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I am good with weighted averages, but I could not understand this question being solved in weighted average method. Please help me understand your method better. Thanks in advance.

gmat1220 wrote:

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...

I am good with weighted averages, but I could not understand this question being solved in weighted average method. Please help me understand your method better. Thanks in advance.

gmat1220 wrote:

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.

Think of it as a mixture problem that uses weighted average. You mix one solution with another in certain proportion to get an overall mixture. Depending on the proportion in which you mix the two, you get the concentration of the final mixture. Here, your two solutions are 'fixed cost' and 'variable cost'. You add them together to get total cost. When these costs change, the overall cost will change. Depending on the proportion in which they come together, the overall cost changes

Say if both costs increase by 10%, the total cost will increase by 10%. If one cost increases by 100% and one increases by 10%, the increase in total cost depends on the proportion of each cost in the total cost. Say, variable cost increases by 100% and fixed cost by 10%. If most of the total cost is fixed cost, the increase in total cost will be a little more than 10%. If most of the total cost is variable cost, the increase in total cost will be close to 100%. So the increase in total cost depends on the "weights" of the fixed cost and variable cost.

The calculation is provided by gmat1220 above. Get back if there are any doubts in the calculations.
_________________

I always thought that weighted average method could be used only for fixed values (like the examples you had mentioned in veritas blog). its the first time that I have seen this method used in percentage changes. Nice to know this method and scope of its uses...

Karishma...jai ho!!!

VeritasPrepKarishma wrote:

mitmat wrote:

Hi gmat1220 and Karishma

I am good with weighted averages, but I could not understand this question being solved in weighted average method. Please help me understand your method better. Thanks in advance.

gmat1220 wrote:

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.

Think of it as a mixture problem that uses weighted average. You mix one solution with another in certain proportion to get an overall mixture. Depending on the proportion in which you mix the two, you get the concentration of the final mixture. Here, your two solutions are 'fixed cost' and 'variable cost'. You add them together to get total cost. When these costs change, the overall cost will change. Depending on the proportion in which they come together, the overall cost changes

Say if both costs increase by 10%, the total cost will increase by 10%. If one cost increases by 100% and one increases by 10%, the increase in total cost depends on the proportion of each cost in the total cost. Say, variable cost increases by 100% and fixed cost by 10%. If most of the total cost is fixed cost, the increase in total cost will be a little more than 10%. If most of the total cost is variable cost, the increase in total cost will be close to 100%. So the increase in total cost depends on the "weights" of the fixed cost and variable cost.

The calculation is provided by gmat1220 above. Get back if there are any doubts in the calculations.

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

Show Tags

13 Aug 2013, 06:54

The method which I used 3 yrs ago was probably the fastest. Its intuitive and somewhat like calculus (you just take care of deltas). But in case you want to use absolute values it works like this - Total cost= fixed + variable = 1.13 f + 0.95 v . Now since f=5v. So total new cost = 1.13 *5v + 0.95 v = 6.6 v. Initially cost = f + v = 6v hence change is (6.6v- 6v / 6v) × 100 =10 %. Hope that helps.

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

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13 Aug 2013, 10:44

I got the solution to this question by the method u had mentioned below and that was fine with me. Your original method was great and as u aptly said, most efficient. I just wanted to learn more about your thought process. Now that I have it, I feel better equipped. Thank you for this method and showing that weighted average method can be applied beyond absolute values.

gmat1220 wrote:

The method which I used 3 yrs ago was probably the fastest. Its intuitive and somewhat like calculus (you just take care of deltas). But in case you want to use absolute values it works like this - Total cost= fixed + variable = 1.13 f + 0.95 v . Now since f=5v. So total new cost = 1.13 *5v + 0.95 v = 6.6 v. Initially cost = f + v = 6v hence change is (6.6v- 6v / 6v) × 100 =10 %. Hope that helps.

I am good with weighted averages, but I could not understand this question being solved in weighted average method. Please help me understand your method better. Thanks in advance.

