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A company sells pens and pencils. The Revenue from pens in 2007 was u

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A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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A company sells pens and pencils. The Revenue from pens in 2007 was up 5% from 2006. The revenue from pencils declined 13% over the same period. Overall revenue was down 1% from 06 to 07. What was the ratio of pencil revenue to pen revenue in 2006.
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 23 Jun 2010, 18:17
Let us assume the following letters for respective revenues:

Pen (2006) - A1
Pencil (2006) - B1
Pen (2007) - A2
Pencil (2007) - B2

Now from the given information, we can translate the words into equations as follows:

A2 = \(\frac{105}{100}\) A1 - Equation 1

and

B2 = \(\frac{87}{100}\) B1 - Equation 2

Also, we know that

A2 + B2 = \(\frac{99}{100}\) (A1 + B1) - Equation 3

Now adding equations 1 and 2 together, we get

A2 + B2 = \(\frac{105}{100}\) A1 + \(\frac{87}{100}\) B1 - Equation 4

Equation 3 = Equation 4

So we get,

\(\frac{105}{100}\) A1 + \(\frac{87}{100}\) B1 = \(\frac{99}{100}\) (A1 + B1) = \(\frac{99}{100}\) (A1) + \(\frac{99}{100}\) (B1)

Now, separating the terms we get:

\(\frac{105}{100}\) A1 + \(\frac{87}{100}\) B1 = \(\frac{99}{100}\) (A1) + \(\frac{99}{100}\) (B1)

Rearranging terms and canceling the denominator 100 on both sides, we get

(99-87) B1 = (105-99) A1

So \(\frac{B1}{A1}\) = \(\frac{105-99}{99-87}\) = \(\frac{6}{12}\) = \(\frac{1}{2}\)

Is this answer right?
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 23 Jun 2010, 18:21
What logic did you use to add equation 1 to equation 2
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 23 Jun 2010, 18:23
Because the second part of the question states a relation between the overall income in 2006 and 2007. Using the variables I've assumed, that's a relation between A1+B1 and A2+B2. So in order to get anything meaningful out of this equation, we'll need another equation with A1+B1 or A2+B2 and hence I decided to add them together in order to get all the terms in the equation in terms of A1 or B1 and hence get the ratio by getting all the similar terms to one side.

Is the answer correct?
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 24 Jun 2010, 02:57
Do these kind of questions appear on the real test? I mean it seems to me like a relatively difficult question to solve if you have 2 minutes.
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 24 Jun 2010, 04:58
I've seen a lot of mixture problems being posted on the forum, and on the few practice tests I've taken, it's been asked. So I am not sure. Maybe someone who's taken the GMAT can answer better.
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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Jinglander wrote:
Can I get someone to walk me through this one too.

A company sells pens and pencils. The Revenue from pens in 2007 was up 5% from 2006. The revenue from pencils declined 13% over the same period. Overall revenue was down 1% from 06 to 07. What was the ratio of pencil revenue to pen revenue in 2006.

Please show your work.


It would be easier if you make a table:
Attachment:
untitled.JPG
untitled.JPG [ 11.88 KiB | Viewed 3505 times ]
We are told that "Overall revenue was down 1% from 06 to 07" --> \(0.99(x+y)=1.05x+0.87y\). Question: \(\frac{y}{x}=?\)

\(0.99(x+y)=1.05x+0.87y\) --> \(0.99x+0.99y=1.05x+0.87y\) --> \(12y=6x\) --> \(\frac{y}{x}=\frac{6}{12}=\frac{1}{2}\).

Hope it's clear.
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 24 Jun 2010, 05:12
This one isn't too bad. Say: pen = n and pencil = p and revenue = r.

p+n = r
1.05p+.87n=.99r
now just add plug in for r.
.06n=.12p
p/n = 1/2

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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 24 Jun 2010, 06:48
First, I think its more of a ratio problem than the mixture.

Secondly, I simply cant understand why we are so reluctant to give kudos. Bunuel! Excellent solution. +1 for you. The very last equation contains a little typo though!
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 28 Jun 2010, 06:36
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Jinglander wrote:
Can I get someone to walk me through this one too.

A company sells pens and pencils. The Revenue from pens in 2007 was up 5% from 2006. The revenue from pencils declined 13% over the same period. Overall revenue was down 1% from 06 to 07. What was the ratio of pencil revenue to pen revenue in 2006.

Please show your work.


Let the revenue of pens be 'x'
Let the revenue of pencils be 'y'

the revenue of pens up from 2006 by 5%=>105%
the revenue of pencils down from 2006 by 13%=>87%

Overall revenue down by 1%=>99%

Attachment:
pic2.JPG
pic2.JPG [ 3.08 KiB | Viewed 3409 times ]


hence the ratio of pencils to pens = 6/12 = 1/2
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 26 Jul 2010, 15:40
achiever01 I dont understand your solution at all
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u [#permalink]

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New post 05 Mar 2017, 09:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u   [#permalink] 05 Mar 2017, 09:38
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