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.
This question was posted in the past and I am not very convinced with the explanations given in the past.
The ans according to MG is 'C' which is logical if it was somehow stated that the fixed cost also changed during the period. (I am not assuming anything based on the word "fixed" in the cost.. thinking of it as any other cost which is adding towards total cost, but the stem of the question never states that the other contributing cost also changed in the period..).
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- amar.singh
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- andrew.k.john
- Course Students
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- Joined: Sun Jun 07, 2009 3:17 pm
Re: DS: The total cost of producing...
Hi Amar.
I will take a stab at addressing your question. Let's begin establishing a baseline for the questions, and then address facts (1) and (2) seperately. We can then address the facts together.
To establish a baseline, let's use what is given in the question itself.
For any given period, T = V + F. We want to see if we can use the percent changes in V and F to determine the percent change in T. Since we know that there is a 5% decrease in V, we change the equation to T = .95V + F.
Fact (1): The fixed cost of producing item X increased by 13% in January.
We know now that T = .95V + 1.13F. However, we don't know the weighting of V and F to start, so Fact(1) alone cannot answer the question. Here are some real numbers to illustrate.
If V = 100 and F = 100 to start, then T = 200. With the price changes, we have V = 95 and F = 113, so T = 208, which is a 4% increase.
However, if V = 100 and F = 200 to start, then T = 300. The changes result in V = 95 and F = 226, so T = 321, which is a 7% increase. We can eliminate A and D because (1) is insufficient.
Fact (2): Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X.
This new fact tells us the ratio of V and F before any changes, so T = V + F = V + 5V. We have that the variable cost goes down 5%, but what is NOT given is the percent change in F. The ratio that is given in Fact(2) will not necessarily hold true after the changes in V and F. (2) is insufficient, so we eliminate B.
Fact (1) and (2): If we know T = V + F = V + 5V before any changes, and we know V turns into .95V, and F turns into 1.13F = 5.65V, then the new T = .95V + 5.65V = 6.6V, which is a definitive 10% increase in T. (1) and (2) together are sufficient. Answer is C.
I will take a stab at addressing your question. Let's begin establishing a baseline for the questions, and then address facts (1) and (2) seperately. We can then address the facts together.
To establish a baseline, let's use what is given in the question itself.
For any given period, T = V + F. We want to see if we can use the percent changes in V and F to determine the percent change in T. Since we know that there is a 5% decrease in V, we change the equation to T = .95V + F.
Fact (1): The fixed cost of producing item X increased by 13% in January.
We know now that T = .95V + 1.13F. However, we don't know the weighting of V and F to start, so Fact(1) alone cannot answer the question. Here are some real numbers to illustrate.
If V = 100 and F = 100 to start, then T = 200. With the price changes, we have V = 95 and F = 113, so T = 208, which is a 4% increase.
However, if V = 100 and F = 200 to start, then T = 300. The changes result in V = 95 and F = 226, so T = 321, which is a 7% increase. We can eliminate A and D because (1) is insufficient.
Fact (2): Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X.
This new fact tells us the ratio of V and F before any changes, so T = V + F = V + 5V. We have that the variable cost goes down 5%, but what is NOT given is the percent change in F. The ratio that is given in Fact(2) will not necessarily hold true after the changes in V and F. (2) is insufficient, so we eliminate B.
Fact (1) and (2): If we know T = V + F = V + 5V before any changes, and we know V turns into .95V, and F turns into 1.13F = 5.65V, then the new T = .95V + 5.65V = 6.6V, which is a definitive 10% increase in T. (1) and (2) together are sufficient. Answer is C.
- amar.singh
- Posts: 2
- Joined: Sun Sep 09, 2007 3:20 pm
Re: DS: The total cost of producing...
Hey Andrew,
Thanks for the much detailed response. I am not convinced and I would illustrate by a similar example.
Q. The perimeter of a rectangle is twice the sum of length and width. A rectangular object was re-sized, find the percentage change in the perimeter when the width was reduced by 5%.
1. the percentage change in length was 3%.
2. the ratio between length and width is 3:1 (before resize).
What would you choose as your answer ?
Thanks for the much detailed response. I am not convinced and I would illustrate by a similar example.
Q. The perimeter of a rectangle is twice the sum of length and width. A rectangular object was re-sized, find the percentage change in the perimeter when the width was reduced by 5%.
1. the percentage change in length was 3%.
2. the ratio between length and width is 3:1 (before resize).
What would you choose as your answer ?
- andrew.k.john
- Course Students
- Posts: 13
- Joined: Sun Jun 07, 2009 3:17 pm
Re: DS: The total cost of producing...
my answer to your proposed question would be exactly the same, assuming your fact 1 means to say that length INCREAES by 3%, not just CHANGES. You need both facts to answer the question, but given both facts, you can find an answer.
Please elaborate on which parts are not convincing. Additionally, please tell me what you think the right answer is and why.
If you are still not convinced for the reasons stated in your original question, then I will try to address those. Here is the passage I'm referring to...
