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The total cost of producing item X is equal to the sum of [#permalink]

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18 Jul 2010, 20:54

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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.

----------- My question is, why isn't the answer B? The prompt didn't say fixed cost MUST change...

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.

----------- My question is, why isn't the answer B? The prompt didn't say fixed cost MUST change...

(2) is not sufficient as we don't know what happened with fixed cost in January. Didi it increase? Decrease? Remained the same? As we have no information about it we can not assume anything. So it's clear C. Below is calculations for C:

Let the total cost in January be \(C_2\) and the total cost before be \(C_1\).

Given: \(C_2=F_2+V_2\) and \(C_1=F_1+V_1\), also \(V_2=0.95V_1\). Question: \(\frac{C_2}{C_1}=\frac{F_2+V_2}{F_1+V_1}=\frac{F_2+0.95V_1}{F_1+V_1}=?\)

(1) The fixed cost of producing item X increased by 13% in January --> \(F_2=1.13F_1\) --> \(\frac{1.13F_1+0.95V_1}{F_1+V_1}=?\). Not sufficient to get the exact fraction.

(2) Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X --> \(F_1=5V_1\) --> \(\frac{F_2+0.95V_1}{5V_1+V_1}=?\). Not sufficient.

(1)+(2) \(F_2=1.13F_1\) and \(F_1=5V_1\) --> \(F_2=1.13F_1=5.65V_1\) --> from (2) \(\frac{F_2+0.95V_1}{F_1+V_1}=?\) --> substituting \(F_2\) and \(F_1\)--> \(\frac{5.65V_1+0.95V_1}{5V_1+V_1}=\frac{6.6}{6}=1.1\) --> in January total cost increased by 10%. Sufficient. (Actually no calculations are needed: stem and statement provide us with such relationships of 4 unknowns that 3 of them can be written with help of the 4th one and when we put them in fraction, which we want to calculate, then this last unknown is reduced, leaving us with numerical value).

To get the percentage change, we need two of the three in the same units: original, change or new. Both statements give us original and new in terms of y so it is sufficient. But 2) alone gives only original in terms of y and 1) gives new fixed cost but the total new is in different units. Combining both in same unit gives us percentage change.
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Karishma Pls can you verify this solution. I think this is a weighted average problem.

Combining 1) + 2) 13% increase in the fixed cost and 5% is decrease in variable cost. We know that the weights w1 : w2 are 5 : 1 i.e. Fixed cost : Variable cost = 5 : 1

Hence the %age in the total cost = (13 * w1 - 5 * w2) / (w1 + w2)

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.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

----------- My question is, why isn't the answer B? The prompt didn't say fixed cost MUST change...

Karishma Pls can you verify this solution. I think this is a weighted average problem.

Combining 1) + 2) 13% increase in the fixed cost and 5% is decrease in variable cost. We know that the weights w1 : w2 are 5 : 1 i.e. Fixed cost : Variable cost = 5 : 1

Hence the %age in the total cost = (13 * w1 - 5 * w2) / (w1 + w2)

Good call! We see that we can use weighted averages. We already have A1, Stmnt1 gives us A2 and Stmnt2 gives us w1/w2 so we can use w1/w2 = (A2 - Avg)/(Avg - A1) and get the answer. We don't even need to calculate. Finally, I feel my effort of showing the utility of 'weighted averages' is paying off! If you were in my class, the day's candy would have been yours!
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My signature gives the link to all my blog posts (they are together under the section 'Quarter Wit, Quarter Wisdom'). I have given the link for the weighted average related posts above.
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I think most people will fall into the trap if they assume FC and VC as some values say 100,200... In this case B will be correct

But this approach will work only if there is a single unknown...This is a classic example when it will not work directly

There are 2 approaches

1) If you like formulas : Weighted average is the best approach as illustrated by Karishma

2) I like the lazy-man approach for DS, so I am assuming FC=x,VC=y...As per qn. y decr. by 5% So we need

Increase/(x+y) x incr. by 13% as per A...But no relation b/w x and y ==> This is insufficient

As per B, x=5y...But what is increase ?

