The total cost of producing item X is

[maratherajesh]

Problem # 12 Free Practice Test

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.

Official answer is C. But my take is B. Below is my reasoning for choosing B.

Data given in problem

Total cost : Ct

Fixed Cost : Cf

Variable Cost : Cv

1. Ct = Cf + Cv - Ct

2. In January Variable Cost = 0.95 * Cv

Statement 2: Before January : Cf = 5 * Cv.

Therefor before January Ct = 5Cv + Cv = 6Cv.

And after January Ct = 6 * 0.95Cv = 5.7Cv.

Hence change in total cost of producing item = [(6Cv - 5.7Cv)/5.7Cv] *100 %

Hence B alone is sufficient.

i am missing anything here?

Mant thanks in advance!!

[maratherajesh]

Problem # 12 Free Practice Test

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.

Official answer is C. But my take is B. Below is my reasoning for choosing B.

Data given in problem

Total cost : Ct

Fixed Cost : Cf

Variable Cost : Cv

1. Ct = Cf + Cv - Ct

2. In January Variable Cost = 0.95 * Cv

Statement 2: Before January : Cf = 5 * Cv.

Therefor before January Ct = 5Cv + Cv = 6Cv.

And in January Ct = 6 * 0.95Cv = 5.7Cv.

Hence change in total cost of producing item = [(6Cv - 5.7Cv)/6Cv] *100 %

Hence B alone is sufficient.

i am missing anything here?

Many thanks in advance!!

[RonPurewal]

i didn't really understand this:

1. Ct = Cf + Cv - Ct

i'm assuming you meant (correctly) that ct = cf + cv, especially because you seemed to follow that formula in the remainder of your work.

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...and here's where you went wrong:

And after January Ct = 6 * 0.95Cv = 5.7Cv.

nope.

if you do that, you're saying that the total cost after january is 95% of the original total cost. that's not necessarily true, unless you make the unwarranted assumption that the fixed cost decreases by the same 5% by which the variable cost decreased. with statement (2) alone, we have no information whatsoever about the % change in the fixed cost, so statement (2) is insufficient.

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you can also just observe that statement (2) only gives information about the variable cost, while it's clear that you need information about both cf and cv in order to make a correct deduction about ct. because statement (1) provides that missing information, the two statements together are sufficient.

[sanjaylakhani]

Hi Ron

Went through this question today.

For choice B - why are we to assume that fixed costs will change. The question stem does not say that both costs have changed.

I think you need to review this question. Would love to hear your comments as the question in present form is not specific.

Sanjay

[JonathanSchneider]

Hm. I'm tempted to agree with you on this one, since it says that it's a "fixed" cost. But be careful: "fixed" does not mean "fixed permanently throughout all time." It just means that there is a certain cost that the company pays regardless of how many units it produces. Moreover, note that were (2) sufficient on its own (by assuming NO change in fixed costs), the two statements would be in disagreement, a situation that cannot occur.

[JonathanSchneider]

Moreover, see here: viewtopic.php?f=32&t=1845

(Sanjay, you posted there as well. Still not convinced though, eh?)