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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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26 Sep 2016, 10:06
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65% (hard)

Question Stats:

55% (01:32) correct 45% (01:38) wrong based on 53 sessions

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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. _________________ The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources. My posts http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924 http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html http://gmatclub.com/forum/possessive-pronouns-200496.html http://gmatclub.com/forum/double-negatives-206717.html http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773 https://gmatclub.com/forum/improve-reading-habit-233410.html#p1802265 ##### Most Helpful Community Reply Senior Manager Joined: 23 Apr 2015 Posts: 322 Location: United States Concentration: General Management, International Business WE: Engineering (Consulting) In the first year of a pyramid scheme, John convinced y of his friend [#permalink] ### Show Tags 26 Sep 2016, 10:24 5 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.

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Joined: 18 Sep 2016
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In the first year of a pyramid scheme, John convinced y of his friend [#permalink]

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26 Sep 2016, 13:06
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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

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

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26 Sep 2016, 13:26
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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06 Apr 2018, 11:18
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the first year of a pyramid scheme, John convinced y of his friend   [#permalink] 06 Apr 2018, 11:18
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