Pg.312 #70 OG12

eclaym2003 wrote:One of my biggest problems with data sufficiency is putting the question in simpler terms so that I can find out what I need to answer the question. This is a question that i am stuck on:

Mary persuaded "n" friends to donate $500 dollars each to her 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.

I do not understand how they got this from the question: ... the amount contributed to the campaign was $500(n^2+n).

If M persuaded n members and each of the n members persuaded n more than total no of members would be n(n+1)

Take e.g. lets n=2, so these 2 guys convinced 2 more guys individually so, total no of guys would be 2+2+2=6=2*3 =n(n+1)

Try for more and check this

so total amount would be n(n+1)*500. Once you know this, there is nothing left

1. n.500=1/16(Total amount)...solve for n

2. n(n+1)*500=120K, you can get one positive and one negative, n cant be negative

D

It becomes easier if you visualize this problem as a tree. For example
let solve it for 'n' = 2. So Mary gets 2 people(A and B) to pay $500 each.
Now A and B get 2 people each to pay $500. That is A gets P and Q to pay
$500 and B gets R and S to pay $500.


......Mary
...../......\
....A........B
../...\...../...\
P.....Q..R.....S


The total amount collected will be:
i) Mary got 2 people to pay, so amt collected by Mary is 2*500
ii) A and B together got 4 people to pay, so the amt collected is 4*500

Total amt = 2*500 + 4*500

Now if we generalize this we get = n*500 + (n^2)*500 = 500(n + n^2)[spoiler][/spoiler]