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Last Sunday a certain store sold copies of Newspaper A for $

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Last Sunday a certain store sold copies of Newspaper A for $

by gmatter2012 » Sat Jun 23, 2012 8:46 am
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

A. 100p / (125 - p)
B. 150p / (250 - p)
C. 300p / (375 - p)
D. 400p / (500 - p)
E. 500p / (625 - p)

Answer Reveal : D

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by GMATGuruNY » Sat Jun 23, 2012 12:48 pm
gmatter2012 wrote:Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

A. 100p / (125 - p)
B. 150p / (250 - p)
C. 300p / (375 - p)
D. 400p / (500 - p)
E. 500p / (625 - p)

Answer Reveal : D

This one really got me frustrated, I seek relief here !![spoiler][/spoiler]
Plug in values that make the math easy.

Let the number of copies of B sold = 4, so that the revenue from B = 4(1.25) = 5.
Let the number of copies of A sold = 4, so that the revenue from A = 4*1 = 4.
Since (copies of A)/(total copies) = 4/8 = 1/2, p = (1/2)100 = 50.
Since (revenue from A)/(total revenue) = 4/9, r = (4/9)100 = 400/9. This is our target.

Now we plug p=50 into the answers to see which yields our target of 400/9.

Answer choice D looks like a good bet, since it includes 400:
(400*50)/(500-50) = (400*50)/450 = 400/9.

The correct answer is D.
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by gmatter2012 » Sun Jun 24, 2012 2:08 am
That was an awesome solution !!

Thank you
Wonder why Anurag or Brent did not contribute to this one.
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by Anurag@Gurome » Sun Jun 24, 2012 5:50 am
gmatter2012 wrote:Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
Let us assume that the store sold a total of 100 newspapers.
Hence, the store has sold p copies of A and (100 - p) of B.

Hence, total revenue = p*1 + (100 - p)*1.25 = (125 - 0.25p) = (500 - p)/4
Hence, percentage revenue from A, q = 100*(p/((500 - p)/4)) = 400p/(500 - p)

The correct answer is D.
Last edited by Anurag@Gurome on Mon Jun 25, 2012 6:14 am, edited 1 time in total.
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by gmatter2012 » Mon Jun 25, 2012 6:11 am
That was an awesome solution too! Anurag , made it look very easy. Very enlightening. Just a small typo
Please do edit to prevent confusion

"Hence, total revenue = p*1 + (100 - p)*1.25 = (125 - 0.25p) =
(500 - 25p)/4
Hence, percentage revenue from A, q = 100*(p/((500 - 0.25p)/4)) = 400p/(500 - p)

The 25p and .25p should only be p. Solution is very nice , Thank you
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by Anurag@Gurome » Mon Jun 25, 2012 6:28 am
Thanks for pointing it out.
Edited the reply.
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