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In the first year of a pyramid scheme, John convinced y of his friend

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In the first year of a pyramid scheme, John convinced y of his friend  [#permalink]

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New post 26 Sep 2016, 09:06
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Question Stats:

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In the first year of a pyramid scheme, John convinced y of his friends to pay 30 dollars each to join a particular website that he created. Each of those y friends then convinced another y people to pay 15 dollars each to join the same website. If no one else joined the website that year and each person joined only once, what was the value of y?

A. The revenue for the website that year was $36,000.
B. The first y friends accounted for 1/25 of the total revenue for the website that year.
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In the first year of a pyramid scheme, John convinced y of his friend  [#permalink]

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New post 26 Sep 2016, 09:24
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Nevernevergiveup wrote:
In the first year of a pyramid scheme, John convinced y of his friends to pay 30 dollars each to join a particular website that he created. Each of those y friends then convinced another y people to pay 15 dollars each to join the same website. If no one else joined the website that year and each person joined only once, what was the value of y?

A. The revenue for the website that year was $36,000.
B. The first y friends accounted for 1/25 of the total revenue for the website that year.



Writing the question in the equation form : \(30y + 15 y^2\) is the total money collected.

A) gives the total revenue : \(30y + 15 y^2 = 36,000\) and it's a quadratic equation with one positive and negative value(-50 and 48 here). Hence sufficient. Select A or D.
B) \(30 y = \frac{1}{25} (30y + 15 y^2)\) and this gives y = 48,. Hence sufficient.

Answer is D
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In the first year of a pyramid scheme, John convinced y of his friend  [#permalink]

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New post 26 Sep 2016, 12:06
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Nevernevergiveup wrote:
In the first year of a pyramid scheme, John convinced y of his friends to pay 30 dollars each to join a particular website that he created. Each of those y friends then convinced another y people to pay 15 dollars each to join the same website. If no one else joined the website that year and each person joined only once, what was the value of y?

A. The revenue for the website that year was $36,000.
B. The first y friends accounted for 1/25 of the total revenue for the website that year.



the question say \(30y+15y*y= k\)
written in a more tidy form===> \(15y^2+30y-k=0\)


1) says that k=36000, so the equation become \(15y^2+30y-36000=0\)
\(30^2+4*15*36000\) is positive so the equation has solutions (one positive and one negative)
1) is sufficient

2) says that \(30y=\frac{1}{25}(15y^2+ 30y)\)
with few aritmethics you can find an equation in the form \(ay^2+by=0\) with two solutions, one =0 and one positive.
so also 2) is sufficient



therefore answer D
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Re: In the first year of a pyramid scheme, John convinced y of his friend  [#permalink]

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New post 26 Sep 2016, 12:26
1
The total revenue can be represented by the equation 30y+15y². 15 is multiplied by y² because those "y" people each told another "y" people.

1. suff.
30y+15y²=36000
simplify and get
y²+2y-2400=0

2. suff

30y/30y+15y²=1/25

cross multiply and get y=48
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Re: In the first year of a pyramid scheme, John convinced y of his friend  [#permalink]

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New post 21 Nov 2018, 12:37
Nevernevergiveup wrote:
In the first year of a pyramid scheme, John convinced y of his friends to pay 30 dollars each to join a particular website that he created. Each of those y friends then convinced another y people to pay 15 dollars each to join the same website. If no one else joined the website that year and each person joined only once, what was the value of y?

A. The revenue for the website that year was $36,000.
B. The first y friends accounted for 1/25 of the total revenue for the website that year.

\({\rm{Total}}\,\,\,{\rm{ = }}\,\,\,30y + 15{y^2}\,\,\,\,\,\left( \$ \right)\)

\(? = y\,\,\,\,\,\left( {y \ge 1\,\,{\mathop{\rm int}} } \right)\)


\(\left( 1 \right)\,\,\,\,15{y^2} + 30y - 36000 = 0\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{roots}}} \,\,\,\,\,{y_1} \cdot {y_2} = - {{36000} \over {15}} < 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,y\,\,\left( {{\rm{root}}} \right)\,\,\, > 0\,\,\,\,{\rm{unique}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{\rm{SUFF}}.\,\)


\(\left( 2 \right)\,\,\,25 \cdot 30y\,\, = \,\,30y + 15{y^2}\,\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,15} \,\,\;\,\,\,25 \cdot 2y = {y^2} + 2y\,\,\,\,\,\, \Rightarrow \,\,\,y\left( {y - 48} \right) = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,y\,\,\left( {{\rm{root}}} \right)\,\,\, > 0\,\,\,\,{\rm{unique}}\,\,\,\,\left( { = 48} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\)


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

Regards,
Fabio.
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Re: In the first year of a pyramid scheme, John convinced y of his friend &nbs [#permalink] 21 Nov 2018, 12:37
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