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

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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...
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Re: very hard - MGMAT  [#permalink]

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18 Jul 2010, 21:44
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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).

Hope it's clear.
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Re: Total Cost of Producing item X  [#permalink]

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05 Oct 2011, 03:15
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GMATD11 wrote:
The total cost of producing item X is equal to the sum of item X's overhead cost and production cost. If the production cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in that same month?

(1) The overhead cost of producing item X increased by 13% in January.

(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.

Guys i marked B but its wrong.

Pls discuss

The reason 'B' is not the answer is that you are not allowed to 'assume' anything in DS questions.
You know that production cost increased by 5%. Using statement 2, you also see that production cost is a sixth of the total cost. So you assume that you know the change in the total cost. But remember, you are assuming here that overhead cost hasn't changed. Since you do not know whether overhead cost is the same or has changed, you cannot say anything about the decrease/increase in the overall cost. Even if you overlooked this, statement 1 should have reminded you that overhead cost could have changed too. Hence the answer has to be (c).
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Re: The total cost of producing item X  [#permalink]

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15 May 2013, 01:28
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WarriorGmat wrote:
The total cost of producing item X is equal to the sum of item X's overhead cost and production cost. If the production cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in that same month?

(1) The overhead cost of producing item X increased by 13% in January.

(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.

T = Total costs
P = production costs

given:- P changes to 0.95P
To find:- T changes to what??

statement 1:- O changes to 1.13O

so T change can be calculated by $$((P+O) - (0.95P + 1.13O))/ (P+O)$$

which gives $$(0.95P + 1.13O)/ (P+O)$$ ---------- 1
we cannot calculate the value here. So A alone is not sufficient. AD out

statement 2:- O is 5 times P . O = 5P
We don't know what the changes in O are to calculate changes in T using B alone. So B is out.

1 and 2 combined

we can substitute the value of O in the 1st equation. In the numerator and denominator we can cancel P therby we can get a numerical value. So C is the answer
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Re: very hard - MGMAT  [#permalink]

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06 May 2011, 21:52
1
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)

%change in total cost = (13 * 5 - 5 * 1) / (5 + 1) = 60/ 6 = 10% increase

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.

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...
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Re: very hard - MGMAT  [#permalink]

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07 May 2011, 11:13
2
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)

%change in total cost = (13 * 5 - 5 * 1) / (5 + 1) = 60/ 6 = 10% increase

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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Re: very hard - MGMAT  [#permalink]

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07 May 2011, 11:28
Karishma - can u plz post ur blogging that dealing with this weighted average system?
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Re: very hard - MGMAT  [#permalink]

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07 May 2011, 11:59
3
144144 wrote:
Karishma - can u plz post ur blogging that dealing with this weighted average system?

Here you go:

http://www.veritasprep.com/blog/2011/03 ... -averages/

http://www.veritasprep.com/blog/2011/04 ... ge-brutes/

http://www.veritasprep.com/blog/2011/04 ... -mixtures/

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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Re: Total Cost of Producing item X  [#permalink]

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03 Oct 2011, 07:51
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Total Cost = T
Production Cost = P

from the question we have: T = P + Q
Statement 1: T1 = .95P +1.13Q
change = T - T1 => 0.05P -0.13Q
hence as we have 2 unknown calculation of % increase/decrease not possible
insufficient.
Statement 2:
O = 5P
therefore T = P + O => T = P+5P
decrease in production cost is known but increase or decrease in overhead is still unknown. We cannot apply the decrease in production cost to the increase/decrease of overhead cost.

hence the actual change will remain unknown. Hence insufficient

Statement 1&2 together. We have the relation ship between P and O and also there individual increase/decrease %
Hence sufficient
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Re: very hard - MGMAT  [#permalink]

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11 Jun 2013, 07:07
(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 ?
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Re: very hard - MGMAT  [#permalink]

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11 Jun 2013, 08:41
venkat18290 wrote:
(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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Re: The total cost of producing item X is equal to the sum of  [#permalink]

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11 Jun 2013, 11:42
1
This question is confusing...

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

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11 Jun 2013, 22:23
dave785 wrote:
This question is confusing...

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

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04 Jul 2013, 00:11
1
Hi Bunnel,

Why we are just using c2/C1 for a percentage change in question ..Shouldn't we using c2-c1/c1 for percentage change!! Please clarify
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Re: very hard - MGMAT  [#permalink]

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12 Aug 2013, 21:54
1
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)

%change in total cost = (13 * 5 - 5 * 1) / (5 + 1) = 60/ 6 = 10% increase

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.
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Re: very hard - MGMAT  [#permalink]

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20 Dec 2013, 06:25
VeritasPrepKarishma wrote:
mitmat wrote:

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)
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Re: very hard - MGMAT  [#permalink]

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20 Dec 2013, 20:18
1
stne wrote:
VeritasPrepKarishma wrote:
mitmat wrote:

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%

%change in total cost = (13 * 5 - 5 * 1) / (5 + 1) = 60/ 6 = 10% increase
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Re: very hard - MGMAT  [#permalink]

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21 Dec 2013, 00:33
VeritasPrepKarishma wrote:
stne wrote:
@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%

%change in total cost = (13 * 5 - 5 * 1) / (5 + 1) = 60/ 6 = 10% increase

let me see if I have understood correctly

-5 ----------x-----------13
1V------------------------5V

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.
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Re: very hard - MGMAT  [#permalink]

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30 Dec 2013, 07:23
stne wrote:
VeritasPrepKarishma wrote:
stne wrote:
@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%

%change in total cost = (13 * 5 - 5 * 1) / (5 + 1) = 60/ 6 = 10% increase

let me see if I have understood correctly

-5 ----------x-----------13
1V------------------------5V

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

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21 Jun 2014, 03:46
VeritasPrepKarishma wrote:
GMATD11 wrote:
The total cost of producing item X is equal to the sum of item X's overhead cost and production cost. If the production cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X change in that same month?

(1) The overhead cost of producing item X increased by 13% in January.

(2) Before the changes in January, the overhead cost of producing item X was 5 times the production cost of producing item X.

Guys i marked B but its wrong.

Pls discuss

The reason 'B' is not the answer is that you are not allowed to 'assume' anything in DS questions.
You know that production cost increased by 5%. Using statement 2, you also see that production cost is a sixth of the total cost. So you assume that you know the change in the total cost. But remember, you are assuming here that overhead cost hasn't changed. Since you do not know whether overhead cost is the same or has changed, you cannot say anything about the decrease/increase in the overall cost. Even if you overlooked this, statement 1 should have reminded you that overhead cost could have changed too. Hence the answer has to be (c).

Hi Karishma, Can you please explain why A can't be the answer.

According to me,
Total cost = OC + PC ------A

Using 1st stat , TC = 1.13 OC + .95 PC ------- B

We can now just substitute some value for OC and PC in A then modify the values to percent in B
Then using A and B we can find the percent change since they are not asking the actual cost.
Re: The total cost of producing item X is equal to the sum of it &nbs [#permalink] 21 Jun 2014, 03:46

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