Combining A and B, there is a non-redundant relation and increase can be calculated So go with C and MOVE ON

Choose the approach that best suites you...Also calculate values only if needed in DS.

Bunuel has shown the complete steps of calculation for purely illustration...
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Labor cost for typing this post >= Labor cost for pushing the Kudos Button http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html

On a different note, I had assumed that Fixed Cost would remain constant(as I think that's the whole meaning of Fixed cost) for the period (January) mentioned until I saw the Statement-1.

Do you guys also think sometimes statements themselves change your approach of approaching the problem? OR we should not be used to understand the problem itself?
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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.

----------- My question is, why isn't the answer B? The prompt didn't say fixed cost MUST change...

(2) is not sufficient as we don't know what happened with fixed cost in January. Didi it increase? Decrease? Remained the same? As we have no information about it we can not assume anything. So it's clear C. Below is calculations for C:

Let the total cost in January be \(C_2\) and the total cost before be \(C_1\).

Given: \(C_2=F_2+V_2\) and \(C_1=F_1+V_1\), also \(V_2=0.95V_1\). Question: \(\frac{C_2}{C_1}=\frac{F_2+V_2}{F_1+V_1}=\frac{F_2+0.95V_1}{F_1+V_1}=?\)

(1) The fixed cost of producing item X increased by 13% in January --> \(F_2=1.13F_1\) --> \(\frac{1.13F_1+0.95V_1}{F_1+V_1}=?\). Not sufficient to get the exact fraction.

(2) Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X --> \(F_1=5V_1\) --> \(\frac{F_2+0.95V_1}{5V_1+V_1}=?\). Not sufficient.

(1)+(2) \(F_2=1.13F_1\) and \(F_1=5V_1\) --> \(F_2=1.13F_1=5.65V_1\) --> from (2) \(\frac{F_2+0.95V_1}{F_1+V_1}=?\) --> substituting \(F_2\) and \(F_1\)--> \(\frac{5.65V_1+0.95V_1}{5V_1+V_1}=\frac{6.6}{6}=1.1\) --> in January total cost increased by 10%. Sufficient. (Actually no calculations are needed: stem and statement provide us with such relationships of 4 unknowns that 3 of them can be written with help of the 4th one and when we put them in fraction, which we want to calculate, then this last unknown is reduced, leaving us with numerical value).

Answer: C.

Hope it's clear.

Hi Bunuel ,

I have a small doubt , it is stated that "BEFORE THE CHANGES IN JANUARY " the fixed costs were so and so , how can we infer from this statement that the proportion could have been the same in january also ???

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.

----------- My question is, why isn't the answer B? The prompt didn't say fixed cost MUST change...

(2) is not sufficient as we don't know what happened with fixed cost in January. Didi it increase? Decrease? Remained the same? As we have no information about it we can not assume anything. So it's clear C. Below is calculations for C:

Let the total cost in January be \(C_2\) and the total cost before be \(C_1\).

Given: \(C_2=F_2+V_2\) and \(C_1=F_1+V_1\), also \(V_2=0.95V_1\). Question: \(\frac{C_2}{C_1}=\frac{F_2+V_2}{F_1+V_1}=\frac{F_2+0.95V_1}{F_1+V_1}=?\)

(1) The fixed cost of producing item X increased by 13% in January --> \(F_2=1.13F_1\) --> \(\frac{1.13F_1+0.95V_1}{F_1+V_1}=?\). Not sufficient to get the exact fraction.

(2) Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X --> \(F_1=5V_1\) --> \(\frac{F_2+0.95V_1}{5V_1+V_1}=?\). Not sufficient.

