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the newspapers that the store sold

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the newspapers that the store sold

by sanju09 » Mon Mar 12, 2012 2:57 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)
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by killer1387 » Mon Mar 12, 2012 3:17 am
IMO D
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by GMATGuruNY » Mon Mar 12, 2012 4:08 am
sanju09 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)

Let:
The number of copies of A sold = 1.
The number of copies of B sold = 4.

Total copies sold = 1+4 = 5.
Since A = 1/5 of the copies sold, p = 1/5*100 = 20.

Revenue from 1 copy of A = $1.
Revenue from 4 copies of B = 4*1.25 = $5.
Total revenue = 1+5 = 6.
Since A = 1/6 of the total revenue, r = 1/6*100 = 50/3. This is our target.

Now we plug p=20 into all the answers to see which yields our target of 50/3.

Only answer choice D works:
(400*20)/(500-20) = 8000/480 = 50/3.

The correct answer is D.
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