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Item X and Y

by GmatKiss » Thu May 17, 2012 11:56 am
The total cost of producing item X is equal to the sum of item X's overhead cost and production cost. If the production cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in that same month?

(1) The overhead cost of producing item X increased by 13% in January.

(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.
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by neelgandham » Thu May 17, 2012 1:20 pm
Let X's overhead cost before January be O
Let X's production cost before January be P
Total cost of producing item X is equal to O+P

Let X's overhead cost after January be O'
and X's production cost after January be 0.95*P
Total cost of producing item X is equal to O'+0.95*P

Percent change in total cost = ((O+P)-(O'+0.95*P))/(O+P) = (O-O'+0.05P)/(O+P). The question can be rephrased to'If blah blah blah (in read), what is the value of (O-O'+0.05P)/(O+P)?'
(1) The overhead cost of producing item X increased by 13% in January.
O' = 1.13*O
Percent change in total cost = (O-O'+0.05P)/(O+P)
Percent change in total cost = (O-1.13*O+0.05P)/(O+P)
Percent change in total cost = (0.13*O+0.05P)/(O+P).
We don't know the value of O and P. So statement 1 is insufficient to answer the question.
(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.
O = 5P
Percent change in total cost = (O-O'+0.05P)/(O+P)
Percent change in total cost = (5P-O'+0.05P)/(5P+P)
Percent change in total cost = (-O'+5.05P)/(6P)
We don't know the value of O' and P. So statement 2 is insufficient to answer the question.
Statement 1 + 2
O' = 1.13*O and O = 5P
So, O' = 5.65P and O = 5P
Percent change in total cost = (O-O'+0.05P)/(O+P)
Percent change in total cost = (5P-5.65P+0.05P)/(5P+P)
Percent change in total cost = (-0.6P)/(6P)
Percent change in total cost = (-0.6P)/(6P)
Percent change in total cost = -1/10 = 10% decrease
So statement 1+2combined is sufficient to answer the question.
IMO C
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by digvijayk » Thu May 17, 2012 2:39 pm
Since this is a DS question, we won't need to solve. Let me crack the case open with a little plug n play:

Pre-Jan:
Overhead cost = 50
Production cost = 50
Total cost = 100

Jan:
Overhead cost = 50
New production cost= 47.5--> changed by 5%
New total cost = 97.5

Total cost change -> -2.5/100 => 2.5% decrease. But this is dependent on the ratio O/P. How do I know that its 1/1
========================================
What I need to know:
The values will change if i change Overhead cost/Production Cost. So what I really need is Overhead and Production costs. If I have just the new production cost, i can find the old one and vice-versa. Overhead cost may change, so need to know that too. Or atleast the O/P ratio.

=========================================
When I look at options:

I look at (2) O/P = 5 => O=5P. So i know the ratio before January. But what about values in Jan. What If Overhead also changed! Can't be sure so, Insufficient.

I look at (1), O increased by 13%. Does nothing for me. Insufficient.

Combined. (1) and (2) -> Sufficient.

So the answer is C
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by Anurag@Gurome » Thu May 17, 2012 7:06 pm
GmatKiss wrote:The total cost of producing item X is equal to the sum of item X's overhead cost and production cost. If the production cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in that same month?

(1) The overhead cost of producing item X increased by 13% in January.

(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.

Let the fixed cost be 'f' and let the variable cost be 'v'.
So, the total cost is 'f + v'.
The variable cost decreases by 5% in January.
But we need to know more about fixed cost.

(1) The overhead cost of producing item X increased by 13% in January.
If the fixed cost is increasing by 13% in January, the percentage change is
{(13/100)*f - (5/100)*v}/(f+v) * 100.
Obviously, this is not enough to answer the question; NOT sufficient.

(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.
This means that f = 5v.
But nothing has been mentioned about the changes; NOT sufficient.

Combining (1) and (2), percentage change is given by (65/100 * v - 5/100 * v)/6v * 100 = 10%; SUFFICIENT.

The correct answer is C.
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