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

Question

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.

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

Senthil1981 · Accepted Answer

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

damybox · Answer

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

Joc456 · Answer

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

fskilnik · Answer

{\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.

Rishitkaul · Answer

How did we get the equation 30y + 15y^2 .can anyone please explain¿

Bunuel · Answer

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 total revenue comes from two parts.

First, y friends each pay 30, so that part is 30y.
 
Second, those y friends each bring in y more people, making y^2 people, and each of them pays 15, so that part is 15y^2.
 
Adding them gives 30y + 15y^2.

For example, if y = 10, that means John convinces 10 friends in the first stage. Each of those friends pays 30, so the first stage revenue is 30 * 10.

Then, in the second stage, each of those 10 friends brings in 10 new people, so the total number of new people is 10 * 10 = 10^2. Each of those 10^2 people pays 15, so the second stage revenue is 15 * 10^2.

Adding them gives 30 * 10 + 15 * 10^2.

Hope it's clear.

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

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