GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Aug 2018, 15:15

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 28 May 2010
Posts: 31
The total cost of producing item X is equal to the sum of  [#permalink]

Show Tags

New post 18 Jul 2010, 20:54
4
6
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:08) correct 37% (01:14) wrong based on 624 sessions

HideShow timer Statistics

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...
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48110
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 18 Jul 2010, 21:44
8
8
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: Total Cost of Producing item X  [#permalink]

Show Tags

New post 05 Oct 2011, 03:15
5
1
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).
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Most Helpful Community Reply
Intern
Intern
User avatar
Joined: 05 Mar 2013
Posts: 44
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06-05-2013
GPA: 3.2
Re: The total cost of producing item X  [#permalink]

Show Tags

New post 15 May 2013, 01:28
8
1
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
_________________

"Kudos" will help me a lot!!!!!!Please donate some!!!

Completed
Official Quant Review
OG - Quant


In Progress
Official Verbal Review
OG 13th ed
MGMAT IR
AWA Structure

Yet to do
100 700+ SC questions
MR Verbal
MR Quant


Verbal is a ghost. Cant find head and tail of it.

General Discussion
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 787
Reviews Badge
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 06 May 2011, 21:52
1
Karishma
Pls can you verify this solution. I think this is a weighted average problem. :-D

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...
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 07 May 2011, 11:13
2
gmat1220 wrote:
Karishma
Pls can you verify this solution. I think this is a weighted average problem. :-D

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! :)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 351
WE 1: Business Development
GMAT ToolKit User
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 07 May 2011, 11:28
Karishma - can u plz post ur blogging that dealing with this weighted average system?
_________________

GMAT Club Premium Membership - big benefits and savings

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
avatar
Joined: 31 May 2011
Posts: 81
Location: India
Concentration: Finance, International Business
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Re: Total Cost of Producing item X  [#permalink]

Show Tags

New post 03 Oct 2011, 07:51
2
3
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
Intern
Intern
avatar
Joined: 01 Apr 2013
Posts: 17
Schools: Tepper '16 (S)
GMAT ToolKit User
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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 ?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48110
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 09 Apr 2013
Posts: 195
Location: United States
Concentration: Finance, Economics
GMAT 1: 710 Q44 V44
GMAT 2: 740 Q48 V44
GPA: 3.1
WE: Sales (Mutual Funds and Brokerage)
Re: The total cost of producing item X is equal to the sum of  [#permalink]

Show Tags

New post 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.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: The total cost of producing item X is equal to the sum of  [#permalink]

Show Tags

New post 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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
avatar
Joined: 02 Sep 2012
Posts: 224
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Re: The total cost of producing item X is equal to the sum of  [#permalink]

Show Tags

New post 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
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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. :-D

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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Director
Director
User avatar
P
Joined: 27 May 2012
Posts: 536
Premium Member
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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)
_________________

- Stne

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Director
Director
User avatar
P
Joined: 27 May 2012
Posts: 536
Premium Member
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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.
_________________

- Stne

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: very hard - MGMAT  [#permalink]

Show Tags

New post 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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
Joined: 05 Feb 2014
Posts: 43
Re: The total cost of producing item X is equal to the sum of it  [#permalink]

Show Tags

New post 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

Go to page    1   2    Next  [ 26 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.