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Tough Word Problem

by ngbrian85 » Mon Apr 02, 2012 6:17 pm
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 revenue 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

This question took me <5 minutes. Shorter method anyone ? There must be an intuitive way to approach this.
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by Anurag@Gurome » Mon Apr 02, 2012 6:56 pm
ngbrian85 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 revenue 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

This question took me <5 minutes. Shorter method anyone ? There must be an intuitive way to approach this.
We can assume that the total number of newspapers sold by the store = 100
So, no. of newspaper A sold = p% of 100 = p
No. of newspaper B sold = 100 - p

It is given that r% of total revenue from papers comes from selling newspaper A.
Revenue from A = p * 1 and revenue from B = (100 - p) * 1.25
So, total revenue from papers = p * 1 + (100 - p) * 1.25 = 125 - 0.25p

Now percentage of total revenue coming from A = (Revenue from A /Total revenue) * 100 = p/(125 - 0.25p) * 100
But it's given that p/(125 - 0.25p) * 100 = r
Now all the answer options have p in the denominator, so we'll have to remove 0.25 from the denominator. Multiplying by 400 removes 0.25
Hence, r = [spoiler]400p/(500 - p)[/spoiler]

The correct answer is D.
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by GMATGuruNY » Mon Apr 02, 2012 9:59 pm
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