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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 [#permalink] New post 23 Aug 2006, 07:06
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)

Ans D had to plug in values to get the answer. Couldnt arrive at the answer algebraically within the 2 minute mark
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 [#permalink] New post 23 Aug 2006, 10:24
total volume = (p/100) of A + (1 - p/100) of B
total revenue = (p/100) * cost of 1 newspaperA + (1 - p/100) * cost of 1 newspaper b
= (p/100) + (1 - p/100)*1.25 --- (i)
%age of revenue contributed by newspaper A = r%
actual revenue of A = p/100 (from i above)
hence,
(r/100)*total revenue = p/100
solve for r in terms of p
ans. 400p/(500-p).
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 [#permalink] New post 23 Aug 2006, 10:56
Value of each Newspaper A is $1

So, total Revenue(A) = Number of NewsPapers(A)

Say total Revenue is R and Total number of News Papers is N

So since price of one Newspaper A is 1,

rR/100 = pN/100

i.e. r = pN/R

R =pN/100 x 1 + [1-p/100] x 1.25N
= (1.25-0.25p/100)N

Thus, r = 100p/(1.25-0.25p)

Simplify it and we get 400p/(500-p)
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 [#permalink] New post 23 Aug 2006, 11:00
Thanks guys appreciate it
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 [#permalink] New post 23 Aug 2006, 13:17
I got the same question on GMAT yesterday. I did get it correct though.
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 [#permalink] New post 23 Aug 2006, 20:54
gmatcrook: just a small correction:

r = 100p/125-.25p = 400p/500-p
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 [#permalink] New post 24 Aug 2006, 05:29
apollo168 wrote:
Thanks guys appreciate it


After this...

Ruby wrote:
I got the same question on GMAT yesterday. I did get it correct though.


I guess where did you get this question from ?
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 [#permalink] New post 24 Aug 2006, 05:57
prashrash wrote:
total volume = (p/100) of A + (1 - p/100) of B
total revenue = (p/100) * cost of 1 newspaperA + (1 - p/100) * cost of 1 newspaper b
= (p/100) + (1 - p/100)*1.25 --- (i)
%age of revenue contributed by newspaper A = r%
actual revenue of A = p/100 (from i above)
hence,
(r/100)*total revenue = p/100
solve for r in terms of p
ans. 400p/(500-p).


I tried to plug in values....

But D does not come up properly....what can be used,,
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 [#permalink] New post 24 Aug 2006, 07:59
Hi what I did was to i used 100 as the total revenue
And I wanted A to comprise 40% of the value or 40
so to get B--> (5/4)B=60 B=48 newspapers which means A=40 newspapers p=40/88--> 45.4 percent and r=40%
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Re: Problem solving newspaper [#permalink] New post 26 Aug 2006, 10:45
apollo168 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)

Ans D had to plug in values to get the answer. Couldnt arrive at the answer algebraically within the 2 minute mark


This is fairly straightforward:

total revenue = a(1.00) + b(1.25)

where a and b are the number of newspapers of type A and B that were sold

now r% = a/(a+1.25b)
simplifying:

b = a/1.25 *(100 - r)/r --- (eq 1)

Additionally we have:

p% = a/(a+b)

Simplying and collecting terms of b:

b = a/p (100 - p ) --- (eq 2)

from 1 and 2,

1/p (100-p) = 0.8(100-r)/r

Simplify and collect terms of p on right side:


1000r - 10rp = 800p - 8rp

r(1000-2p) = 800p

therefore: r = 400p/(500-p) Ans: D
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 [#permalink] New post 26 Aug 2006, 13:53
let total papers =100

No. of papers of type A sold = p
No. of papers of type A sold = 100-p

No. of papers of type B sold = p.1
No. of papers of type B sold = (100-p).(1.25)

Percentage of sales from A

r = p.1/[p.1 + (100-p).(1.25)]
=400p/(500-p)
  [#permalink] 26 Aug 2006, 13:53
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