 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} Math Expert Joined: 02 Sep 2009 Posts: 33547 Followers: 5942 Kudos [?]: 73722 [0], given: 9903 Re: Mary persuaded n friends [#permalink] ### Show Tags 14 Apr 2012, 03:01 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.

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.
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10 Jan 2014, 09:08
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. Current Student Joined: 21 Oct 2013 Posts: 194 Location: Germany GMAT 1: 660 Q45 V36 GPA: 3.51 Followers: 1 Kudos [?]: 26 [0], given: 19 Re: Mary persuaded n friends to donate$500 each to her election [#permalink]

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13 Mar 2014, 07:42
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!
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19 Apr 2014, 06:58
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.
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13 Aug 2014, 18:49
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.

Not the OP but I was stuck at the same point -- I didn't know how to go a level after N. I started plugging in numbers but that turned out to be a huge mess.

Couple of questions:

1) I couldn't really understand (while first reading the question) as to when n would stop factoring. Meaning, if n was 3, would it go own 2 levels or 3 levels? meaning, would the total be 500(n + n^2 + n3)

2) a little confused as to why it's not 3n^2? sorry, having a hard time visualizing the total number of people.

3) would the third level be cubed like i wrote above or would it be n^4(squared of n^2?)

Thanks!
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10 Nov 2014, 02:35
1
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Expert's post
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.
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