Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 11:00

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Running at their respective constant rate, machine X takes 2

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 909
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 13

Kudos [?]: 189 [0], given: 18

GMAT Tests User
Running at their respective constant rate, machine X takes 2 [#permalink] New post 22 Mar 2009, 20:53
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (03:04) correct 39% (03:35) wrong based on 42 sessions
Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

A. 4
B. 6
C. 8
D. 10
E. 12

OPEN DISCUSSION OF THIS QUESTION IS HERE: running-at-their-respective-constant-rate-machine-x-takes-98599.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Sep 2013, 09:51, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
1 KUDOS received
Manager
Manager
avatar
Joined: 07 Feb 2009
Posts: 50
Followers: 0

Kudos [?]: 12 [1] , given: 1

Re: PS: Machine rates [#permalink] New post 22 Mar 2009, 23:03
1
This post received
KUDOS
What is the OA?

I got E. 12

Explanation:
Suppose Y takes t days to deliver w work, then X takes t+2 days for w work.
We can also say that, X works w/(t+2) work in 1 day and Y works w/t work in 1 day.
So, if X & Y work together they deliver [w/(t+2)+w/t] work in 1 day.
So, X+Y work 3*[w/(t+2)+w/t] in 3 days, which is equal to 5w/4 work.
so, 3*[w/(t+2)+w/t] = 5w/4
or, 3*[1/(t+2)+1/t] = 5/4
or, (2t+2)/t(t+2) = 5/12
or, 24t+24 = 5t^2+10t
or, 5t^2+-14t-24=0
or, 5t^2-20t+6t-24=0
or, 5t(t-4)+6(t-4) = 0
or,(t-4)(5t+6)=0
so, t=4 or t=-6/5
time can't be a negative value.
hence, t=4 days

So, X does w work in t+2 days or in 4+2=6 days
hence X does 2w work in 12 days.
Manager
Manager
User avatar
Joined: 22 Feb 2006
Posts: 97
Followers: 1

Kudos [?]: 2 [0], given: 0

PS. Rate with variables. [#permalink] New post 26 May 2009, 15:57
Could you guys provide your logic? Thank you,
----
(Test 1) Q26:
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A. 4
B. 6
C. 8
D. 10
E. 12
Intern
Intern
avatar
Joined: 17 May 2009
Posts: 10
Location: USA
Schools: Kellogs, Wharton, Chicago
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: PS. Rate with variables. [#permalink] New post 26 May 2009, 17:44
let machine y takes n days to produce w
==> x will take n+2 days.
one day produce of y = (w)/(n)
one day produce of x = (w)/(n+2)
in 3 days both working together will produce = (3w)/(n) + (3w)/(n+2) =5w/4 (given)
==> w will get cancel in this equation as common in RHS and LHS
==> 5n^2-14n-24 = 0
==> n = 4 (ignore the -ve as days cannot be -ve)
==> x one day produce = w/(4+2)
==> x will take 12 days to produce 2w.
Ans = 12.
Senior Manager
Senior Manager
avatar
Joined: 08 Jan 2009
Posts: 332
Followers: 2

Kudos [?]: 63 [0], given: 5

GMAT Tests User
Re: PS. Rate with variables. [#permalink] New post 26 May 2009, 17:46
Y takes a days = w
X take a+2 days = w

X + Y takes 3 days = 5/4w
X+Y = 5 / 12 w

w/a + w/a+2 = 5/12w

1/a + 1/a+2 = 5/12

solve u will get 5a^2 - 14a -24 = 0

solving the eqn a = 4 and a = -6/5

a has to be +ve so a = 4

X will take 6 days = w
X will take 12 days = 2w

Ans E

X wi
Manager
Manager
User avatar
Joined: 08 Feb 2009
Posts: 147
Schools: Anderson
Followers: 3

Kudos [?]: 31 [0], given: 3

Re: PS. Rate with variables. [#permalink] New post 29 May 2009, 17:34
TriColor wrote:
BTW, have any of you thought of using substitution method instead?

I would like to see if there is a faster and smarter method of solving this problem. Thank you.



