Data Sufficiency

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 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

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
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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.

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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