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# Paula and Sandy were among those people who sold raffle

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Manager
Joined: 02 Dec 2012
Posts: 178
Paula and Sandy were among those people who sold raffle [#permalink]

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06 Dec 2012, 07:06
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Difficulty:

35% (medium)

Question Stats:

68% (00:54) correct 32% (00:52) wrong based on 793 sessions

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Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 of the tickets, how many of
the tickets did Paula sell?

(1) Sandy sold 2/3 as many of the raffle tickets as Paula did.
(2) Sandy sold 8 percent of all the raffle tickets sold for Club X.
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Joined: 02 Sep 2009
Posts: 46128
Re: Paula and Sandy were among those people who sold raffle [#permalink]

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06 Dec 2012, 07:10
2
Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 of the tickets, how many of the tickets did Paula sell?

Given that $$p+s=100$$, where $$p$$ and $$s$$ are the number of tickets sold by Paula and Sandy, respectively.

(1) Sandy sold 2/3 as many of the raffle tickets as Paula did --> $$s=\frac{2}{3}p$$. We have two distinct linear equations with two unknowns ($$p+s=100$$ and $$s=\frac{2}{3}p$$), thus we can solve for both of them. Sufficient.

(2) Sandy sold 8 percent of all the raffle tickets sold for Club X --> we don't know the total number of the raffle tickets sold, thus we cannot find $$s$$, which means that we cannot find $$p$$. Not sufficient.

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Re: Paula and Sandy were among those people who sold raffle [#permalink]

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17 May 2014, 08:33
1
Bunuel wrote:
Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 of the tickets, how many of the tickets did Paula sell?

Given that $$p+s=100$$, where $$p$$ and $$s$$ are the number of tickets sold by Paula and Sandy, respectively.

(1) Sandy sold 2/3 as many of the raffle tickets as Paula did --> $$s=\frac{2}{3}p$$. We have two distinct linear equations with two unknowns ($$p+s=100$$ and $$s=\frac{2}{3}p$$), thus we can solve for both of them. Sufficient.

(2) Sandy sold 8 percent of all the raffle tickets sold for Club X --> we don't know the total number of the raffle tickets sold, thus we cannot find $$s$$, which means that we cannot find $$p$$. Not sufficient.

I believe the key premise for statement 2 is that there could be others as well who sold tickets for Club X. Right ?
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Joined: 02 Sep 2009
Posts: 46128
Re: Paula and Sandy were among those people who sold raffle [#permalink]

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17 May 2014, 08:45
himanshujovi wrote:
Bunuel wrote:
Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 of the tickets, how many of the tickets did Paula sell?

Given that $$p+s=100$$, where $$p$$ and $$s$$ are the number of tickets sold by Paula and Sandy, respectively.

(1) Sandy sold 2/3 as many of the raffle tickets as Paula did --> $$s=\frac{2}{3}p$$. We have two distinct linear equations with two unknowns ($$p+s=100$$ and $$s=\frac{2}{3}p$$), thus we can solve for both of them. Sufficient.

(2) Sandy sold 8 percent of all the raffle tickets sold for Club X --> we don't know the total number of the raffle tickets sold, thus we cannot find $$s$$, which means that we cannot find $$p$$. Not sufficient.

I believe the key premise for statement 2 is that there could be others as well who sold tickets for Club X. Right ?

Yes, we are directly told that there in fact ARE some other people selling tickets: "Paula and Sandy were among those people who sold tickets".
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Re: Paula and Sandy were among those people who sold raffle [#permalink]

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17 Sep 2017, 08:45
Top Contributor
Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 of the tickets, how many of
the tickets did Paula sell?

(1) Sandy sold 2/3 as many of the raffle tickets as Paula did.
(2) Sandy sold 8 percent of all the raffle tickets sold for Club X.

Target question: How many of the tickets did Paula sell?

Given: Paula and Sandy sold a total of 100 of the tickets
Let x = number of tickets that Paula sold
This means 100-x = number of tickets that Sandy sold

Statement 1: Sandy sold 2/3 as many of the raffle tickets as Paula did.
We can write: (# of tickets Sandy sold) = (2/3)(# of tickets Paula sold)
Or... 100-x = (2/3)x
Eliminate the fractions by multiplying both sides by 3 to get: 300 - 3x = 2x

ASIDE: At this point, we should recognize that we CAN solve this equation for x, which means we CAN answer the target question with certainty. But for "fun" let's finish the math...

Add 3x to both sides to get: 300 = 5x
Solve: x = 60
In other words, Paula sold 60 tickets
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Sandy sold 8 percent of all the raffle tickets sold for Club X.
We don't know how many tickets were sold for Club X. All we know is that Paula and Sandy sold a total of 100 tickets.
Since we don't know how many tickets were sold for Club X, we can't determine the number of tickets Sandy sold.
If we can't determine the number of tickets Sandy sold, then we can't determine the number of tickets Paula sold.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Re: Paula and Sandy were among those people who sold raffle [#permalink]

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18 Sep 2017, 11:13
By Using statement 1 we can make a equation

2/3 * p+p=100 (Where "P" is the number of tickets sold by Paula)

Solving the equation we can get p=60

In statement 2 we do not know total number of tickets sold for club X

Re: Paula and Sandy were among those people who sold raffle   [#permalink] 18 Sep 2017, 11:13
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