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.

OAC

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.

We could also just say that

o + p = x

where o and p are the costs in December. We know that January has something*o + .95*p, so let's work from there.

S1:: We've now got 1.13o + .95p. But we can't say how much greater this is than o + p, as there's no way of removing both variables; NOT SUFFICIENT.

S2:: o = 5p; same idea, this doesn't tell us the increase in o, so it's NOT SUFFICIENT.

Together:: December was o + p, or 5p + p. January is 1.13*(5p) + .95*p, or 6.6p. So we've gone from 6p to 6.6p, a 10% increase - SUFFICIENT!

(Note that this is 66/60, not 61/60, but that doesn't matter for the purposes of this problem.)