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

 It is currently 22 Oct 2019, 07:46

### 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

# Machine A can do a job in 24 hours at a constant rate and machine A do

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8027
GMAT 1: 760 Q51 V42
GPA: 3.82
Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

Updated on: 13 Mar 2016, 06:10
1
7
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:41) correct 21% (02:03) wrong based on 241 sessions

### HideShow timer Statistics

Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

* A solution will be posted in two days.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 11 Mar 2016, 06:04. Last edited by MathRevolution on 13 Mar 2016, 06:10, edited 3 times in total. Math Expert Joined: 02 Aug 2009 Posts: 8006 Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink] ### Show Tags 11 Mar 2016, 06:35 MathRevolution wrote: Machine A can do a job in 24 hours at a constant rate and machine A do the job in 8 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone? A. 12hrs B. 16hrs C. 24hrs D. 28hrs E. 32hrs * A solution will be posted in two days. Hi, The Q does not seem to be properly framed.. I believe it should be-- Machine A can do a job in 24 hours at a constant rate and machine A does the job alone for 8 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone? solution machine A will do 8/24 in 8 hrs, so A does 1/3 of the work .. Therefore, B will do the remaining 2/3 rd work alone.. As the speed of B is 2/3 rate of A, B will do the 2/3rd work in same time that A takes to complete full job... ans 24 C _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8027 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink] ### Show Tags 13 Mar 2016, 06:11 Sorry for the confusion. I have revised the question. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8027
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

13 Mar 2016, 22:16
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

Power of Machine A=W/24hrs. Since Machine A does the job for 8 hours, which becomes (W/3)/8hrs and 2W/3 is left. However, as power of Machine B is 2/3 of Machine A, power of B is (2/3)(W/24hrs)=(2W/3)/24hrs. Eventually, it takes 24 hours for Machine B to do the rest of the job.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 09 Jun 2015
Posts: 86
Re: Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

13 Mar 2016, 22:24
1
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

* A solution will be posted in two days.

In 8 hours A can complete one third work. The remaining work is two thirds.
B performs two third of the efficiency of A; So B takes 36 hours to complete the full task.
Now B has to do only two thirds of the work. Therefore, two thirds of 36 hours = 24 hours.
Director
Joined: 17 Dec 2012
Posts: 626
Location: India
Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

13 Mar 2016, 22:44
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

* A solution will be posted in two days.

We can equate work done as follows:
8/24 + x/36 = 1

x/36=2/3
x=24 hrs
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Intern
Joined: 28 May 2017
Posts: 18
Re: Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

25 Aug 2017, 09:05
Ans c 24 hours
Given
A takes 24 hours
And

The machine b is 2/3 as consistent as a

So time taken by it would be 3/2 as A

A works for 8 hours so 8/24 = 1/3 work is done

Remaining work = 1-1/3= 2/3

A completed 1/3 of work in 8 hours and b would take 3/2 as time as A so
A would complete the same work in 3/2*8= 12 hours

So 1/3 of work is completed by b in 12 hours
So 2/3 will be done in 24 hours

Hope it helps
Peace

Sent from my iPhone using GMAT Club Forum mobile app
Senior SC Moderator
Joined: 22 May 2016
Posts: 3574
Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

26 Aug 2017, 12:40
2
1
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

* A solution will be posted in two days.

A's rate = $$\frac{1}{24}$$

B's rate is $$\frac{2}{3}$$ (of) A:

$$\frac{1}{24}$$ * $$\frac{2}{3}$$ = $$\frac{1}{36}$$ = B's rate

Amount of work for B? A works for 8 hours. $$(\frac{1}{24})$$ * 8 = $$\frac{1}{3}$$ of the work is finished.

1 - $$\frac{1}{3}$$ = $$\frac{2}{3}$$ of work remains.

Time for B to finish? B has to finish remaining $$\frac{2}{3}$$ of work. At B's rate, W/r = t, that will take

$$\frac{\frac{2}{3}}{\frac{1}{36}}$$ =

$$\frac{2}{3}$$ * 36 = 24 hours

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

27 Aug 2017, 21:09
1
1
Since Machine A does a job in 24 hours,
lets assume the number of units of work done to be a multiple of 24(for eg, 72 units)
So the rate of Machine A doing the work is 3 units/hour

It has been given that B does the work at $$\frac{2}{3}$$rd the rate of A.
Therefore Machine B does the work at the rate of 2 units/hour

Since Machine A does the work for 8 hours,
Machine B does the rest of the work for x days till the work is complete.

8*3 + x*2 = 72(total units of work)
2x = 48
x = 24
Therefore, Machine B takes 24 hours to complete the remaining work(Option C)
_________________
You've got what it takes, but it will take everything you've got
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

31 Aug 2017, 10:22
1
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

The rate of machine A is 1/24, so in 8 hours 1/3 of the job is completed, and thus 2/3 of the job is left to be completed.

If the rate of machine B is 2/3 that of machine A, then the rate of machine B is (2/3)(1/24) = 1/36.

Thus, it will take machine B (2/3)/(1/36) = 2/3 x 36 = 24 hours to complete the rest of the job.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP
Joined: 07 Dec 2014
Posts: 1224
Re: Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

31 Aug 2017, 13:07
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

B's time=(3/2)*24=36 hours
(2/3 job)/(1/36 rate)=24 hours
C
Non-Human User
Joined: 09 Sep 2013
Posts: 13393
Re: Machine A can do a job in 24 hours at a constant rate and machine A do  [#permalink]

### Show Tags

14 Oct 2018, 11:37
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: Machine A can do a job in 24 hours at a constant rate and machine A do   [#permalink] 14 Oct 2018, 11:37
Display posts from previous: Sort by