The total cost of producing item X....

X = o + p.
x' = o + .95p
A) x'' = 1.13o + .95p
Insufficient as we can't find actual percent
B) o=5p.
thus X = 6p. but we don't know by how much o increases.
A&B) o=5p.
x=6p
o' = 1.13*5p.5.65p
p' = .95p
thus x' = 5.65p + .95p = 6.6p
Thus we can find % change
IMO C

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.

To determine the percent change in the total cost, we need to know the RATIO between the new cost and the original cost.
Question rephrased: What is the value of (new cost)/(original cost)?

Statement 1: The overhead cost of producing item X increased by 13% in January.
Test one case that also satisfies statement 2 and one case that DOESN'T also satisfy statement 2.

Case 1:
Original overhead cost = 100, original production cost = 20, original total cost = 100+20 = 120.
13% higher overhead cost = 113, 5% lower production cost = 19, new total cost = 113+19 = 132.
Resulting ratio:
(new cost)/(original cost) = 132/120 = 11/10.

Case 2:
Original overhead cost = 100, original production cost = 40, original total cost = 100+40 = 140.
13% higher overhead cost = 113, 5% lower production cost = 38, new total cost = 113+38 = 151.
Resulting ratio:
(new cost)/(original cost) = 151/140.

Since different ratios are possible, INSUFFICIENT.

Statement 2: Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.
No information about how the overhead cost changes in January.
INSUFFICIENT.

Statements combined:
Case 1 satisfies both statements.
Test one more case that satisfies both statements.

Case 3:
Original overhead cost = 200, original production cost = 40, original total cost = 200+40 = 240.
13% higher overhead cost = 226, 5% lower production cost = 38, new total cost = 226+38 = 264.
Resulting ratio:
(new cost)/(original cost) = 264/240 = 11/10.

Since Case 1 and Case 3 yield the same ratio, the two statements combined indicate that (new cost)/(original cost) = 11/10.
SUFFICIENT.

The correct answer is C.

Why not B itself sufficient? Is it because we also need to know if the over head price increased or decreased or remain same?

ashutoshkumar7 wrote:Why not B itself sufficient? Is it because we also need to know if the over head price increased or decreased or remain same?

Correct! With statement 2, we know the initial ratio of production cost to overhead cost and the percent increase in the production cost, but we don't know by what percentage the overhead cost changed.