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# Machine A can do a job in 12 hours at a constant rate and machine A do

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Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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03 Nov 2016, 01:28
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35% (medium)

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74% (02:04) correct 26% (02:10) wrong based on 219 sessions

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Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 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

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"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: 05 Jun 2015 Posts: 74 Location: United States WE: Engineering (Transportation) Re: Machine A can do a job in 12 hours at a constant rate and machine A do [#permalink] ### Show Tags 03 Nov 2016, 01:38 2 Machine A worked for 4 hours => completed 1/3rd of the work. Machine B does the work at 2/3 rate of A => time taken by B to complete = $$\frac{3}{2} *12$$ = 18 hours. B needs to complete 2/3rd of the work. Let time taken be x $$\frac{1}{18} * x =\frac{2}{3}$$ x = 12 Option A Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4856 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: Machine A can do a job in 12 hours at a constant rate and machine A do [#permalink] ### Show Tags 03 Nov 2016, 09:06 1 MathRevolution wrote: Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 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 Let total work be 36 Efficiency of A = 3 Efficiency of B = 2 A works for 4 hours so it completes 12 units, hence work left is 24 units Since B does 24 units , time required by it is 24/2 = 12 Hence, Correct answer is (A).. _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8425 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Machine A can do a job in 12 hours at a constant rate and machine A do [#permalink] ### Show Tags 07 Nov 2016, 00:51 ==> Machine A works for 12 hours, but only did 4 hours, which is 1/3 of the job. Then, 2/3 of the job remains. Since the power of B is 2/3 of A’s, it takes 12 hours for B to do the remaining job. Hence, the answer is A. Answer: A _________________ 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"
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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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06 Mar 2018, 03:52
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MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate but machine A do the job for 4 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

Isn't this wording more appropriated?
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Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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06 Mar 2018, 08:55
MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 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

MvArrow , I got confused, too. I rewrote:

Machine A can do a job in 12 hours at a constant rate. Machine A works for 4 hours. Machine B, working at a constant rate, can do the same job at 2/3 of the rate of machine A. If machine B does the rest of the job alone, how many hours does it take for Machine B to finish?

Amount of work completed by Machine A?
Work = 1 job
Rate of A: $$\frac{1Job}{12hrs}=\frac{1}{12}$$
Time that Machine A worked: 4 hours
Amount of work, $$W,$$ that Machine A completes:
$$W = R * T$$
$$W=(\frac{1}{12} *4)=\frac{4}{12}=\frac{1}{3}$$
of Work finished

Work remaining for B:$$\frac{2}{3}$$

B's rate? B is slower than A
B's rate is $$\frac{2}{3}$$ the rate of (= multiply) A
B's rate: $$(\frac{1}{12}*\frac{2}{3})=\frac{2}{36}=\frac{1}{18}$$ = rate of B

Time needed for B to finish work remaining?
$$\frac{2}{3}$$ of work remains
$$R * T= W$$, so $$T = \frac{W}{R}$$

Time for B:$$\frac{\frac{2}{3}}{\frac{1}{18}}=(\frac{2}{3}*\frac{18}{1})=12$$ hours

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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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19 Mar 2018, 03:29
MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 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

Please correct the wording here. What is the question trying to say?
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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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18 Jun 2018, 06:50
1
generis wrote:
MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 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

MvArrow , I got confused, too:
Machine A can do a job in 12 hours at a constant rate. Machine A works for 4 hours. Machine B, working at a constant rate, can do the same job at 2/3 the rate of machine A. If machine B does the rest of the job alone, how many hours does it take for Machine B to finish?

Amount of work completed by Machine A?
Work = 1 job
Rate of A: $$\frac{1Job}{12hrs}=\frac{1}{12}$$
Time that Machine A worked: 4 hours
Amount of work Machine A completes:
$$W = R * T$$
$$W = \frac{1}{12} * 4=\frac{4}{12}=\frac{1}{3}$$
of Work finished

Work remaining for B:$$\frac{2}{3}$$

B's rate? B is slower than A
B's rate is $$\frac{2}{3}$$ the rate of (= multiply) A
B's rate: $$(\frac{1}{12}*\frac{2}{3})=\frac{2}{36}=\frac{1}{18}$$ = rate of B

Time needed for B to finish work remaining?
$$\frac{2}{3}$$ of work remains
$$R * T= W$$, so $$T = \frac{W}{R}$$

Time for B:$$\frac{\frac{2}{3}}{\frac{1}{18}}=(\frac{2}{3}*\frac{18}{1})=12$$ hours

True... Wording of question is very poor. Hopefully GMAC never does such things. It is a relief that many have been confused by the wording, otherwise I was blaming myself.
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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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20 Jun 2018, 17:03
1
MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 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

The rate of Machine A is 1/12, and the rate of Machine B is 2/3 x 1/12 = 1/18.

Machine A works for 4 hours, so it completes 4 x (1/12) = 1/3 of the job.

When machine A stops working, 2/3 of the job remains to be finished by machine B. Thus, machine B works for (2/3)/(1/18) = 36/3 = 12 hours alone.

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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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03 Dec 2019, 23:18
Confusing wording:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours.
Re: Machine A can do a job in 12 hours at a constant rate and machine A do   [#permalink] 03 Dec 2019, 23:18
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