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# Mary persuaded n friends to donate $500 each to her election  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Director Joined: 29 Aug 2005 Posts: 882 Followers: 7 Kudos [?]: 124 [0], given: 7 Mary persuaded n friends to donate$500 each to her election [#permalink]  07 Apr 2009, 14:51
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Difficulty:

35% (medium)

Question Stats:

55% (02:14) correct 44% (01:19) wrong based on 180 sessions
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: 17011 Followers: 2787 Kudos [?]: 17764 [9] , given: 2280 Re: Need Solution for some DS problems from SET1 [#permalink] 23 Jun 2010, 14:04 9 This post received KUDOS Expert's post 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.

_________________
Manager
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Posts: 91
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31
GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)
Followers: 0

Kudos [?]: 21 [0], given: 4

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: 17011
Followers: 2787

Kudos [?]: 17764 [0], given: 2280

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: 774 Followers: 12 Kudos [?]: 75 [0], given: 42 Re: Mary persuaded n friends [#permalink] 12 Mar 2011, 17:50 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: 2058 Followers: 122 Kudos [?]: 815 [0], given: 376 Re: Mary persuaded n friends [#permalink] 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. (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!!!
_________________

~fluke

Director
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 655
Followers: 29

Kudos [?]: 153 [0], given: 32

Same approach from every body and same from me. Basically it is OG approach.
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I am student of everyone-baten
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
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
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Manager
Joined: 22 Feb 2012
Posts: 93
Schools: HBS '16
GMAT 1: 740 Q49 V42
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WE: Corporate Finance (Aerospace and Defense)
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Kudos [?]: 17 [0], given: 25

Re: Mary persuaded n friends to donate $500 each to her election [#permalink] 03 Mar 2012, 21:54 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] 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: 7
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Kudos [?]: 0 [0], given: 2

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: 17011 Followers: 2787 Kudos [?]: 17764 [0], given: 2280 Re: Mary persuaded n friends [#permalink] 14 Apr 2012, 02:01 Expert's post 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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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] 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. Manager Joined: 12 Jan 2013 Posts: 247 Followers: 0 Kudos [?]: 5 [0], given: 47 Re: Mary persuaded n friends to donate$500 each to her election [#permalink]  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. Manager Joined: 21 Oct 2013 Posts: 101 Location: Germany Concentration: Accounting, International Business GPA: 3.91 Followers: 0 Kudos [?]: 9 [0], given: 14 Re: Mary persuaded n friends to donate$500 each to her election [#permalink]  13 Mar 2014, 06:42
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!
Math Expert
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Kudos [?]: 17764 [0], given: 2280

Re: Mary persuaded n friends to donate $500 each to her election [#permalink] 13 Mar 2014, 07:57 Expert's post 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 114 times ] Hope it's clear. _________________ Re: Mary persuaded n friends to donate$500 each to her election   [#permalink] 13 Mar 2014, 07:57
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