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data sufficiency, official guide 12th edition #70

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data sufficiency, official guide 12th edition #70

by jzw » Mon Mar 05, 2012 1:47 pm
Mary persuaded n friends to donate $500 each to her election campaign, and then each of these 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.

So, I mistakenly got C, when in reality the answer is D. The explanation I have is from my PR instructor who did a whole bunch of equations - but I'm not going to be able to reconstruct this type of thing on the actual exam. I know myself. Is there any way to know that each is sufficient (or not sufficient as the future case may be, by having some sort of chart as to what is needed to solve in this type of problem? Or do I just have to accept that I'm going to get this type of question wrong and all is lost?
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by [email protected] » Mon Mar 05, 2012 6:54 pm
n friends contributed and then n friends told n other friends i.e, n^2 more.
So, the total number of contributors = n + n^2

Statement 1:
n/(n + n^2) = 1/16
16n = n + n^2
n=15 since n can't be 0
SUFFICIENT

Statement 2:
500(total number of contributors) = 120,000
500(n + n^2) = 120,000
500n + 500n^2 = 120,000
n^2 + n - 240 = 0
(n+16)(n-15)=0
Since n must be positive, n=15
SUFFICIENT

So the answer is D
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by Anurag@Gurome » Mon Mar 05, 2012 7:07 pm
jzw wrote:Mary persuaded n friends to donate $500 each to her election campaign, and then each of these 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.

So, I mistakenly got C, when in reality the answer is D. The explanation I have is from my PR instructor who did a whole bunch of equations - but I'm not going to be able to reconstruct this type of thing on the actual exam. I know myself. Is there any way to know that each is sufficient (or not sufficient as the future case may be, by having some sort of chart as to what is needed to solve in this type of problem? Or do I just have to accept that I'm going to get this type of question wrong and all is lost?
Donation by n friends = 500n
Then each of these n friends persuaded n more people to donate $500 each to Mary's campaign implies Donation = 500n²
Total donation = 500n + 500n² = 500n(n + 1)
We have to find n.

(1)(1/16){500n(n + 1)} = 500n, which can be solved for n.
So, (1) is SUFFICIENT.

(2) 500n(n + 1) = 120000, which can again be solved for n.
So, (2) is SUFFICIENT.

The correct answer is D.
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