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MGMAT percent change

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MGMAT percent change

by HPengineer » Tue Dec 28, 2010 12:41 pm
A company sells only pens and pencils. The revenue from pen sales in 2007 was up 5% from 2006, but the revenue from pencil sales declined 13% over that same period. If overall revenue was down 1% from 2006 to 2007, what was the ratio of Pencil revenue to pen revenue in 2006.

no answer choices provided by MGMAT..


I worked as follows but i may have made a mistake

2006 Pen Rev = X
2007 Pen Rev = 1.05x

2006 Pencil Rev = y
2007 Pencil rev = .87y

Then i set up following equation

.99(x+y) = 1.05x + .87y

does this seem correct?
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by Target2009 » Tue Dec 28, 2010 1:42 pm
Yes.

Ratio Must be 2:1.
Whats OA.
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by HPengineer » Tue Dec 28, 2010 2:15 pm
the offical answer is 1:2

I also came out to 2:1 are we wrong??
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by clock60 » Tue Dec 28, 2010 3:04 pm
not sure that i can spot mistakes, below my reasoning
x- are pens, and y- are pencils
in 2006: x+y=100%=1 (100%/100)
in 2007: 1,05+0,87y=99%=0.99

so we have two equations
x+y=1
1,05x+0,87y=0,99,
x=1-y
1,05(1-y)+0,87y=0,99
1.05-1.05y+0,87y=0,99
0,18y=0,06
y=1/3 and x=2/3
we need to find ratio of y/x (pencils/pens)=(1/3)/(2/3)=1/2
oa seems correct
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by Target2009 » Tue Dec 28, 2010 3:06 pm
I guess we all were correct.. We given Pen : pencil = 2 : 1 so Pencil revenue to pen revenue = 1:2
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by HPengineer » Tue Dec 28, 2010 3:18 pm
ha but if both 2-1 and 1-2 are listed as answer choice i would not be confident of my selection now :)
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by HPengineer » Tue Dec 28, 2010 3:25 pm
2006 Pen Rev = X
2007 Pen Rev = 1.05x

2006 Pencil Rev = y
2007 Pencil rev = .87y

Then i set up following equation

.99(x+y) = 1.05x + .87y



.99x +.99y = 1.05x +.87y


.12y = .6x

ok i found my mistake

should be .12y = .06x solve for X it becomes 2 so

y/2 or 1 to 2
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by Geva@EconomistGMAT » Wed Dec 29, 2010 1:17 am
An alternative solution method and a way to clear up the 2:1 or 1:2 ratio confusion:
What we have here is a weighted average between
x quantity of +5% and
y quantity if -13%.

If the quantities were equal, the average would be the exact midpoint of the range between +5% and -13%: the range of 18 % between the two ends is divided equally and the average is -4% (the point that is 9% away from both ends).

We can construct the following visual representation:

(y) -13 ----------------(-4)------------------+5 (x)

In effect, the real average is -1%, and not the midpoint -4, so clearly the quantities are not equal. This graphic representation is useful, because it exemplifies the following rule, which applies to all weighted averages:

1) The weighted average is closer to the larger group.

(y) -13 ----------------(-4)---- (-1)----------+5 (x)

since the average is closer to the x end than to the y end, x must be the greater group - x must be the 2 in the 1:2 ratio.

So even if you find the the ratio of 1:2 or 2:1 by other means such as equations, the fact that the average is closer to X than to Y is the rule to follow to see that X must be the greater group, no matter what your equations seem to say.
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by Geva@EconomistGMAT » Wed Dec 29, 2010 1:28 am
continued:
The graphic representation also allows you to find the actual ratio without equations, using the following rule:
2) The ratio of the group's weights is equal to the ratio of division of the range between the two ends.

we've already seen that a regular average divides the range between 5 and -13 equally: the 18 between the ends are split 9 and 9, or 1:1, so in this case the two quantities are the same.

