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Manager  Joined: 24 May 2010
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A company sells pens and pencils. The Revenue from pens in 2007 was u  [#permalink]

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Question Stats: 69% (02:12) correct 31% (02:02) wrong based on 56 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
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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.

It would be easier if you make a table:
Attachment: untitled.JPG [ 11.88 KiB | Viewed 5457 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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Manager  Joined: 15 Mar 2010
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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.

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 [ 3.08 KiB | Viewed 5352 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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1
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

Posted from my mobile device
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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:
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.

Responding to a pm:

Yes, we can use weighted averages here since there are two components and we have the total.

w1/w2 = (A2 - Aavg)/(Aavg - A1)

Say, w1 is the weight of pencil revenue and w2 is the weight of pen revenue in 2006 (increase in revenue is over previous revenue so the ratio we get will be of the revenues of 2006)

w1/w2 = (5 - (-1)) / (-1 - (-13)) = 6/12 = 1/2

Revenue of pencils : Revenue of pens = 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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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?
Manager  Joined: 24 May 2010
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u  [#permalink]

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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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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?
Director  Joined: 23 Apr 2010
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u  [#permalink]

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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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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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GMAT 1: 680 Q48 V34 Re: A company sells pens and pencils. The Revenue from pens in 2007 was u  [#permalink]

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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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achiever01 I dont understand your solution at all
Intern  B
Joined: 28 Oct 2017
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Re: A company sells pens and pencils. The Revenue from pens in 2007 was u  [#permalink]

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This question can also be solved using mixture/alligation technique.

Pen revenue = +5% (increase)
Pencil revenue = -13% (decrease)
Overall = -1% (decrease)
Pen Pencil
+5% -13%

-1%

[-1-(-13)]=12 [5-(-1)]=6

Ratio = Pencil:Pen
6:12=1:2

Thanks.
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Joined: 22 Sep 2018
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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:
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.

forgot about percentage and change into numericals.

in 2006 the price of pen and pencil both are 100. so the total average of revenue is 100 too.

in 2007 the price of pen is 105 and pencil is 87. As it was mentioned in question average slipped by 1 point so 99.

6 12
105-------99--------------87

the ratio will be 12:6 of pen to pencil ratio. i.e., 2:1

but, it was asked for pencil to pen so it is 1:2...

this is one of the best method you can try for all mixture problems. Re: A company sells pens and pencils. The Revenue from pens in 2007 was u   [#permalink] 02 Oct 2018, 00:18
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