Think of it as a mixture problem that uses weighted average. You mix one solution with another in certain proportion to get an overall mixture. Depending on the proportion in which you mix the two, you get the concentration of the final mixture. Here, your two solutions are 'fixed cost' and 'variable cost'. You add them together to get total cost. When these costs change, the overall cost will change. Depending on the proportion in which they come together, the overall cost changes

Say if both costs increase by 10%, the total cost will increase by 10%. If one cost increases by 100% and one increases by 10%, the increase in total cost depends on the proportion of each cost in the total cost. Say, variable cost increases by 100% and fixed cost by 10%. If most of the total cost is fixed cost, the increase in total cost will be a little more than 10%. If most of the total cost is variable cost, the increase in total cost will be close to 100%. So the increase in total cost depends on the "weights" of the fixed cost and variable cost.

The calculation is provided by gmat1220 above. Get back if there are any doubts in the calculations.

@Karishma Was able to solve this problem by the traditional way , but couldn't figure out the weighted averages way I am aware of the concept

Using the scale method

.95V --------- Avg -----------1.13 (5V) ---------------------------------- V ---------------------------- 5V

on the left side we have the variable cost and on the right , the Fixed cost however using this I am not able to figure out how to find the percent change Now what I am getting is

( V/5V) = (1.13(5V) - avg )/ ( Avg - .95V)

or even if I use

V/5V = ( 13V - avg ) / (Avg- 5V) still I am not getting the answer

How to do this correctly using the scale method ?

the new fixed price is 1.13*5V = 5.65V isn't it? and new variabe price .95V

so how does this equation give us the percent change?

I am good with weighted averages, but I could not understand this question being solved in weighted average method. Please help me understand your method better. Thanks in advance.

Think of it as a mixture problem that uses weighted average. You mix one solution with another in certain proportion to get an overall mixture. Depending on the proportion in which you mix the two, you get the concentration of the final mixture. Here, your two solutions are 'fixed cost' and 'variable cost'. You add them together to get total cost. When these costs change, the overall cost will change. Depending on the proportion in which they come together, the overall cost changes

Say if both costs increase by 10%, the total cost will increase by 10%. If one cost increases by 100% and one increases by 10%, the increase in total cost depends on the proportion of each cost in the total cost. Say, variable cost increases by 100% and fixed cost by 10%. If most of the total cost is fixed cost, the increase in total cost will be a little more than 10%. If most of the total cost is variable cost, the increase in total cost will be close to 100%. So the increase in total cost depends on the "weights" of the fixed cost and variable cost.

The calculation is provided by gmat1220 above. Get back if there are any doubts in the calculations.

@Karishma Was able to solve this problem by the traditional way , but couldn't figure out the weighted averages way I am aware of the concept

Using the scale method

.95V --------- Avg -----------1.13 (5V) ---------------------------------- V ---------------------------- 5V

on the left side we have the variable cost and on the right , the Fixed cost however using this I am not able to figure out how to find the percent change Now what I am getting is

( V/5V) = (1.13(5V) - avg )/ ( Avg - .95V)

or even if I use

V/5V = ( 13V - avg ) / (Avg- 5V) still I am not getting the answer

How to do this correctly using the scale method ?

the new fixed price is 1.13*5V = 5.65V isn't it? and new variabe price .95V

so how does this equation give us the percent change?

( V/5V) = (5.65V - avg )/ ( Avg - .95V)

You want to find the average change in the price given the change in the price of fixed cost and variable cost.

Change in the fixed cost = 13% Change in variable cost = -5% (Average) Overall change = ? We know that the weights w1 : w2 are 5 : 1 i.e. Fixed cost : Variable cost = 5 : 1

Hence the Average Change = (13 * 5 - 5 * 1) / (5 + 1) = 10%

@Karishma Was able to solve this problem by the traditional way , but couldn't figure out the weighted averages way I am aware of the concept

Using the scale method

.95V --------- Avg -----------1.13 (5V) ---------------------------------- V ---------------------------- 5V

on the left side we have the variable cost and on the right , the Fixed cost however using this I am not able to figure out how to find the percent change Now what I am getting is

( V/5V) = (1.13(5V) - avg )/ ( Avg - .95V)

or even if I use

V/5V = ( 13V - avg ) / (Avg- 5V) still I am not getting the answer

How to do this correctly using the scale method ?

the new fixed price is 1.13*5V = 5.65V isn't it? and new variabe price .95V

so how does this equation give us the percent change?

