It is currently 22 Jun 2017, 09:53

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Working simultaneously and independently at an identical

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

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 28 Aug 2010
Posts: 257
Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 10 Dec 2010, 06:21
1
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (02:15) correct 23% (01:50) wrong based on 471 sessions

HideShow timer Statistics

Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8
[Reveal] Spoiler: OA

_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Expert Post
4 KUDOS received
Math Expert
User avatar
D
Joined: 02 Sep 2009
Posts: 39587
Re: Rate problem [#permalink]

Show Tags

New post 10 Dec 2010, 06:37
4
This post received
KUDOS
Expert's post
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8


The rate of 4 machines is rate=job/time=x/6 units per day --> the rate of 1 machine 1/6*(x/6)=x/24 units per day;

Now, again as {time}*{combined rate}={job done} then 4*(m*x/24)=3x --> m=18.

Or as 3 times more job should be done in 1.5 times less days than 3*1.5=4.5 times more machines will be needed 4*4.5=18.

Answer: B.
_________________

New to the Math Forum?
Please read this: 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

3 KUDOS received
Intern
Intern
User avatar
Joined: 31 Aug 2014
Posts: 23
GMAT ToolKit User CAT Tests
Re: Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 14 Sep 2015, 06:54
3
This post received
KUDOS
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8


solving in shortcut

m1 d1 h1 / w1 = m2 d2 h2/w2
4x6/x = mx4/3x

solving we get m=18

answer b

press kudos if you love my shortcut :-D
_________________

Please press+ 1kudos if you appreciate this post and for motivation !!

2 KUDOS received
Manager
Manager
avatar
Status: swimming against the current
Joined: 24 Jul 2009
Posts: 244
Location: Chennai, India
Re: Rate problem [#permalink]

Show Tags

New post 10 Dec 2010, 06:33
2
This post received
KUDOS
3
This post was
BOOKMARKED
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8


4 machines and 6 days so the total work done is 24

4x6=24
now 3 times the work is 72

So in 4 days if the work is to be completed its 72/4 = 18
_________________

Gonna make it this time

2 KUDOS received
SVP
SVP
User avatar
B
Joined: 14 Apr 2009
Posts: 2085
Location: New York, NY
Re: Rate problem [#permalink]

Show Tags

New post 21 Sep 2012, 15:19
2
This post received
KUDOS
1
This post was
BOOKMARKED
This is a variation of the Distance = Rate * Time

Except we modify and say Output = # Machines * (Rate * Time)

X = # * r*t

X = 4 * r * 6
x = 24r
r = x/24

Solve for r because we want to find out the rate...then apply that rate to the new situation, which is output of 3x in 4 days

3x = N * r * 4

3x = N * (x/24) * 4
3x = N * (x/6)

18x = N *x
18 = N
2 KUDOS received
Intern
Intern
avatar
Joined: 09 Apr 2016
Posts: 1
Re: Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 09 Apr 2016, 15:05
2
This post received
KUDOS
4 machines can do x work in 6 days
4 machines can do x/6 work in 1 day
1 machine can do x/6*1/4 work in 1 day

so,

n machines in 4 days= 3x work
n machines in 1 day = n * (x/6*1/4)
n machines in 4 days = n * (x/6*1/4)*4

Hence, n machines can do n*(x/6*1/4)*4 work in 4 days i.e. n*(x/6*1/4)*4 =3x ====>>>> n=18
2 KUDOS received
Manager
Manager
User avatar
B
Joined: 20 Jan 2017
Posts: 65
Location: United States (NY)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
Re: Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 30 Jan 2017, 04:45
2
This post received
KUDOS
1) First let's set up an equation for the 4 machines and find a rate of each machine: \(4r*6=x; 4r=\frac{x}{6}, r=\frac{x}{6}*\frac{1}{4}, r=\frac{x}{24}\)
2) Now let's set up an equation for 3x units: let N be the number of machines, then \(N*\frac{x}{24}*4=3x; N*\frac{x}{6}=3x, N=\frac{3x}{x/6}=18\)

The correct answer is B.
1 KUDOS received
Manager
Manager
avatar
Joined: 25 Jun 2012
Posts: 71
Location: India
WE: General Management (Energy and Utilities)
Re: Rate problem [#permalink]

Show Tags

New post 21 Sep 2012, 11:16
1
This post received
KUDOS
Rate*Time = Work
(4R)*(6)=x ( Total 4 machines)
therefore R=x/24

now again (n)*(x/24)*(4) = 3x

solving for n, we get n=18 nos.
1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: Rate problem [#permalink]

Show Tags

New post 21 Sep 2012, 12:42
1
This post received
KUDOS
1
This post was
BOOKMARKED
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8



4 machines----------x units-----------6days
4 machines---------3x units-----------3*6 = 18 days
M machines---------3x unites----------4 days
The number of days and the number of machines which produce a certain number of units (in this case 3x) are inversely proportional.
This is because all the machines have the same constant rate.
Necessarily 4*18=M*4, therefore M = 18.

Answer B
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 14 Nov 2012, 06:50
\(\frac{4}{m}=\frac{x}{6}==>m=\frac{24}{x}\)

Calculate number of machines to produce 3x in 4 days:

\(N(\frac{x}{24})(4)=3x==> N=18\)
_________________

Impossible is nothing to God.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15912
Premium Member
Re: Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 09 Sep 2015, 19:47
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
avatar
B
Joined: 25 Jun 2016
Posts: 61
GMAT 1: 780 Q51 V46
Re: Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 08 Jan 2017, 17:41
Here's a way to solve this question quickly:



Here's a more in-depth look at a reliable approach for combined work questions with multiple identical machines:

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1044
Re: Working simultaneously and independently at an identical [#permalink]

Show Tags

New post 02 Feb 2017, 11:58
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8


We are given that 4 machines can complete x units in 6 days. Thus, the rate of the 4 machines is x/6.

Next we need to determine the number of machines needed to produce a rate of 3x/4. To calculate that number of machines, we can use the following proportion in which the value in each numerator is the number of machines and the value in each denominator is the corresponding rate of those machines. We can let n = the number of machines needed:

4/(x/6) = n/(3x/4)

24/x = 4n/3x

72x = 4nx

18 = n

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: Working simultaneously and independently at an identical   [#permalink] 02 Feb 2017, 11:58
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Three machines are operating simultaneously and independently at diffe Bunuel 4 17 Apr 2017, 12:43
49 Experts publish their posts in the topic Working simultaneously and independently at an identical constant rate Bunuel 17 08 Oct 2016, 21:06
31 Experts publish their posts in the topic Three machines operating independently, simultaneously, and kiseki 8 17 Jul 2016, 12:48
42 Experts publish their posts in the topic Two water pumps, working simultaneously at their respective kmasonbx 21 10 Jun 2017, 14:23
135 Experts publish their posts in the topic Working simultaneously at their respective constant rates, M Walkabout 30 03 Jun 2017, 06:44
Display posts from previous: Sort by

Working simultaneously and independently at an identical

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


GMAT Club MBA Forum Home| About| 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®.