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Register now and save up to $200 Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code ## OG12 #70 - value of n? Why isnt n =0 ?? tagged by: Brent@GMATPrepNow This topic has 2 expert replies and 3 member replies rohit_gmat Master | Next Rank: 500 Posts Joined 16 Jun 2010 Posted: 158 messages Followed by: 1 members Upvotes: 13 #### OG12 #70 - value of n? Why isnt n =0 ?? 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]

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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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 = nÂ²
This gives us a total of 500(nÂ²) dollars in this round

TOTAL DONATIONS = 500n dollars + 500(nÂ²) dollars
We can rewrite this: 500nÂ² + 500n dollars

So, statement 2 tells us that 500nÂ² + 500n = 120,000
This is a quadratic equation, so let's set it equal to zero to get: 500nÂ² + 500n - 120,000 = 0
Factor out the 500 to get: 500(nÂ² + 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 = 500nÂ² + 500n
So, we can write: 500n = (1/16)[500nÂ² + 500n]
Multiply both sides by 16 to get: 8000n = 500nÂ² + 500n
Set this quadratic equation equal to zero to get: 500nÂ² - 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

Cheers,
Brent

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### GMAT/MBA Expert

Testluv GMAT Instructor
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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
...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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selango Legendary Member
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Sun Oct 10, 2010 8:02 am
rohit bro,

You mentioned that in stmt2 that n=-16 is not possible..then how come n=0 also possible?It means there are 0 number of friends (or) no friends at all(or) in this case no question at all unless the total amount is zero.
Here n represents number of friends.So we need to assume that n>0.

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

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rohit_gmat Master | Next Rank: 500 Posts
Joined
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Sun Oct 10, 2010 7:39 pm
Hi Selango,

Im genuinely in doubt man!... I assumed n not equal to -16 since negative 16 is not a possible number of friends (or people)... but zero is... isnt it? ... Mary was probably a loser and had no friends who gave no money...??

Actually, after posting this I saw a post from another guy with a similar issue... and a GMAT guru advised that in the GMAT for real life problems, the trick is never "assuming 0".... theres another question in the OG abt 2 cities' populations and their leaders or smth like tht... and if one assumes that population is zero then the question goes crazy...

thanks for ur support anyway

Viktri Junior | Next Rank: 30 Posts
Joined
12 Aug 2010
Posted:
12 messages
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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