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Mary persuaded n friends to donate $500 each to her election

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NEWKID
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Mary persuaded n friends to donate $500 each to her election [#permalink] New post   Updated on: 06 Nov 2004, 11:26
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A
B
C
D
E

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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.

A. Statement (1) ALONE is sufficient, but statement (2) alone

is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone

is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER

statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficie



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Originally posted by NEWKID on 06 Nov 2004, 10:29.
Last edited by NEWKID on 06 Nov 2004, 11:26, edited 1 time in total.
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] New post   06 Nov 2004, 11:02
There is a typo in choice 1
If we know the amount donated by the first n persons, we can get answer and D would be my pick
500 * n^2 = t
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] New post   06 Nov 2004, 11:26
The typo has been corrected Paul.It was 1/16
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] New post   06 Nov 2004, 11:41
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.

Amount donated by first n = 500 *n

Total Amount donated = 500 * n^2

1. 500n = 1/16 * 500 * n ^2
or n ^ 2/n = 16 or n =16

2. 500* n^2 = 120000


my answer is D as we can find n, however in 2nd case n does not come out to be a natural number.
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink] New post   06 Nov 2004, 11:55
D would still be the answer
1- has been demonstrated by practicemore
2- 500n^2 + 500n = 120,000$
The first 500n^2 accounts for the "friends of friends" without accounting for the first n friends which is accounted for by adding 500n
You then have 500n(n+1) = 120,000
n(n+1) = 240
Only positive integer that fits is n=16



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Thank you for understanding, and happy exploring!
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Re: Mary persuaded n friends to donate $500 each to her election [#permalink]
06 Nov 2004, 11:55
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