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

It is currently 22 Feb 2019, 05:25

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

Machine A working alone can complete a job in 3 1/2 hours. Machine B

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

Hide Tags

 
Intern
Intern
avatar
Joined: 04 Feb 2011
Posts: 49
Location: US
Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

Show Tags

New post 08 Mar 2011, 01:23
2
6
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:24) correct 20% (02:04) wrong based on 284 sessions

HideShow timer Statistics

Machine A working alone can complete a job in \(3 \frac{1}{2}\) hours. Machine B working alone can do the same job in \(4 \frac{2}{3}\) hours. How long will it take both machines working together at their respective constant rates to complete the job?


A. 1 hr 10 min

B. 2hr

C. 4hr 5 min

D. 7hr

E. 8 hr 10 min
Manager
Manager
avatar
Joined: 14 Feb 2011
Posts: 174
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

Show Tags

New post 08 Mar 2011, 01:37
Lolaergasheva wrote:
Machine A working alone can complete a job in hours. Machine B working alone can do the same job in hours. How long will it take both machines working together at their respective constant rates to complete the job?

(A) 1 hr 10 min
(B) 2 hr
(C) 4 hr 5 min
(D) 7 hr
(E) 8 hr 10 min

I got answer E but it is incorrect


I think the question is incomplete in its present form. The details of number of hours for both machines is not there. If they were given (say x and y), then you could get the total number of hours by simple formula of 1/x+1/y = 1/combined rate
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53066
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

Show Tags

New post 08 Mar 2011, 02:16
1
3
Lolaergasheva wrote:
Machine A working alone can complete a job in hours. Machine B working alone can do the same job in hours. How long will it take both machines working together at their respective constant rates to complete the job?

(A) 1 hr 10 min
(B) 2 hr
(C) 4 hr 5 min
(D) 7 hr
(E) 8 hr 10 min

I got answer E but it is incorrect


PLEASE CHECK THE QUESTIONS WHEN POSTING.

Original question:
Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?
A. 1 hr 10 min
B. 2hr
C. 4hr 5 min
D. 7hr
E. 8 hr 10 min

General formula for multiple entities is \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.

For example if:
Time needed for A to complete the job is A hours;
Time needed for B to complete the job is B hours;
Time needed for C to complete the job is C hours;
...
Time needed for N to complete the job is N hours;

Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.

For two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two entities A and B working simultaneously to complete one job:

Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)).

For our original questions it'll be: 1/(7/2)+1/(14/3)=1/T --> T=2.

Answer: B.

Must know to solve work problems: word-translations-rates-work-104208.html#p812628
_________________

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

Intern
Intern
avatar
Joined: 16 Sep 2013
Posts: 2
Location: United States
GPA: 3.75
WE: Information Technology (Consulting)
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

Show Tags

New post 26 Sep 2014, 11:57
Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?

--just remember rate*time=job
Lets consider they both need to work for t hours to get the job done..

So, rate*time=job (Here job is 1 as it needs to be completed)
rate for type A machine =1/210 -- converting hrs to minutes
similarly rate for type A machine =1/280

Finally we have,
(1/210)*t + (1/280)*t=1
t=280*210/490
t=120 mins=2 hrs

Answer B should be correct.
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1820
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

Show Tags

New post 30 Sep 2014, 00:36
4
\(3 \frac{1}{2}\) Hours \(= 3*60 + \frac{1}{2} * 60 = 210\)Minutes

\(4 \frac{2}{3} Hours = 4*60 + \frac{2}{3} * 60 = 280\) Minutes

Combined rate of both machines

\(= \frac{1}{210} + \frac{1}{280} = \frac{7}{840}\)

Time required\(= \frac{840}{7} = 120 Minutes = 2 Hours\)

Answer = B
_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
avatar
Joined: 26 Jan 2013
Posts: 4
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

Show Tags

New post 30 Sep 2014, 23:14
The question is quit simple, we need not convert them to minutes.

Machine A : 3 1/2 hrs = 7/2 hrs. So, in one hour the work would be 2/7.

Machine A : 4 2/3 hrs = 14/3 hrs. So, in one hour the work would be 3/14.

Combined rate of both machines,

2/7 + 3/14 = 7/14 = 1/2.

So, the complete work is done in 2 hours.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9888
Premium Member
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B  [#permalink]

Show Tags

New post 23 Jan 2019, 17:14
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

GMAT Club Bot
Re: Machine A working alone can complete a job in 3 1/2 hours. Machine B   [#permalink] 23 Jan 2019, 17:14
Display posts from previous: Sort by

Machine A working alone can complete a job in 3 1/2 hours. Machine B

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


Copyright

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®.