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

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?

What logic did you use to add equation 1 to equation 2

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?

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.

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.

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

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!

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

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.

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.

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