The faster way would save time on solving the quadratic equation.

To get to the point of quadratic equation it would take about 30 seconds.
Assuming, (a + 2) is the number of days it takes X to produce w widgets, we need to find 2 (a + 2) = 2a + 4.
For every answer choice subtract 4 and divide by two.

Choice a : Eliminate this as answer choice because 2a + 4 will be more than 4

Choice b : \frac{6-4}{2} = 1

Choice c : \frac{8-4}{2} = 2

Choice d : \frac{10-4}{2} = 3

Choice e : \frac{12-4}{2} = 4


Substitute 1,2,3 and 4 into the quadratic. Since 4 satisfies the quadratic, that is the answer.
Although the explanation seems long, the calculations will be faster as they are just simple calculations.
Manager
Manager
User avatar
Joined: 12 May 2009
Posts: 54
Followers: 2

Kudos [?]: 46 [0], given: 18

Re: PS: Machine rates [#permalink] New post 20 Jul 2009, 15:07
Hi guys!

sorry to bring this post up again but I need some guidance to beat this problem!

So here what I have trouble understanding:

(1) The text states that the 2 machines combined can produce 5/4w units in 3 hours. So 5/4w is the work output and 3 hours is the time, giving us 5/4w=5/12w*3 (pls correct me if my reasoning is wrong)

(2) Now, we need to set-up the equation for the combined rate:

5/12w=w/t + w/(t+2) (THAT'S WHAT EVERYONE ELSE GOT; I get something different; see below)

5/12w=(5/4w)/t + (5/4w)/(t+2) (See what I did? Since the rate 5/12w is related to the work output 5/4w, we need to take this into consideration when setting up the equation, right?)

I hope someone can trace my wrong reasoning and give me a hint how to solve this kind of problem in the future.

Thank you very much!
Steve
Manager
Manager
User avatar
Joined: 13 Aug 2009
Posts: 204
Schools: Sloan '14 (S)
Followers: 3

Kudos [?]: 73 [0], given: 16

GMAT Tests User
Re: PS: Machine rates [#permalink] New post 17 Aug 2009, 07:24
Here is how I solved it:

let Y = number of days for machine Y to produce w widgets

Rate of Y = w widgets / Y days
Rate of X = w widgets / (Y+2) days

Formula: Rate (together) = Rate of Machine X + Rate of Machine Y

(5/4)*w/3 = w/Y+w/(Y+2)
or
(5/4)/3 = 1/Y+1/(Y+2)

simplify:

5*Y^2-14Y-24=0

then I used the quadratic formula to get Y = 4

therefore,

2w widgets * 1/Rate of X
2w widgets * (Y+2) days / w widgets
2w widgets * 6 days / w widgets = 12 days

ANSWER: E. 12 days
1 KUDOS received
Manager
Manager
avatar
Joined: 17 Dec 2007
Posts: 106
Followers: 0

Kudos [?]: 49 [1] , given: 8

Re: PS: Machine rates [#permalink] New post 17 Aug 2009, 08:23
1
This post received
KUDOS
h2polo wrote:
Here is how I solved it:

let Y = number of days for machine Y to produce w widgets

Rate of Y = w widgets / Y days
Rate of X = w widgets / (Y+2) days

Formula: Rate (together) = Rate of Machine X + Rate of Machine Y

(5/4)*w/3 = w/Y+w/(Y+2)
or
(5/4)/3 = 1/Y+1/(Y+2)

simplify:

5*Y^2-14Y-24=0

then I used the quadratic formula to get Y = 4

therefore,

2w widgets * 1/Rate of X
2w widgets * (Y+2) days / w widgets
2w widgets * 6 days / w widgets = 12 days

ANSWER: E. 12 days


I went the following route

let work done by y in a day = w/y
work done by x in a day = w/y+2

now (w/y+w/y+2 )*3 = 5/4w
writing y in terms of x, then y+2 = x and y = x-2

(1/x+1/x-2)*3w = 5/4w

12(2x-2) = 5(x*x - 2x)

solving the quantratic equation , you get x = 6 ; x = 5/4

so X can make w widgets in 6 days , hence 2w in 12 days
Manager
Manager
User avatar
Joined: 13 Aug 2009
Posts: 204
Schools: Sloan '14 (S)
Followers: 3

