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OG12 #70 - value of n? Why isnt n =0 ??

This topic has 2 expert replies and 3 member replies
rohit_gmat Master | Next Rank: 500 Posts
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OG12 #70 - value of n? Why isnt n =0 ??

Post Sun Oct 10, 2010 7:32 am
Mary persuaded n friends to donate $500 each to her election campaign, and each of those n friends persuaded n more friends 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.

The OA is D

But I thought B was the correct answer.
With both statments we get quadratic equations :
Statement 1 gives us : n =0 or 15
Statement 2 gives us : n = -16 or 15 (this is clear since -16 people is not possible, so 15 must be the value)
But GMAC says - "Assuming n>0" statement 1 gives us n = 15....... WHY CAN'T n = 0 ??
When can we assume in the GMAT that n>0?? And when can we not?? i.e. when the question doesn't clearly specify...

[/b]

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Post Wed Oct 13, 2010 9:48 pm
selango wrote:
rohit bro,

PS:By the way u think the question ll be stated in this way huh?


Mary persuaded n friends to donate $500 each to her election campaign, and each of those n friends persuaded n more friends 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?
Note that n is an positive integer since it represent the number of friends.

Just Kidding yaar Mr. Green
...hilarious.

In PS word problems that describe a situation, you can always assume that the number of entities is such that the situation exists (this usually means that they are all positive integers.) Or as selango points out, if we let n = 0, then Mary has no friends, and there is no question at all (because the situation wouldn't exist).

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Post Sun Nov 12, 2017 8:08 am
rohit_gmat wrote:
Mary persuaded n friends to donate $500 each to her election campaign, and each of those n friends persuaded n more friends 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.

The OA is D
[/b]
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 = 15
Since 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 = 500n
TOTAL 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 = 15
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Answer: D

Cheers,
Brent

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Post Wed Oct 13, 2010 9:48 pm
selango wrote:
rohit bro,

PS:By the way u think the question ll be stated in this way huh?


Mary persuaded n friends to donate $500 each to her election campaign, and each of those n friends persuaded n more friends 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?
Note that n is an positive integer since it represent the number of friends.

Just Kidding yaar Mr. Green
...hilarious.

In PS word problems that describe a situation, you can always assume that the number of entities is such that the situation exists (this usually means that they are all positive integers.) Or as selango points out, if we let n = 0, then Mary has no friends, and there is no question at all (because the situation wouldn't exist).

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Kaplan Teacher in Toronto

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Post Sun Nov 12, 2017 8:08 am
rohit_gmat wrote:
Mary persuaded n friends to donate $500 each to her election campaign, and each of those n friends persuaded n more friends 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.

The OA is D
[/b]
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 = 15
Since 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 = 500n
TOTAL 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 = 15
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Answer: D

Cheers,
Brent

_________________
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Check out the online reviews of our course
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Viktri Junior | Next Rank: 30 Posts Default Avatar
Joined
12 Aug 2010
Posted:
12 messages
Post Wed Oct 13, 2010 9:26 pm
Data given:

n x 500 + n x n x 500
total = 1500n

i) (n+500) x 16 = 1500n
solvable

ii) 1500n = 120,000
solvable



rohit_gmat wrote:
Mary persuaded n friends to donate $500 each to her election campaign, and each of those n friends persuaded n more friends 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.

The OA is D

But I thought B was the correct answer.
With both statments we get quadratic equations :
Statement 1 gives us : n =0 or 15
Statement 2 gives us : n = -16 or 15 (this is clear since -16 people is not possible, so 15 must be the value)
But GMAC says - "Assuming n>0" statement 1 gives us n = 15....... WHY CAN'T n = 0 ??
When can we assume in the GMAT that n>0?? And when can we not?? i.e. when the question doesn't clearly specify...

[/b]

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