MGMAT CAT Problem...

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thp510: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Sat Apr 03, 2010 8:35 pmFollowed by: 1 member; Thanked: 1 times

by thp510 » Sat Feb 26, 2011 9:29 am

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.

OA: C. Why?

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Source: Beat The GMAT — Data Sufficiency | Sat Feb 26, 2011 9:29 am

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Sat Feb 26, 2011 9:56 am

thp510 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.

OA: C. Why?

X (old cost) = P (Production cost) + O (operating cost)
P' (new prod cost) = 0.95 P
x'(new cost) = kX = ?

Statement 1:
The overhead cost of producing item X increased by 13% in January.

O'(new operating cost) = 1.13 O
X' = 1.13 O + 0.95 P
X = O + P
We can't relate X and X' as there are equations in 2 vars (P and O) and we don't have any relationship b/w them. - Insufficient

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

O = 5P
=> X = O+P = 6P
No, info about the changes in the operating cost (it would have been nice to mention in the question though that there was a change in operating cost in Jan) - Insufficient

Combined :
X = 6P
X' = 1.13 O + 0.95 P = 1.13 * 5 P + 0.95 P = 6.6 P
So, we can calculate the % change in total cost (Here it is 10% ; 0.6/6 * 100). -- Sufficient C

Thanks
Anshu

(Every mistake is a lesson learned )

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Sat Feb 26, 2011 9:58 am

hi thp10
say overheadcost=a, and production cost=b. before january with total =(a+b)
in january overhead cost=a1, and production cost=0,95b with total cost in january (a1+0,95b)
we need to find
(a1+0,95b)/(a+b)-? (total cost in january/total cost before january)
(1)a1=1.13a,
(1.13a+0,95b)/(a+b)-unsovable as don`t know the values of a, b nether the relation between a and b
so insufficient
(2) a=5b insufficint as we dont know were any changes with overhead cost in january
both sufficient
(1.13*5b+0,95b)/(5b+b) from here we can cancel b and got exact number so suff

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eatpraylove: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Mon Jul 12, 2010 9:33 am

by eatpraylove » Sat Feb 26, 2011 10:24 am

Ans. (B)

C=O+P
After changes in Jan, C=O2+.95P

1)Statment 1 gives change in value of O, so now C=1.13O+.95P
But we still dont know the relation between O and P, so it remaines unsolved.
Insufficient

2)Statement 2 gives relation between O and P before Jan itself.
So C=O+P=>C=6P

From the statement we know P changed to .95P , so C=6*.95P
This is sufficient to find the new cost.

Ans:
C1=6*P
C2=6*0.95P=5.7P
Hence, %change=.3P/6P * 100 = 5%
Therefore, 5% reduction in overall cost of production.

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Sat Feb 26, 2011 10:29 am

aakanksha003 wrote:Ans. (B)

C=O+P
After changes in Jan, C=O2+.95P

1)Statment 1 gives change in value of O, so now C=1.13O+.95P
But we still dont know the relation between O and P, so it remaines unsolved.
Insufficient

2)Statement 2 gives relation between O and P before Jan itself.
So C=O+P=>C=6P

From the statement we know P changed to .95P , so C=6*.95P
This is sufficient to find the new cost.

Ans:
C1=6*P
C2=6*0.95P=5.7P
Hence, %change=.3P/6P * 100 = 5%
Therefore, 5% reduction in overall cost of production.

Right, as the question doesn't mention if there was any change in the operating cost in Jan.
However, the OA is C and is based on the assumption that there was a change in operating cost as well, as I briefly mentioned in the solution above. Should be made clear in the question.

Thanks
Anshu

(Every mistake is a lesson learned )

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eatpraylove: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Mon Jul 12, 2010 9:33 am

by eatpraylove » Sat Feb 26, 2011 10:39 am

Since by Statement 2, we know that total cost is dependent only on production cost (as the O factor has been replaced by P) using Statement 2, its irrelevant whether there was any change in overhead cost.

