Last visit was: 24 Jul 2024, 15:34 It is currently 24 Jul 2024, 15:34
Toolkit
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

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.

# Three machines, individually, can do a certain job in 4, 5,

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94609
Own Kudos [?]: 643639 [43]
Given Kudos: 86737
Director
Joined: 03 Feb 2013
Posts: 793
Own Kudos [?]: 2606 [12]
Given Kudos: 567
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE:Engineering (Computer Software)
Math Expert
Joined: 02 Sep 2009
Posts: 94609
Own Kudos [?]: 643639 [9]
Given Kudos: 86737
General Discussion
Manager
Joined: 09 Apr 2013
Posts: 73
Own Kudos [?]: 332 [3]
Given Kudos: 24
Location: India
WE:Supply Chain Management (Consulting)
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
3
Kudos
Machine 1 in one hour can perform 1/4th job
Machine 2 in one hour can perform 1/5th job
Machine 3 in one hour can perform 1/6th job

Combinations of two machines working together can do 9/20, 10/24 and 11/30 parts of the job.

Now 9/20 is the greatest among the three combinations and hence B is the answer.
Intern
Joined: 10 May 2010
Posts: 4
Own Kudos [?]: 37 [7]
Given Kudos: 0
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
7
Kudos
Whenever you see a work problem, jot down the formula W=RT (Work = Rate*Time).

We are looking for the greatest amount of work that can be done in 1 hour, so we look at the two machines with the two fastest rates.
Specifically the machines that finish the job in 4 and 5 hours whose rates are 1/4 and 1/5 respectively. (To find the rate given the time: If a machine finishes a task in 4 hours we think of the completed task as 1, so by plugging into the formula, we have W=RT, 1 = R*4 or 1/4 =Rate)

Since the machines are working together we add the individual rates together.
W = R*T
W = (1/4+1/5)*1
W = 9/20
Manager
Joined: 13 Dec 2012
Posts: 60
Own Kudos [?]: 38 [4]
Given Kudos: 4
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
4
Kudos
B, here's why:

you can skip an awful lot of math if you recognize that the machines 1 and 2 are the fastest, so just combine their rates:

1 (job) / 4 (hrs) = 1/4 (job per hour)
1 (job) / 5 (hrs) = 1/5 (job per hour)

1/4 + 1/5 = 5/20 + 4/20 = 9/20 (jobs per hour)

--> every hour, Machines 1 and 2 together, can perform 9/20ths (or 45%) of the job, answer B

Note: no other combination (machine 1 and 3 together, or machine 2 and 3 together) can come close (since 3 is the slowest machine) so don't bother doing that math (@cssk: ur math was correct, but you did more work than you had to)
Director
Joined: 25 Apr 2012
Posts: 529
Own Kudos [?]: 2322 [1]
Given Kudos: 740
Location: India
GPA: 3.21
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
1
Kudos
Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6

Sol: We know Work= Rate*Time

The greatest part of the work in 1 hour will be done by machines which take the lowest time to get the work done individually. Here machines with individual rates and 4 and 5 hours will do the maximum work in 1 hour.

Work Done in 1 hour will be 1/4+1/5= 9/20.
Ans B
Tutor
Joined: 20 Dec 2013
Posts: 104
Own Kudos [?]: 246 [3]
Given Kudos: 1
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
3
Kudos
Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6

Let us say that the total work is of 60 units then the number of units finished in one hour will be 15, 12 and 10 units per hour respectively.
Greatest number of units finished: 15 + 12 = 27

Fraction of work: 27/60 = 9/20
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30863 [0]
Given Kudos: 799
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
Top Contributor
Bunuel wrote:
Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6

Assign a "nice" value to the job (i.e., a value that works well with the given numbers, 4, 5 and 6)
Since 4, 5 and 6 all divide into 60, let's say that completing the job means making 60 widgets

So, the first machine can make 60 in 4 hours, which means its rate is 15 widgets per hour.
The second machine can make 60 in 5 hours, which means its rate is 12 widgets per hour.
The 3rd machine can make 60 in 6 hours, which means its rate is 10 widgets per hour.

So, the first machine and second machine are the two fastest.
Their combined rate = 15 + 12 = 27 widgets per hour
So, in one hour, those two machines can make 27 widgets, which means they can complete 27/60 of the job.

27/60 simplifies to be 9/20
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19191
Own Kudos [?]: 22718 [1]
Given Kudos: 286
Location: United States (CA)
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
1
Kudos
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6

Solution:

We see that the rates of the three machines are 1/4, 1/5, and 1/6, respectively. Thus, if the two machines with the greatest rates work together, then the greatest part of the job that can be done in one hour is 1/4 + 1/5 = 5/20 + 4/20 = 9/20.

Intern
Joined: 13 Jun 2020
Posts: 23
Own Kudos [?]: 0 [0]
Given Kudos: 95
Location: India
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
Solution :

Unit of work completed (LCM of time given for each machine, i,e 4,5 and 6) =60 Unit
No. of Unit by machine 1 = 60/4 = 15 unit
No. of Unit by machine 1 = 60/5 = 12 unit
No. of Unit by machine 1 = 60/10 = 6 unit

Greatest part of Job = 15+12 = 27 unit , 27/60 = 9/20
Senior Manager
Joined: 23 Dec 2022
Posts: 312
Own Kudos [?]: 36 [0]
Given Kudos: 199
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
Let's consider all possible pairs of machines and find the rate at which they work together (in units per hour).

Machine A and B: A can do the job in 4 hours, so its rate is 1/4 of the job per hour. Similarly, B's rate is 1/5. Together, their rate is 1/4 + 1/5 = 9/20.

Machine A and C: A's rate is 1/4, and C's rate is 1/6. Together, their rate is 1/4 + 1/6 = 5/12.

Machine B and C: B's rate is 1/5, and C's rate is 1/6. Together, their rate is 1/5 + 1/6 = 11/30.

The question asks for the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates. So we want to find the maximum of the rates we just calculated.

The maximum is 9/20, which is achieved when machines A and B work together.

Therefore, the answer is (B) 9/20.
Non-Human User
Joined: 09 Sep 2013
Posts: 34080
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
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.
Re: Three machines, individually, can do a certain job in 4, 5, [#permalink]
Moderator:
Math Expert
94609 posts