before change in january total cost T1 = f + v ----- (1)
After change in jan T2 = kf + 0.95v
|T2 - T1|/T1 = ??
consider stm1
T2 = 1.13f + 0.95v ------------------------------(2)
can't calculate %change in total cost.

st2.
f = 5v ------------------------------------------(3)
st2 alone is not sufficient.
using both statement1 and statement2 we can find out %age change of tc in jan
So, I'll go for C

ru2008 wrote:The total cost of producing item X is equal to the sum of item X's fixed cost and variable cost. If the variable cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in January?

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

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

think it is C

we know from the question
T = F(fixed cost) + V(variable cost)
In jan , we know the variable cost increased by 5%
(in Jan)T = F(in Jan) + 1.05 V


Statement 1
In Jan , the fixed cost of producing item X increased by 13%...So the new fixed cost is 1.13F
So
(in Jan)T = 1.13 F + 1.05 V
current T = F+V
% Increase in total cost = [ (in Jan)T - (current) T / (current) T] * 100
We will still have 2 variables remaining after making the substitutions and cleaning up

So insufficient

Statement 2

Before the changes in January,fixed cost of producing item X was 5 times the variable cost of producing item X
So
F (current ) = 5 V (current)
So (current) T = F + V = 6V
And (Jan) T = F(Jan) + 1.05 V because we do not know from this statement what happened to the fixed cost - increase / decrease / remained same

So , this is insufficient

Using both , we know
(Jan) T = F(Jan) + 1.05 V
and F(Jan) = 1.13 F (current) = 1.13 * 5 V(current)
So (Jan) T = 1.13 * 5 V(current) + 1.05 V (current)
and we already know that
T (current) = 6V

From the above 2 we can find the % increase in the total cost