(1)+(2) \(F_2=1.13F_1\) and \(F_1=5V_1\) --> \(F_2=1.13F_1=5.65V_1\) --> from (2) \(\frac{F_2+0.95V_1}{F_1+V_1}=?\) --> substituting \(F_2\) and \(F_1\)--> \(\frac{5.65V_1+0.95V_1}{5V_1+V_1}=\frac{6.6}{6}=1.1\) --> in January total cost increased by 10%. Sufficient. (Actually no calculations are needed: stem and statement provide us with such relationships of 4 unknowns that 3 of them can be written with help of the 4th one and when we put them in fraction, which we want to calculate, then this last unknown is reduced, leaving us with numerical value).

Answer: C.

Hope it's clear.

Hi Bunuel ,

I have a small doubt , it is stated that "BEFORE THE CHANGES IN JANUARY " the fixed costs were so and so , how can we infer from this statement that the proportion could have been the same in january also ???

(1)+(2) \(F_2=1.13F_1\) and \(F_1=5V_1\) --> \(F_2=1.13F_1=5.65V_1\) --> from (2) \(\frac{F_2+0.95V_1}{F_1+V_1}=?\) --> substituting \(F_2\) and \(F_1\)--> \(\frac{5.65V_1+0.95V_1}{5V_1+V_1}=\frac{6.6}{6}=1.1\) --> in January total cost increased by 10%. Sufficient. (Actually no calculations are needed: stem and statement provide us with such relationships of 4 unknowns that 3 of them can be written with help of the 4th one and when we put them in fraction, which we want to calculate, then this last unknown is reduced, leaving us with numerical value).

Please check the bold part .. you have taken F2=1.13F1 and F1=5V1 . My doubt was how did you take F1=5V1 when combining both the statements .

IMO : Statement 2 was all about before price change in January , so the statement 2 does not give us any information about the price in January . So how can we even consider statement 2 ?

Or is it that i am interpreting the statement wrong ?

(1)+(2) \(F_2=1.13F_1\) and \(F_1=5V_1\) --> \(F_2=1.13F_1=5.65V_1\) --> from (2) \(\frac{F_2+0.95V_1}{F_1+V_1}=?\) --> substituting \(F_2\) and \(F_1\)--> \(\frac{5.65V_1+0.95V_1}{5V_1+V_1}=\frac{6.6}{6}=1.1\) --> in January total cost increased by 10%. Sufficient. (Actually no calculations are needed: stem and statement provide us with such relationships of 4 unknowns that 3 of them can be written with help of the 4th one and when we put them in fraction, which we want to calculate, then this last unknown is reduced, leaving us with numerical value).

Please check the bold part .. you have taken F2=1.13F1 and F1=5V1 . My doubt was how did you take F1=5V1 when combining both the statements .

IMO : Statement 2 was all about before price change in January , so the statement 2 does not give us any information about the price in January . So how can we even consider statement 2 ?

Or is it that i am interpreting the statement wrong ?

(2) says: before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X --> F(before)=5*V(before) --> \(F_1=5V_1\) (F1 and V1 are costs before January and F2 and V2 are costs in January).
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If the fixed cost truly is fixed, then B. should be sufficient.

If the fixed cost can change, then the variable cost should change not only based off of price change but off of total units as well..

But I see what the question is asking... my microecon training just doesn't like how it's phrased.

In the question, it is implied that the fixed cost and variable cost are in per unit terms. Total cost = Fixed Cost + Variable Cost Item X's variable cost will be cost per unit so fixed cost will also be in terms of cost per unit.

As you noted, fixed cost per unit (e.g. leased land) changes with the number of units and variable cost changes with change in variable factors (e.g. cost of raw material) and might change with change in number of units too (e.g. say you need to make 110 units instead of 100 so you hire one extra person though you don't utilize him fully and hence variable cost increases for all the units). In any given month, both fixed cost per unit and variable cost per unit can change. It is definitely possible that one increases and the other decreases.

I don't think there is a problem in the question but probably a clearly mentioned 'fixed cost per unit' would have been better.
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