Kudos [?]: 73 [0], given: 16

GMAT Tests User
Re: PS. Rate with variables. [#permalink] New post 17 Aug 2009, 11:43
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A. 4
B. 6
C. 8
D. 10
E. 12

let Y = number of days for machine Y to produce w widgets

Rate of Y = w widgets / Y days
Rate of X = w widgets / (Y+2) days

Formula: Rate (together) = Rate of Machine X + Rate of Machine Y

(5/4)*w/3 = w/Y+w/(Y+2)
or
(5/4)/3 = 1/Y+1/(Y+2)

simplify:

5*Y^2-14Y-24=0

then I used the quadratic formula to get Y = 4

therefore,

2w widgets * 1/Rate of X
2w widgets * (Y+2) days / w widgets
2w widgets * 6 days / w widgets = 12 days

ANSWER: E. 12 days
Director
Director
avatar
Joined: 03 Aug 2012
Posts: 883
Concentration: General Management, General Management
Schools: IIM A '15
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
Followers: 11

Kudos [?]: 158 [0], given: 298

Premium Member CAT Tests
Re: PS. Rate with variables. [#permalink] New post 28 Sep 2013, 09:58
Directly to the equation:

w/t + w/(t+2) = (w)5/12

5t^2 - 14t -24 =0

t=4

For w widgets machine x takes t+2 = 6

For 2w it would take 12

_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Intern
Intern
avatar
Joined: 28 Sep 2013
Posts: 14
Followers: 0

Kudos [?]: 3 [0], given: 34

CAT Tests
Re: PS. Rate with variables. [#permalink] New post 28 Sep 2013, 10:43
There are so many questions here i have only 5 weeks left, can some one advice me how to use this fiorum.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 17 Apr 2013
Posts: 499
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT Date: 11-30-2013
GPA: 3.3
Followers: 1

Kudos [?]: 35 [1] , given: 231

Re: PS. Rate with variables. [#permalink] New post 28 Sep 2013, 10:44
1
This post received
KUDOS
crunchboss wrote:
There are so many questions here i have only 5 weeks left, can some one advice me how to use this fiorum.



You cant solve all the qns, its tempting for quant you can solve collection of expert faculty bunuel, all questions are there in his signature.

_________________

Like my post Send me a Kudos :) It is a Good manner.

Intern
Intern
avatar
Joined: 28 Sep 2013
Posts: 14
Followers: 0

Kudos [?]: 3 [0], given: 34

CAT Tests
Re: PS. Rate with variables. [#permalink] New post 28 Sep 2013, 10:45
honchos wrote:
crunchboss wrote:
There are so many questions here i have only 5 weeks left, can some one advice me how to use this fiorum.



You cant solve all the qns, its tempting for quant you can solve collection of expert faculty bunuel, all questions are there in his signature.


how can I get his qns are they Free?
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 17 Apr 2013
Posts: 499
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT Date: 11-30-2013
GPA: 3.3
Followers: 1

Kudos [?]: 35 [1] , given: 231

Re: PS. Rate with variables. [#permalink] New post 28 Sep 2013, 10:48
1
This post received
KUDOS
crunchboss wrote:
honchos wrote:
crunchboss wrote:
There are so many questions here i have only 5 weeks left, can some one advice me how to use this fiorum.



You cant solve all the qns, its tempting for quant you can solve collection of expert faculty bunuel, all questions are there in his signature.


how can I get his qns are they Free?



this is the bunels ID-
members/member-73391.html

His signature has links to all the execellent questions, you can alternatively purchase gmatlcub.com tests also.

_________________

Like my post Send me a Kudos :) It is a Good manner.

