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.

Target question: What was the value of n?When I

scan the two statements, it seems that statement 2 is easier, so I'll start with that one first...

Statement 2: The total amount donated was $120,000 Let's summarize the given information....

First round: n friends donate 500 dollars.

This gives us a total of

500n dollars in this round

Second round: n friends persuade n friends each to donate

So, each of the n friends gets n more people to donate.

The total number of donors in this round = n²

This gives us a total of

500(n²) dollars in this round

TOTAL DONATIONS =

500n dollars +

500(n²) dollars

We can rewrite this: 500n² + 500n dollars

So, statement 2 tells us that 500n² + 500n = 120,000

This is a quadratic equation, so let's set it equal to zero to get: 500n² + 500n - 120,000 = 0

Factor out the 500 to get: 500(n² + n - 240) = 0

Factor more to get: 500(n + 16)(n - 15) = 0

So, EITHER n = -16 OR n = 15

Since n cannot be negative, it must be the case that

n = 15Since we can answer the

target question with certainty, statement 2 is SUFFICIENT

Statement 1: The first n people donated 1/16 of the total amount donated. First round donations =

500nTOTAL donations = 500n² + 500n

So, we can write:

500n = (1/16)[500n² + 500n]

Multiply both sides by 16 to get: 8000n = 500n² + 500n

Set this quadratic equation equal to zero to get: 500n² - 7500n = 0

Factor to get: 500n(n - 15) = 0

Do, EITHER n = 0 OR n = 15

Since n cannot be zero, it must be the case that

n = 15Since we can answer the

target question with certainty, statement 1 is SUFFICIENT

Answer:

Cheers,

Brent

_________________

Brent Hanneson – Founder of gmatprepnow.com