Data Sufficiency

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.

Let TC=FC+VC, where TC=Total Costs, FC=Fixed Costs and VC=Variable Costs

VC decreased 5%

1) FC Increased by 13%. WE don't know the components of FC and VC to actually calculate the change in TC. insufficient.

2) FC= 5VC
TC=5VC+VC
TC=6VC.

Since we know that VC went down 5% we can calculate the change in TC. Sufficient.

Ans. B.

iwant700plus wrote:Let TC=FC+VC, where TC=Total Costs, FC=Fixed Costs and VC=Variable Costs

VC decreased 5%

1) FC Increased by 13%. WE don't know the components of FC and VC to actually calculate the change in TC. insufficient.

2) FC= 5VC
TC=5VC+VC
TC=6VC.

Since we know that VC went down 5% we can calculate the change in TC. Sufficient.

Ans. B.

IMO it is C.

In statement 2, we don’t know how much the fixed cost has changed. This info is provided only by statement 1.

-BM-

So, as per the answers, the answer is C and not B.
bluementor got it right.
I also went for B.

But my question is,
Why should we consider the fixed cost to change.
Coz if fixed cost changes, its no longer fixed, it becomes variable.

I'm not clear why.

TC = VC + FC
VC increased by 5%

Lets say in January TC = $120.

Statement 2 gives us the info on the proportion of VC to FC:

FC = 5*VC, so VC = $20 and FC = $100.

A 5% decrease in VC results VC = $19. If the fixed cost had not varied, the total cost will now be $119. The resulting change in TC is (1/120)*100%

However, if FC has also changed, then TC will also change. From statement 2 alone, we don't know anything about the change in FC. So we cannot conclude anything from here. But together with statement 1, we can conclusively evaluate the change in TC.

hth.

-BM-

I und ur point and explanation.

But my question still remains,
Why should we consider a change in fixed cost at all.
What does the word "fixed" mean then.

I dont think this good question from GMAT perspective.

Anshul coming back to your question
Why should we consider a change in fixed cost at all.
What does the word "fixed" mean then.

I Produce a product A with Fixed cost( Rent+ machine expenditure) + variable cost(raw material etc.)

If my rent will increase then fixed cost per unit A will increase.

So Fixed cost also increases with the factors it involves.

I hope you get the idea.

anshulseth wrote:I und ur point and explanation.

But my question still remains,
Why should we consider a change in fixed cost at all.
What does the word "fixed" mean then.

Ah, I see what you mean now.

Hemantsood has already given a good brief explanation on this. I'll try to explain a little more.

In production economics, fixed cost does not mean it will be fixed all the time. Fixed cost is usually attributed to cost of assets (such as machinery used in the production process) and other overhead cost. So a company can make an investment in additional machinery, resulting an increase in its fixed cost.

On the other hand, variable cost is usually attributed soleley into what goes into the product. And this is usually materials and labour. Variable cost will only depend on the quantity of products that are produced. The higher the number of products produced, the higher the variable cost.

P.S. I am no expert in this, so others may want to correct this if I am wrong.

-BM-

I have to disagree.

The GMAT is written (so they say) so that a test taker should not have to know anything about economics or accounting or stuff like that.

My opinion is that this is just a POORLY written question. Statements 1 and 2 are suppose to be taken independently of one another, right? That is what makes DS so hard sometimes. So, according to the prompt and statement 2, statement 2 is in fact sufficient to answer the question. If it were not, they should have put something in the prompt like "In January BOTH the fixed and variable cost changed. The variable cost changed by 5%". Otherwise, statement 2 gives us a fixed ratio, and with a fixed ratio we can calculate a percentage change of a total.

I think, as the question is written, you HAVE to go with B. Otherwise you violet the way the test was written. That's why I am saying this is a poorly written question.

Am I missing something? Is there some wording in the prompt or statements that should cause us to know (not assume) there is a change in fixed cost?