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

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03 Oct 2011, 07:26

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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 = T Production Cost = P Overhead Cost = O

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

A is insufficient because it doesn't tell us how the overhead and production costs relate

B is insufficient because it doesn't tell us how much the overhead costs changed

The answer is C, because with A and B together we know by what percentage both the overhead and production costs increased, as well as how they are proportional to each other.

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 O = Overhead costs P = production costs

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

AD/BCE

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: The total cost of producing item X [#permalink]

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15 May 2013, 01:30

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.

The answer would be [C]. Let the total cost of Production be X = O + P where, O - Overhead Cost P - Production Cost

In Jan, X1 = O1 + P1 = O1 + 95*P/100.

Statement 1: Now currently the above equation has 2 variables which determine the value of X. Statement 1 offers the rate of increase of O in Jan. But in the end, no relation can be established between O and P to represent X in common terms. Hence, its insufficient. The equation at this stage can be represented as:

X1 = 113*O/100 + 95*P/100, where X1 is the total cost of Product in Jan.

Statement 2 establishes a relation between O and P i.e. O = 5P, individually the above is insufficient since, we are unsure as to what changes happened in the Overhead cost in Jan. But when we combine the two statements we can find the change in values in terms of the old values easily.

Hence, both the statements are necessary. Please correct me if I am wrong

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.

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 it [#permalink]

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12 Jul 2015, 08:18

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

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02 Dec 2016, 12:50

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

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

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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.

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: