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by sana.noor » Fri Oct 04, 2013 7:29 am
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.

OA is D
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Oct 04, 2013 7:48 am
sana.noor 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.

OA is D
Target question: What was the value of y?

Statement 1: The revenue for the website that year was $36,000.
First round of "investors": y people paying $30 each = 30y dollars
Second round of "investors": y² people paying $15 each = 15y² dollars
Total revenue = 15y² + 30y
So, 15y² + 30y = 36,000
Set equal to zero: 15y² + 30y - 36,000 = 0

IMPORTANT: This is a quadratic equation, and quadratic equations typically have 2 solutions. IF there are two valid solutions to this equation, then statement 1 is not sufficient.
Divide both side by 15 to get: y² + 2y - 2400 = 0
At this point, we should recognize that we IF we were to factor the left-side, we'd get (y + something)(y - something) = 0, which means one possible value for y is positive, and one possible value for y is negative.
Since the number of friends MUST be positive, we can be certain that the equation has ONLY ONE valid solution.
This means that IF WE WERE to solve the equation, we'd be able to target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: The first y friends accounted for 1/25 of the total revenue for the website that year
In other words, (1st round of investments) = (1/25)(total investments)
30y = (1/25)(15y² + 30y)
Multiply both sides by 25 to get: 750y = 15y² + 30y
Rearrange: 15y² - 720y = 0
Factor: 15y(y - something) = 0
At this point, we can be certain that there is only 1 valid solution for y (since y = 0 is an invalid solution).
So, IF WE WERE to solve the equation, we'd be able to target question with certainty.
Statement 2 is SUFFICIENT

Answer = D

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by GMATGuruNY » Fri Oct 04, 2013 10:26 am
sana.noor 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.

OA is D
Number of friends convinced by John = y.
If y=2, and each of these 2 friends convinces 2 OTHER people, then the total number of ADDITIONAL people convinced = 2*2 = 2² = y².
If y=3, and each of these 3 friends convinces 3 OTHER people, then the total number of ADDITIONAL people convinced = 3*3 = 3² = y².
Thus, the total number of ADDITIONAL people convinced by the y friends = y².

Since the y friends each pay $30, the total paid by the y friends = 30y.
Since the y² additional people each pay $15, the total paid by the y² additional people = 15y².

Statement 2: The first y friends accounted for 1/25 of the total revenue for the website that year.
Thus, of every $25 donated, $1 was paid by the y friends, while $24 was paid by the y² additional people.
Thus:
30y / 15y² = 1/24
2/y = 1/24
y=48.
SUFFICIENT.

Statement 1: The revenue for the website that year was $36,000..
Since y=48 in statement 1, let's see whether this value also satisfies statement 2.
If 48 friends pay $30 each, and 48² friends pay $15 each, we get:
Total revenue = (48*30) + (48*48*15) = (48*15)(2 + 48) = 720 * 50 = 36,000.
This works!
If the value of y changes, so will the total amount of revenue.
Thus -- like statement 2 -- statement 1 indicates that y=48.
SUFFICIENT.

The correct answer is D.
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