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

[rohit_gmat]

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]

[selango]

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 :mrgreen:

[rohit_gmat]

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]

Data given:

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

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

ii) 1500n = 120,000
solvable

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]

[Testluv]

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 :mrgreen:

...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).

[Brent@GMATPrepNow]

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

[Scott@TargetTestPrep]

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.

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. Since each of the first n people donated $500, we know:

500n = amount donated by the first n people

Since each of these n people also persuaded n more people, we know that an additional n × n = n^2 people donated. Since each of these n^2 people also donated $500, we know:

500n^2 = amount donated by the additional n^2 people

Thus,

500n + 500n^2 = total amount donated

We need to determine the value of n.

Statement One Alone:

The first n people donated 1/16 of the total amount donated.

From our given information we know that 500n + 500n^2 represents the total amount donated and that the first n people donated a total of 500n dollars. From statement one, we know that the first n people donated 1/16 of the total amount donated. Thus, we can create the following equation:

500n = 1/16(500n + 500n^2)

(500n)(16) = 500(n + n^2)

16n = n + n^2

n^2 - 15n = 0

n(n - 15) = 0

n = 0 or n = 15

We understand from the statement that after n friends donate, each of those n friends persuade additional n friends to donate as well. This statement would make no sense if n were zero; therefore, we can eliminate the case n = 0. Since n cannot be zero, n must be 15. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The total amount donated was $120,000.

Since we know the total amount donated is 500n + 500n^2, we can create the following equation:

500n + 500n^2 =120,000

500(n + n^2) =120,000

n + n^2 = 120,000/500

n + n^2 = 240

n^2 + n - 240 = 0

(n - 15)(n + 16) = 0

n = 15 or n = -16

Since n cannot be negative, n must be 15. Statement two alone is also sufficient to answer the question.

Answer: D

[fskilnik@GMATH]

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.

$${\rm{Total}}\,\, = \,\,500 \cdot n + 500 \cdot n \cdot n\,\,\,\,\,\,\left[ \$ \right]$$
$$? = n$$
$$\left( 1 \right)\,\,\,500 \cdot n = {1 \over {16}} \cdot 500 \cdot n \cdot \left( {1 + n} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\,\left( {500\,n} \right)\,\,\,\left[ {\,n\, \ne \,0\,} \right]} \,\,\,1 = {1 \over {16}} \cdot \left( {1 + n} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,n\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,\,500 \cdot n\left( {1 + n} \right) = 120000\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,500} \,\,\,\,n\left( {1 + n} \right) = 240\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,n\,\, > 0\,\,\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$
$$\left( * \right)\,\,15 \cdot 16 = 240\,\,\, \Rightarrow \,\,\,\left\{ \matrix{
\,n\left( {n + 1} \right) < 240\,\,{\rm{for}}\,\,0 < n < 15 \hfill \cr
\,n\left( {n + 1} \right) > 240\,\,{\rm{for}}\,\,n \ge 16 \hfill \cr} \right.\,\,\,\,\,\,\left( {{\rm{Now}}\,\,{\rm{rethink}}\,\,{\rm{without}}\,\,{\rm{knowing}}\,\,{\rm{that}}\,\,n = 15...} \right)$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.