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Feb 26, 2011 10:47 am

Is this really MGMAT question? I find an answer (OA) to this problem confusing. We are given only total cost of producing item X. Then we are given variability in the costs of overhead and production for the month of January. Why we should assume that the previous cost accumulated should be directly proportional. It says that decrease of production costs in January was 5% and increase in overhead was 13%. Further it gives statement (2) with the overhead costs before January (accumulated till January) - where can we read in this question and/or its statements that the proportion of Overhead to Operational costs was constant throughout January i.e. 1:5? OP/OV could have resulting proportion of 1:5 with the last proportion of 1:30 too, e.g. 1/30 + 1/6 makes on average 1:5 (accumulated costs before January) and 2/15 proportion for the month before January - one assumption, which is quite possible but not exactly true. We are not advised about the business/production cycle in this DS i.e. whet it starts (begin in January, ends December?).

I found this DS with official answer A very confusing ... I would go for E

the numbers above could be anything like 1/10 + 1/10 too; the question is why we should assume that the proportion of costs was kept as constant when it doesn't say so?

thp510 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.

OA: C. Why?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Feb 26, 2011 11:58 am

thp510 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.

We can solve this problem with 0 calculations if we understand the concept of weighted averages. Remember, for data sufficiency we don't care what the answer is, just whether we can find one.

We want to find the percent change in total cost; we know the % change in production cost, but we don't know the % change in overhead cost or the proportion of total cost made up by production and overhead.

So, to solve we need the weights of production and overhead in the total cost and the change in overhead cost.

(1) overhead cost change, but still don't know the weights: insufficient.

(2) weights (before changes, production have 5/6 weight and overhead had 1/6 weight), but no info about changes to overhead: insufficient.

Combined: we now have production change, overhead change and the weights: sufficient, choose (C).

If you wanted to actually set up equations to help you understand the concepts:

total % change = (weight of production)(production % change) + (weight of overhead)(overhead % change)

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Feb 26, 2011 12:38 pm

thp510 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.

OA: C. Why?

An easy way to determine whether the two statements combined are sufficient:

1) Plug in twice.
2) If the ratio of old total:new total is the same in each case, the two statements are sufficient. If the ratio of old total:new total is not the same in each case, the two statements are insufficient.

Before January:
Production cost = 100, overhead cost = 5*100 = 500, total cost = 100+500 = 600.
In January:
Production cost = .95*100 = 95, overhead cost 1.13*500= 565, total cost = 95+565 = 660.
Old total:new total = 600:660.

Before January:
Production cost = 200, overhead cost = 5*200 = 1000, total cost = 200+1000 = 1200.
In January:
Production cost = .95*200 = 190, overhead cost 1.13*1000 = 1130, total cost = 190+1130 = 1320.
Old total:new total = 1200:1320 = 600:660.

Since the ratio of old total:new total is the same in each case, sufficient.

The correct answer is C.

Last edited by GMATGuruNY on Sat Feb 26, 2011 1:00 pm, edited 2 times in total.

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Feb 26, 2011 12:43 pm

where can we read in this question and/or its statements that the proportion of Overhead to Operational costs was constant before the required month of January i.e. 1:5?

all solutions are based on one assumption made by us and not stated in the question: Production costs/Overhead Costs=const

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Feb 26, 2011 12:49 pm

Hi,

let's take a look at statement (2):

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

Do we need this ratio to hold constant? No, in fact based on the info in the stem and (1), we know that it won't hold constant (since each is changing by a different percent). We just needed a starting point from which to apply the changes.

For example, if we pick:

starting prod cost = 500
starting overhead cost = 100
old total cost = 600

(holding our 5:1 ratio pre-January changes), we get:

new prod cost = 475
new overhead cost = 113
new total cost = 588

and we can certainly calculate the percent change from 600 to 588.

Using variables instead of numbers:

V= starting overhead cost
P = starting production cost
P = 5V
starting total cost = 6V

new prod cost = .95(5V)
new overhead cost = 1.13V
new total cost = .95(5V) + 1.13V

% change = (new - old)/old * 100%
% change = ((4.75V + 1.13V) - 6V)/6V * 100%

the Vs will cancel out, so we have a definite answer.

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