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

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KarishmaB
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   22 Jun 2014, 21:12
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gauravsoni wrote:
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.


Ok, let's continue and find the percent change in total cost.

TC = OC + PC

We don't know how much of total cost is OC and how much is PC. Let's assume that total cost is 200 and OC = 100, PC = 100

New TC = 1.13 OC + .95 PC
New TC = 1.13*100 + .95*100 = 208
This is a 4% increase.

Now let's assume that of the total cost of 200, OC = 50, PC = 150

New TC = 1.13*50 + .95*150 = 199
This is a 0.5% decrease.

Note that the % change in total cost is dependent on how the total cost is divided between OC and PC. Since statement 1 alone doesn't tell us how it is divided, we don't know whether there is an increase/decrease in total cost and how much.
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   23 Jan 2017, 11:54
Can someone please post a full resolution for this thing? I dont get the algebra...

And why is B not sufficient???
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   24 Jan 2017, 10:47
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iliavko wrote:
Can someone please post a full resolution for this thing? I dont get the algebra...

And why is B not sufficient???


Stmnt 2 is not sufficient.

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.

Total Cost = Overhead Cost + Production Cost

We need to find the change in total cost. The question stem gives the percent decrease in production cost. But stmnt 1 gives the percent change in overhead cost. Without knowing the change in overhead cost, you cannot calculate the change in total cost. You cannot assume that there is no change in overhead cost.
Stmnt 2 tells us that if total cost was 120, 100 was overhead cost and production cost was 20. We know how 20 changed. But we also need to know whether and how 100 changed to know how 120 changed.

Hence, both statements are needed.

Answer (C)
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   28 May 2017, 20:05
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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.

Show Spoiler
Guys i marked B but its wrong.

Pls discuss


Goal: determine the exact percent increase/decrease in the total cost of producing item X in January. In order to arrive at a specific value, we need to know the relative change for the overhead and production costs, since they sum to the total cost, as well as their relative size. We are told that production costs fell by 5%.

Statement 1) We know that the overhead cost increased by 13%, but we don't know its size or the size of the production costs. Insufficient.

Statement 2) We are told that the overhead costs are 5 times the production costs, but we don't know the size of either. Without the size, we can't do a weighted average to find the overall change. Insufficient.

Statements 1+2) We are told that the relative sizes of both as well as the change to the variable costs over the period we care about, so we can set up a weighted average formula:

1/6*(-5%) + 5/6(13%) = 10%

Sufficient.
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   17 Feb 2018, 06:00
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.

Show Spoiler
Guys i marked B but its wrong.

Pls discuss



Hi,

I saw many replies to this and people rejected B because QUESTION DOES NOT TELL US ABOUT CHANGES IN OVERHEAD COST!

My query is WHY ON EARTH ARE WE WORRIED ABOUT Overhead cost?


We are given
C= O+P

and P in January became = 95/100 *P
Cost in January will be = O + 95/100 * P

Statement 2 ) Before changes, O = 5P

So our original eqn will be

C= 6P ...................................... eqn 1 (before change)
C = 6 * 95/100 * P....................... eqn 2 (after change)

Hence we can find out percent change! isn't it?


I need help please GMATNinja bb VeritasPrepKarishma Bunuel
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   19 Feb 2018, 03:48
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rocko911 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.

Show Spoiler
Guys i marked B but its wrong.

Pls discuss



Hi,

I saw many replies to this and people rejected B because QUESTION DOES NOT TELL US ABOUT CHANGES IN OVERHEAD COST!

My query is WHY ON EARTH ARE WE WORRIED ABOUT Overhead cost?


We are given
C= O+P

and P in January became = 95/100 *P
Cost in January will be = O + 95/100 * P

Statement 2 ) Before changes, O = 5P

So our original eqn will be

C= 6P ...................................... eqn 1 (before change)
C = 6 * 95/100 * P....................... eqn 2 (after change)

Hence we can find out percent change! isn't it?


I need help please GMATNinja bb VeritasPrepKarishma Bunuel


The problem with your method is that you are assuming that the overhead cost REMAINS SAME. That may not be true.

Before changes, O = 5P
C = O + P
After changes O may not be 5 times P. What if O actually increases? Since P decreases in Jan, O will be more than 5 times P.
So you cannot write C = 5P + P for January.

Statement 1 should anyway give you a hint that statement 2 is not sufficient since you do not know the change in O. Stmnt 1 tells us that there is a change in O and the two statements cannot be in conflict.
Hope this helps.
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   12 Jun 2019, 00:35
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VeritasKarishma 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).


Quote:

In the ques if total cost is fixed cost + variable cost, then fixed cost should be fixed so therefore answer should be (B). I am not assuming anything. I am just considering fixed cost as fixed.

But most of the people answered option C as correct. Please help me.


What is the meaning of fixed cost of producing something? It is the overhead cost that must be paid irrespective of how many units are produced. For example, rent of the premises must be paid and is the same irrespective of whether you manufacture 10 units or 10,000.
Variable cost depends on number of units produced - say cost of raw material. If more units need to be produced, this cost is more.

Fixed cost does not mean that it cannot change. When you assume that fixed cost is the same month on month, you are assuming that say the rent has not increased etc.
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   11 Jul 2020, 02:02
man, you always rock!!

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.
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   16 Jun 2022, 21:08
I think B has to be sufficient here. From the day we started studying DS, we have been told that when evaluating each of statement 1) and 2), we need to evaluate them independently and in isolation.

1) here is clearly not sufficient. When we evaluate 2), this is the information we have with us:

a. Total cost = Fixed + Variable
b. Variable cost decreased by 5%
c. Fixed cost = 5 times of Variable cost

By what percent did the total cost of producing item X change in January?

We can answer this question. If nothing has been given about Fixed cost, surely we have to assume that it did not change. I don't think we need to account for the possibility that Fixed cost could have changed too, we need to operate strictly within the boundaries of the information provided to us. You would not need to account for such random assumptions in an official GMAT question, or even a GMATClub question for that matter.
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   25 Sep 2022, 09:11
KarishmaB wrote:
144144 wrote:
Karishma - can u plz post ur blogging that dealing with this weighted average system?


Here you go:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... ge-brutes/

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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.



KarishmaB
These links don't work anymore. Can you share updated links?
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The total cost of producing item X is equal to the sum of [#permalink] New post   26 Sep 2022, 03:58
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Namangupta1997 wrote:
KarishmaB wrote:
144144 wrote:
Karishma - can u plz post ur blogging that dealing with this weighted average system?


Here you go:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... ge-brutes/

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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.



KarishmaB
These links don't work anymore. Can you share updated links?


Namangupta1997
Please check my signature for the link to the relevant blog posts.
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Re: The total cost of producing item X is equal to the sum of [#permalink] New post   24 May 2023, 03:35
I was able to solve this question quickly without any calculation by using the mixtures / weighted averages concept.

Item 1: overhead cost
Item 2: production cost
Two items combined: total cost

"Weight" of item 1: Not given
"Weight" of item 2: Not given

"Average" % change of item 1: Not given
"Average" % change of item 2: 5%

S1. Provides the average % change of item 1 but we still need the relative weight of the two items to know how much each change in average impacts the combined item: total cost

INSUFFICIENT

S2. Provides relative weight of the two items but we now don't have the average % change of item 1

INSUFFICIENT

Combining the statements, we have all the info we need for a definitive value.

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