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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:

57% (02:22) correct
42% (01:23) wrong based on 345 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.

Re: Need Solution for some DS problems from SET1 [#permalink]
23 Jun 2010, 14:04

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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.

Re: Mary persuaded n friends [#permalink]
14 Nov 2010, 11:59

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.

Re: Mary persuaded n friends [#permalink]
14 Nov 2010, 12:21

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.

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.

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]
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!!!

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.

Re: Mary persuaded n friends [#permalink]
13 Apr 2012, 22:13

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

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.

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]
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.

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.