"The ans according to MG is 'C' which is logical if it was somehow stated that the fixed cost also changed during the period. (I am not assuming anything based on the word "fixed" in the cost.. thinking of it as any other cost which is adding towards total cost, but the stem of the question never states that the other contributing cost also changed in the period..)."
The stem of the question doesn't mention anything about fixed costs changing. You are correct about this. But it doesn't have to. This fact is given in fact 1. Without this fact, you cannot determine the % change in the total cost. However, this fact alone is not sufficient to determine total cost, as illustrated in my example using real numbers. This fact needs to be paired with fact 2, which deals with the ratios between fixed and variable costs, for us to determine to % change in total cost.
Please elaborate on which parts are not convincing. Additionally, please tell me what you think the right answer is and why.
If you are still not convinced for the reasons stated in your original question, then I will try to address those. Here is the passage I'm referring to...
"The ans according to MG is 'C' which is logical if it was somehow stated that the fixed cost also changed during the period. (I am not assuming anything based on the word "fixed" in the cost.. thinking of it as any other cost which is adding towards total cost, but the stem of the question never states that the other contributing cost also changed in the period..)."
The stem of the question doesn't mention anything about fixed costs changing. You are correct about this. But it doesn't have to. This fact is given in fact 1. Without this fact, you cannot determine the % change in the total cost. However, this fact alone is not sufficient to determine total cost, as illustrated in my example using real numbers. This fact needs to be paired with fact 2, which deals with the ratios between fixed and variable costs, for us to determine to % change in total cost.
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: DS: The total cost of producing...
hi -
a couple of things.
(1) i'm not sure exactly what you're asking here; i don't see an actual question in your post.
if you're not convinced that the answer is (c), then what do you propose is the answer to the question, and why?
(2) if the question stem doesn't state that the FC has changed, then the FC could EITHER have changed (by any percentage that's possible) OR have stayed the same.
this is the case with ALL quantities that are not mentioned in "change over time" word problems: they may have changed, or they may not have changed. you must consider both possibilities.
note that this is also, happily, in EXACT accordance with the way these statements and assumptions work in the real world. Viz., let's say you have to go to the gas station (petrol station, perhaps, depending on where you live) to buy gas (petrol) and cigarettes. you tell your friend, "hey, i gotta go buy some gas and cigarettes." your friend tells you, "oh man, gas has gone up 50% in the last month."
this clearly does NOT imply that the price of cigarettes has remained exactly the same, just because your friend has neglected to mention (or just flat out doesn't know) that price.
same deal here, and in the "rectangle area" problem created by you. all the same. uncertainty is uncertainty.
remember that this is a data sufficiency problem. the WHOLE POINT is that there are things you know and things you don't know; figuring those things out is the essence of data sufficiency.
(3) you seem to be implying that you took the question stem to imply that the fixed cost remained constant. (correct me if i'm wrong here.)
first of all, that's just incorrect; see #2. you can't just make assumptions like that.
second, you KNOW that's not correct, since statement (1) describes a change in the fixed cost. if you interpret the question stem as implying that the fixed cost hasn't changed, then that is in direct contradiction of statement (1).
statements can't contradict the question stem (or contradict each other), so you know that interpretation is incorrect.
amar.singh Wrote:The ans according to MG is 'C' which is logical if it was somehow stated that the fixed cost also changed during the period. (I am not assuming anything based on the word "fixed" in the cost.. thinking of it as any other cost which is adding towards total cost, but the stem of the question never states that the other contributing cost also changed in the period..).
a couple of things.
(1) i'm not sure exactly what you're asking here; i don't see an actual question in your post.
if you're not convinced that the answer is (c), then what do you propose is the answer to the question, and why?
(2) if the question stem doesn't state that the FC has changed, then the FC could EITHER have changed (by any percentage that's possible) OR have stayed the same.
this is the case with ALL quantities that are not mentioned in "change over time" word problems: they may have changed, or they may not have changed. you must consider both possibilities.
note that this is also, happily, in EXACT accordance with the way these statements and assumptions work in the real world. Viz., let's say you have to go to the gas station (petrol station, perhaps, depending on where you live) to buy gas (petrol) and cigarettes. you tell your friend, "hey, i gotta go buy some gas and cigarettes." your friend tells you, "oh man, gas has gone up 50% in the last month."
this clearly does NOT imply that the price of cigarettes has remained exactly the same, just because your friend has neglected to mention (or just flat out doesn't know) that price.
same deal here, and in the "rectangle area" problem created by you. all the same. uncertainty is uncertainty.
remember that this is a data sufficiency problem. the WHOLE POINT is that there are things you know and things you don't know; figuring those things out is the essence of data sufficiency.
(3) you seem to be implying that you took the question stem to imply that the fixed cost remained constant. (correct me if i'm wrong here.)
first of all, that's just incorrect; see #2. you can't just make assumptions like that.
second, you KNOW that's not correct, since statement (1) describes a change in the fixed cost. if you interpret the question stem as implying that the fixed cost hasn't changed, then that is in direct contradiction of statement (1).
statements can't contradict the question stem (or contradict each other), so you know that interpretation is incorrect.
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