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Mary : Donations, Simultaneous equations

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Mary : Donations, Simultaneous equations

by anirudhbhalotia » Thu Mar 10, 2011 9:35 am
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

OA- D
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by ankur.agrawal » Thu Mar 10, 2011 10:48 am
anirudhbhalotia 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

OA- D
Total amount collected = (500n+500n^2)

1) (1/16) * (500n+500n^2) = 500n ---- Solve for n ; n=15

2) (500n+500n^2) = 120,000 Solve for n ;n=15

D
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by clock60 » Thu Mar 10, 2011 10:51 am
first assume that n=2, then these 2 brings (500+500)=2*500, and involveed every one two more friends=total 4. with total ammoun of money
(500+500)+(500+500+500+500)=2*500+4*500=2*500+(2^2)*500, we know that n=2, so in general terms it will looks like: 500*n+500*n^2, and we need to find the value of n
(1) The first n people donated 1/16 of the total amount donated
500*n=1/16(500*n+500*n^2)-solve it,
after little transforming
n(n-15)=0, n=15-sufficient
(2)The total amount donated was $120,000
here not trivial quadratic equation
500*n+500*n^2=120000
n^2+n-240=0
n1=15, n2=-16, we reject negative answer
and left with n=15, suff
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by Night reader » Thu Mar 10, 2011 2:39 pm
Since this DS is in English we read it straight --> Mary persuaded/they donated - count n*500, next EACH of n persuaded n more people (n MORE means +n, BUT here it means n, which is incorrect, and I guess OUT of GMAT scope, this problem could never be from OG 11 or 12, my personal opinion) - count final expression as n*(n)*500. We are asked to find the value of n with the given conditions - let's call total donation X, and we know that n*500 +n*(n)*500=X finalizing 500n(1+n)=X

st(1) ponder before writing, each donated $500 and first donations came from n people --> 16(n*500)=X, enough? Yes, 16(n*500)=500n(1+n), Cancel n and 500 on both sides (we cancel n as n CANNOT be 0) --> 16=(1+n), n=15
st(2) X=120,000 OR 500n(1+n)=120,000 here from the both side we MAY cancel zeros and numbers --> n(1+n)=240. Now to solve for n we can find approximate square of 240 and +-1 number next to it. Let's try 15^2 should work, as we get 15*16 which is 15*(15+1)=230 Sufficient

answer D.

anirudhbhalotia 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

OA- D
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by anirudhbhalotia » Thu Mar 10, 2011 10:17 pm
How and why are we putting n square(n^2) ?
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by ankur.agrawal » Thu Mar 10, 2011 10:41 pm
anirudhbhalotia wrote:How and why are we putting n square(n^2) ?
N friends contributing 500 each; Total contribution = 500N . Agree?

Now each of N friends persuaded N more people to donate $500. Note the word Each.

So N more people will donate $ 500 Each =500N Agree?--- This corresponds to each of 'n' friends & since there are n firends all together = (500n) *n

Total = 500n + 500n ^2.

Its difficult to understand by Language . Pick up some numbers & try to see it for yourselves.

Hope it helps.
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by Night reader » Fri Mar 11, 2011 9:40 am
besides putting n^2 we have to solve for n using this equation n(1+n)=240, agree? I have decided to aggressively proceed to the target, i.e. finding n - even if it's n^2 +-1 ...
anirudhbhalotia wrote:How and why are we putting n square(n^2) ?
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by anirudhbhalotia » Tue Mar 15, 2011 9:20 am
ankur.agrawal wrote:
anirudhbhalotia wrote:How and why are we putting n square(n^2) ?
N friends contributing 500 each; Total contribution = 500N . Agree?

Now each of N friends persuaded N more people to donate $500. Note the word Each.

So N more people will donate $ 500 Each =500N Agree?--- This corresponds to each of 'n' friends & since there are n firends all together = (500n) *n

Total = 500n + 500n ^2.

Its difficult to understand by Language . Pick up some numbers & try to see it for yourselves.

Hope it helps.
Aha got it! Me and my thick brain cells!
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