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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 11 Mar 2008, 09:15
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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?

100p/(125-p)
150p/(250-p)
300p/(375-p)
400p/(500-p)
500p/(625-p)
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Re: gmatp ratios [#permalink] New post 11 Mar 2008, 10:18
D

Say m and n are the number are papers sold of A and B respectively

p=100m/(m+n) => n=m(100/p-1)

r=100m/(m+1.25n) substituting the value of n from above

you get r=4p/(500-p)
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Re: gmatp ratios [#permalink] New post 12 Mar 2008, 01:58
is there a mistake in the answer choices?

my final answer is 100p / (125 - 1.25p)
that equates to 400p / (500 - 5p)
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Re: gmatp ratios [#permalink] New post 12 Mar 2008, 07:37
bmwhype2 wrote:
is there a mistake in the answer choices?

my final answer is 100p / (125 - 1.25p)
that equates to 400p / (500 - 5p)


I double checked, and still getting r=400p/(500-p). That seems to be correct answer.

Can you elaborate the highlighted part?
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Re: gmatp ratios [#permalink] New post 12 Mar 2008, 09:45
sreehari wrote:
bmwhype2 wrote:
is there a mistake in the answer choices?

my final answer is 100p / (125 - 1.25p)
that equates to 400p / (500 - 5p)


I double checked, and still getting r=400p/(500-p). That seems to be correct answer.

Can you elaborate the highlighted part?

r = 100A / (A + 1.25B)


p = 100A / (A+B)
p(A+B) = 100A
pA + pB = 100A
pB = 100A – pA
B = (100A – pA) / p
B = A(100-p) / p → A * [(100-p)/p]

r = 100A / (A + 1.25B)
r = 100A / (A + 1.25 [A * [(100-p)/p]])
r = 100 / 1.25 ((100-p)/p)
r = 100 / (125 – 1.25p / p)
r = 400p/(500-5p)
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Re: gmatp ratios [#permalink] New post 12 Mar 2008, 10:05
marcodonzelli 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?

100p/(125-p)
150p/(250-p)
300p/(375-p)
400p/(500-p)
500p/(625-p)


This one was actually very tough for me. I first read it as r is for Newspaper A and p is for Newspaper B...

I was getting really frustrated as you can imagine.

Even when I reread this, it was still tough to come across the answer.

Il break it down:

x and y are the number of papers sold for A and B respectively.

100x/(x+y)=p and 100x/(x+1.25y)=r

lets rework p.

100x=px+py ---> 100x=p(x+y) ---> 100x/p=x+y ---> 100x/p-x=y

Plug in y in the second equation for r.

100x/(x+1.25(100x/p-x) multiply by p (make p the commen denominator)---> 100x/(xp/p+(125x-1.25xp)/p)

100x/((125x-.25xp)/p) take out the x---> 100x/x((125-.25p)/p) ---> 100p/(125-.25p) ---> 100p/(500/4-p/4)

100p/((500-p)/4) ---> 400p/(500-p)


D.

This was ridiculous!!!
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Re: gmatp ratios [#permalink] New post 12 Mar 2008, 12:15
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bmwhype2 wrote:
r = 100A / (A + 1.25 [A * [(100-p)/p]])
r = 100 / 1.25 ((100-p)/p)


The highlighted part should be

r = 100 / [1 + 1.25 ((100-p)/p)]
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Re: gmatp ratios [#permalink] New post 12 Mar 2008, 13:38
sreehari wrote:
bmwhype2 wrote:
r = 100A / (A + 1.25 [A * [(100-p)/p]])
r = 100 / 1.25 ((100-p)/p)


The highlighted part should be

r = 100 / [1 + 1.25 ((100-p)/p)]

thanks. this is why i shouldnt do math in the morning...
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Re: gmatp ratios [#permalink] New post 10 Oct 2008, 10:24
Anyone tried to solve this problem by substituting numbers?
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Re: gmatp ratios [#permalink] New post 10 Oct 2008, 18:41
marcodonzelli 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?

100p/(125-p)
150p/(250-p)
300p/(375-p)
400p/(500-p)
500p/(625-p)


Agree with above explanations.

Is this a GMATPrep question ??

@vksunder We cannot try plugging in numbers because the answer choices are in terms of P.
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Re: gmatp ratios   [#permalink] 10 Oct 2008, 18:41
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