Intern
Intern
avatar
Joined: 28 Sep 2013
Posts: 14
Followers: 0

Kudos [?]: 3 [0], given: 34

CAT Tests
Re: PS. Rate with variables. [#permalink] New post 28 Sep 2013, 10:50
This forum has free SC videos also.
Senior Manager
Senior Manager
avatar
Joined: 17 Apr 2013
Posts: 499
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT Date: 11-30-2013
GPA: 3.3
Followers: 1

Kudos [?]: 35 [0], given: 231

Re: PS. Rate with variables. [#permalink] New post 28 Sep 2013, 10:52
crunchboss wrote:
This forum has free SC videos also.


No, Please take some time to visit this forum before posting so many questions...

_________________

Like my post Send me a Kudos :) It is a Good manner.

Director
Director
avatar
Joined: 03 Aug 2012
Posts: 883
Concentration: General Management, General Management
Schools: IIM A '15
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
Followers: 11

Kudos [?]: 158 [0], given: 298

Premium Member CAT Tests
Re: PS. Rate with variables. [#permalink] New post 29 Sep 2013, 02:18
crunchboss wrote:
There are so many questions here i have only 5 weeks left, can some one advice me how to use this fiorum.



Do questions in the topics in which you are weak.

For example, this weekend I dedicated my time to Rate/Work problems as I was weak in this section and now I am not :-D

_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22272 [0], given: 2610

Re: Running at their respective constant rate, machine X takes 2 [#permalink] New post 29 Sep 2013, 09:52
Expert's post
Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.
A. 4
B. 6
C. 8
D. 10
E. 12

For work problems one of the most important thin to know is rate*time=job \ done.

Let the time needed for machine X to produce w widgets be t days, so the rate of X would be rate=\frac{job \ done}{time}=\frac{w}{t};

As "machine X takes 2 days longer to produce w widgets than machines Y" then time needed for machine Y to produce w widgets would be t-2 days, so the rate of Y would be rate=\frac{job \ done}{time}=\frac{w}{t-2};

Combined rate of machines X and Y in 1 day would be \frac{w}{t}+\frac{w}{t-2} (remember we can sum the rates). In 3 days two machines together produce 5w/4 widgets so: 3(\frac{w}{t}+\frac{w}{t-2})=\frac{5w}{4} --> \frac{w}{t}+\frac{w}{t-2}=\frac{5w}{12}.

\frac{w}{t}+\frac{w}{t-2}=\frac{5w}{12} --> reduce by w --> \frac{1}{t}+\frac{1}{t-2}=\frac{5}{12}.

At this point we can either solve quadratic equation: 5t^2-34t+24=0 --> (t-6)(5t-4)=0 --> t=6 or t=\frac{4}{5} (which is not a valid solution as in this case t-2=-\frac{6}{5}, the time needed for machine Y to ptoduce w widgets will be negatrive value and it's not possible). So t=6 days is needed for machine X to produce w widgets, hence time needed for machine X to produce 2w widgets will be 2t=12 days.

OR try to substitute the values from the answer choices. Remember as we are asked to find the time needed for machine X alone to produce 2w widgets then the answer should be 2t among answer choices: E work - 2t=12 --> t=6 --> \frac{1}{6}+\frac{1}{6-2}=\frac{5}{12}.

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: running-at-their-respective-constant-rate-machine-x-takes-98599.html

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22272 [0], given: 2610

Re: PS. Rate with variables. [#permalink] New post 29 Sep 2013, 09:53
Expert's post
crunchboss wrote:
There are so many questions here i have only 5 weeks left, can some one advice me how to use this fiorum.


Go through this post "All you need for Quant": new-to-the-math-forum-please-read-this-first-140445.html

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: PS. Rate with variables.   [#permalink] 29 Sep 2013, 09:53
    Similar topics Author Replies Last post
Similar
Topics:
Running at their respective constant rates, machine X takes ricokevin 2 11 Mar 2007, 17:07
Running at their respective constant rates, machine X takes Iawfy 2 29 Dec 2006, 18:51
Running at their respective constant rates, machine X takes joemama142000 3 06 Feb 2006, 21:56
Running at their respective constant rates, machine X takes duttsit 6 07 Dec 2005, 14:43
Running at their respective constant rates, machine X takes chunjuwu 3 22 Aug 2004, 02:18
Display posts from previous: Sort by

Running at their respective constant rate, machine X takes 2

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.