In our question, the range of 18 is split at -1%, which is 6% away from the right side, but 12% away from the left side. Since the range split is 6:12, or 1:2, the group's weights x and y must follow the same ratio of 1:2, according to our rule above.

to sum up our visual representation of weighted average method:

(y) -13 ----------------(-4)---- (-1)----------+5 (x)

1) The range split determines the weight ratio, and vice versa: if the range is split at 6:12, the weight ratio is 1:2.
2) The group that is closer to the weighted average is the larger group. When debating whether y to x is 1:2 or 2:1, look which is closer to the average: x is closer, so x must be the 2.

Try it out:
x liters of 5% proof beer is mixed with y liters of 65% vodka. If the final beverage is 20% proof, what is the ratio of x:y?

A) 1:3
B) 1:2
C) 1:1
D) 2:1
E) 3:1
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by anuptvm » Wed Dec 29, 2010 5:03 am
Geva@MasterGMAT wrote:
If the quantities were equal, the average would be the exact midpoint of the range between +5% and -13%: the range of 18 % between the two ends is divided equally and the average is -4% (the point that is 9% away from both ends).

We can construct the following visual representation:

(y) -13 ----------------(-4)------------------+5 (x)

In effect, the real average is -1%, and not the midpoint -4, so clearly the quantities are not equal. This graphic representation is useful, because it exemplifies the following rule, which applies to all weighted averages:
Geva,

I liked the approach, but something that still isn't clear to me is how did we calculate that the weighted average is 1%. We are not given the values of X or Y.
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by HPengineer » Wed Dec 29, 2010 8:00 pm
Geva,

Lets see if i got ur method correct is the answer to the booze question A?
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by Geva@EconomistGMAT » Wed Dec 29, 2010 11:27 pm
anuptvm wrote:
Geva@MasterGMAT wrote:
If the quantities were equal, the average would be the exact midpoint of the range between +5% and -13%: the range of 18 % between the two ends is divided equally and the average is -4% (the point that is 9% away from both ends).

We can construct the following visual representation:

(y) -13 ----------------(-4)------------------+5 (x)

In effect, the real average is -1%, and not the midpoint -4, so clearly the quantities are not equal. This graphic representation is useful, because it exemplifies the following rule, which applies to all weighted averages:
Geva,

I liked the approach, but something that still isn't clear to me is how did we calculate that the weighted average is 1%. We are not given the values of X or Y.
The -1% result is given in the question itself: "If overall revenue was down 1% from 2006 to 2007"
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by Geva@EconomistGMAT » Wed Dec 29, 2010 11:32 pm
HPengineer wrote:Geva,

Lets see if i got ur method correct is the answer to the booze question A?
You got the ratios right, but the direction wrong. The midpoint of 5% and 60% is 27.5%; 20% is thus closer to 5% than to 60%, so X must be the greater group.
Remember: whichever of the groups the weighted average is closer to, that is the bigger group. Think of it as a tug-of-war between X and Y: X is the bigger group, so they pull the average towards them.
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by HPengineer » Wed Dec 29, 2010 11:44 pm
Your original problem stated 65% vodka would that not make the mid point 30?


X 5..................(20)..........30...............................65Y

So if i got this correct above which im sure i dont :)

5 is 15 units from the average of 20 and y is 45 units away which to me says X = 1 Y = 3... YOur saying that hsould be reversed due to X carying more weight?
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by Geva@EconomistGMAT » Wed Dec 29, 2010 11:48 pm
HPengineer wrote:Your original problem stated 65% vodka would that not make the mid point 30?


X 5..................(20)..........30...............................65Y

So if i got this correct above which im sure i dont :)

5 is 15 units from the average of 20 and y is 45 units away which to me says X = 1 Y = 3... YOur saying that hsould be reversed due to X carying more weight?
The above makes x closer to the average. The weighted average must be closer to the greater group, so X is the greter one: x is the 3, and y is the 1. Fix this in your mind to avoid further confusion with this sort of questions.

An you're right - the midpoint is 30, not 27.5.
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