I got it wrong; I selected B.

Reason: The cost of item X has two parts: fixed and variable. If one part is fixed then it should not vary. With this logic, I thought 2 statement is sufficient. Suppose value of variable component was x before jan then the percentage change
= (((5x + 0.95x) - (5x+x))/(5x+x))*100
= 5/6%

Is it possible that fixed component varies? and if yes then what the difference between fixed component and variable component?

https://www.beatthegmat.com/fixed-cost-a ... 17188.html

Stuart has provided an explanation. I understand your interpretation of word fixed (in strict sense something that stays constant) but in the gmat ds world unless we are given fixed cost is the same we cannot assume it is.

fixed means something that does not vary with quantity. Variable costs vary with quantity.
TC: F+VC, VC=Vq (Variable part increases when quantity increases, decreases when quantity decreases)

F and V can be increased, if F increases by 13%, new Fixed cost= 1.13F, new VC=0.95VC, with statement 1 we still have 2 variables F and VC

statement 2: relation between F and VC.no information on change
combining, all VCs expressed as F, the % change can be found

fixed means something that does not vary with quantity.

Like I said above for this problem we cannot assume it is based on a definition of term "fixed". It leads us in to a DS trap.

Therefore the answer is not [spoiler]B)[/spoiler] but [spoiler]C)[/spoiler]

Hope this helps!

scoobydooby wrote:fixed means something that does not vary with quantity. Variable costs vary with quantity.
TC: F+VC, VC=Vq (Variable part increases when quantity increases, decreases when quantity decreases)

F and V can be increased, if F increases by 13%, new Fixed cost= 1.13F, new VC=0.95VC, with statement 1 we still have 2 variables F and VC

statement 2: relation between F and VC.no information on change
combining, all VCs expressed as F, the % change can be found

Your definitions of fixed and variable components are absolutely correct. But with your expressions, TC: F+VC, you have added one more variable C, and you are assuming C is constant. And fortunately C is indeed constant, equal to 1. How?

Problem talks about "total cost of producing item X." That means, through out it's talking about single item.

Now things are falling into place. Thanks cramya and scoobydooby.