( V/5V) = (5.65V - avg )/ ( Avg - .95V)

You want to find the average change in the price given the change in the price of fixed cost and variable cost.

Change in the fixed cost = 13% Change in variable cost = -5% (Average) Overall change = ? We know that the weights w1 : w2 are 5 : 1 i.e. Fixed cost : Variable cost = 5 : 1

Hence the Average Change = (13 * 5 - 5 * 1) / (5 + 1) = 10%

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

Show Tags

29 Dec 2013, 06:07

I have a question for whomever has the answer:

In a question like this, is it not enough just to know the ratio of "weights" (using the term weights very loosely here) between fixed and variable cost, together with the change in percent of fixed cost?

This is how I interpret it:

Total Cost = FC + VC, where FC = w1*A1 and VC = w2*A2..

Since we KNOW A2 from the stem, we have three unknowns: w1, A1 and w2..

1) This gives us A1 but neither of the "weights", insufficient. 2) This gives us the weights, but not A1, insufficient.

---> Combine both and we have solved all of the variables : Answer is C

@Karishma Was able to solve this problem by the traditional way , but couldn't figure out the weighted averages way I am aware of the concept

Using the scale method

.95V --------- Avg -----------1.13 (5V) ---------------------------------- V ---------------------------- 5V

on the left side we have the variable cost and on the right , the Fixed cost however using this I am not able to figure out how to find the percent change Now what I am getting is

( V/5V) = (1.13(5V) - avg )/ ( Avg - .95V)

or even if I use

V/5V = ( 13V - avg ) / (Avg- 5V) still I am not getting the answer

How to do this correctly using the scale method ?

the new fixed price is 1.13*5V = 5.65V isn't it? and new variabe price .95V

so how does this equation give us the percent change?

( V/5V) = (5.65V - avg )/ ( Avg - .95V)

You want to find the average change in the price given the change in the price of fixed cost and variable cost.

Change in the fixed cost = 13% Change in variable cost = -5% (Average) Overall change = ? We know that the weights w1 : w2 are 5 : 1 i.e. Fixed cost : Variable cost = 5 : 1

Hence the Average Change = (13 * 5 - 5 * 1) / (5 + 1) = 10%

where x is the average or percent change after fixed price was increased and variable price was decreased so \(\frac{1}{5} =\frac{13-x} {x-(-5)}\)

after solving we get x+5 = 65-5x 6x=60 x= 10%

Is this ok? Couldn't understand it when it wasn't presented in this format. Would you classify it as a different kind of weighted averages problem?

Thank you +1.

It is the same formula. Note that the original formula is Cavg = (C1*w1 + C2*w2)/(w1 + w2) We just re-arranged it to get w1/w2 = (C2 - Cavg)/(Cavg - C1)

When we need the ratio of w1/w2, it is easier to use the rearranged version. If we need to get Cavg, its easier to use the original formula.
_________________

In a question like this, is it not enough just to know the ratio of "weights" (using the term weights very loosely here) between fixed and variable cost, together with the change in percent of fixed cost?

This is how I interpret it:

Total Cost = FC + VC, where FC = w1*A1 and VC = w2*A2..

Since we KNOW A2 from the stem, we have three unknowns: w1, A1 and w2..

1) This gives us A1 but neither of the "weights", insufficient. 2) This gives us the weights, but not A1, insufficient.

---> Combine both and we have solved all of the variables : Answer is C

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

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20 Aug 2016, 11:00

Bunuel wrote:

knabi 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.

----------- 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.

Bunuel if we are asked %change why didnt we use that formula and took ratio instead?

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