Value of n

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Sun Oct 05, 2008 5:28 pm

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 th of the total amount donated.
(2) The total amount donated was $120,000.

OA is: D

Last edited by mehravikas on Tue Oct 07, 2008 1:03 am, edited 1 time in total.

Source: Beat The GMAT — Data Sufficiency | Sun Oct 05, 2008 5:28 pm

stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

by stop@800 » Mon Oct 06, 2008 9:41 pm

(1) The first n people donated 161 of the total amount donated.

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Tue Oct 07, 2008 1:04 am

Apologies, it was a copy paste error. Have corrected it in the post.
Thanks.

stop@800 wrote:(1) The first n people donated 161 of the total amount donated.

stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

by stop@800 » Tue Oct 07, 2008 1:30 am

first n ppl donated 500n amount

round 2
no of ppl = n^2
donation = 500 * n^2

total no of ppl = n+n^2
total donation = 500(n+n^2)

let total donation be T

A
500n = [500(n+n^2) ] /16
we can solve but no need [n=15]
sufficient

B
500(n+n^2) = 12000
solve for n
quadretic
one positive and one negative root
take positive one
as no of ppl can not be negative

so ans is D

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cubicle_bound_misfit: Master | Next Rank: 500 Posts; Posts: 246; Joined: Mon May 19, 2008 7:34 am; Location: Texaco Gas Station; Thanked: 7 times

by cubicle_bound_misfit » Tue Oct 07, 2008 12:23 pm

One thing I can not understand is n friends each persuading n people to donate

If I assume so then

Total money = 500n^2+ 500n

Given 16.500n = 500n^2 +500n

Or 15n = n^2

N =15

Again from 2

500n +500 n^2 = 120,000

n^2 + n = 240

n = 16

hence answer is D

Cubicle Bound Misfit

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