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Mary persuaded n friends to donate $500 each to her election [#permalink]

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07 Apr 2009, 15:51

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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.

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.

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.

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.

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!!! _________________

Re: Mary persuaded n friends to donate $500 each to her election [#permalink]

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03 Mar 2012, 22:54

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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!!!

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.

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

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}

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 \(n=15\).

Re: Mary persuaded n friends to donate $500 each to her election [#permalink]

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24 Aug 2013, 18:49

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.

Re: Mary persuaded n friends to donate $500 each to her election [#permalink]

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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.

Mary persuaded n friends to donate $500 each to her election [#permalink]

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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?)

Re: Mary persuaded n friends to donate $500 each to her election [#permalink]

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09 Nov 2014, 08:34

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.

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 \(500n=\frac{1}{16}(500n+500n^2)\) --> \(16(500n)=500n+500n^2\).

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