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Randy can rebuild an automobile engine in a hours. Alvin can

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Manager
Joined: 23 Oct 2011
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Location: Ukraine
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GMAT 1: 650 Q44 V35
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Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 09:41
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Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)
[Reveal] Spoiler: OA
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Joined: 27 Oct 2011
Posts: 13
Schools: Cambridge
Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 11:59
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JubtaGubar wrote:
Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
A) ab/(a+b)
B) (a-b)/(a+b)
C) b/(b-a)
D) a/(a+b)
E) b/(a+b)

Let total work completion be denoted as 1.
Randy and Alvin can together complete work in ab/a+b hours.
Randy's 1hr work is 1/a.
Alvin's 1 hr work is 1/b.

Alvin's portion of total work = Alvin's 1hr work /total 1 hr work.
=(1/b)/((a+b)/ab)
=a/(a+b)
That's the portion of work Randy need not do.

D.

Hope that helps.
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Joined: 23 Oct 2010
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 12:19
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Rate of Randy - 1/a
Rate of Alvin 1/b

sum of their rates =1/a+1/b=(a+b)/ab

the job that Randy will not have to complete = 1 - (rate of randy/total rate)=
=1- (1/a)/(a+b)/ab=a/(a+b)

d is the answ
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Joined: 02 Sep 2009
Posts: 44600
Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 15:28
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JubtaGubar wrote:
Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)

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Manager
Joined: 23 Oct 2011
Posts: 51
Location: Ukraine
Schools: LBS '14 (M)
GMAT 1: 650 Q44 V35
WE: Corporate Finance (Mutual Funds and Brokerage)
Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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02 May 2012, 05:32
Thank you for explanation, but I still cannot understand what is asked in a question:
which of the following represents the portion of the job that Randy will not have to complete

could you please explain the task clearer?
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Joined: 16 Oct 2010
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Location: Pune, India
Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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02 May 2012, 09:03
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JubtaGubar wrote:
Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)

Randy can do the job in a hrs, Alvin can do the job in b hrs.

When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.

Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)

So Randy does b/(a+b) of the work and Alvin does a/(a+b) of the work.

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 44600 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] Show Tags 02 May 2012, 09:18 9 This post received KUDOS Expert's post 8 This post was BOOKMARKED JubtaGubar wrote: Thank you for explanation, but I still cannot understand what is asked in a question: which of the following represents the portion of the job that Randy will not have to complete could you please explain the task clearer? Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete? A. ab/(a+b) B. (a-b)/(a+b) C. b/(b-a) D. a/(a+b) E. b/(a+b) The rate of Randy is $$\frac{1}{a}$$ job/hour; The rate of Alvin is $$\frac{1}{b}$$ job/hour; Their combined rate is $$\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}$$, so working together they will complete the job in $$\frac{ab}{a+b}$$ hours. Now, in $$\frac{ab}{a+b}$$ hours Alvin will complete $$\frac{1}{b}*\frac{ab}{a+b}=\frac{a}{a+b}$$ part of the job (rate*time=job) and this will be the part which Randy will not have to complete. Answer: D. _________________ Senior Manager Joined: 28 Dec 2010 Posts: 302 Location: India Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] Show Tags 27 May 2012, 04:35 thanks Bunuel. its clear now! Senior Manager Joined: 13 Aug 2012 Posts: 444 Concentration: Marketing, Finance GPA: 3.23 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] Show Tags 15 Nov 2012, 23:04 $$R-rate=\frac{1}{ahrs}$$ $$A-rate=\frac{1}{bhrs}$$ Rate of working together $$\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}$$ Time=reciprocal of rate together $$t=\frac{ab}{a+b}$$ Work done by Alvin $$W=\frac{1}{b}(ab/a+b)=\frac{a}{a+B}$$ Answer:D _________________ Impossible is nothing to God. Director Joined: 03 Aug 2012 Posts: 838 Concentration: General Management, General Management GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32 GPA: 3.7 WE: Information Technology (Investment Banking) Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] Show Tags 28 Sep 2013, 02:25 1 This post received KUDOS a=2 b=3 1/a + 1/b = 5/6 Rate Rate * Time = Work 5/6 * Time = 1 Time = 6/5 Hence both of them work for 6/5 hours Work done by b in 6/5 hours is 1/3 * 6/5 = 2/5 Check the options for work done = 2/5 for above given values of a and b _________________ Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________ Manager Joined: 26 Sep 2013 Posts: 204 Concentration: Finance, Economics GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] Show Tags 21 Nov 2013, 11:46 I solved by plugging smart numbers. I don't get it conceptually though, how can the amount of work someone DOESN'T have to do be their time to do the job, divided by the total time each would take to do the job. Seems like that would give you the amount of time it took Randy to do the work, not the portion he DIDN'T have to do. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8028 Location: Pune, India Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] Show Tags 21 Nov 2013, 21:16 4 This post received KUDOS Expert's post 1 This post was BOOKMARKED AccipiterQ wrote: I solved by plugging smart numbers. I don't get it conceptually though, how can the amount of work someone DOESN'T have to do be their time to do the job, divided by the total time each would take to do the job. Seems like that would give you the amount of time it took Randy to do the work, not the portion he DIDN'T have to do. When the question asks you: which of the following represents the portion of the job that Randy will not have to complete? it is just another way of saying: which of the following represents the portion of the job that Alvin will do? If I and you are working on something, you will not have to do the work that I am completing. So look at it from Alvin's perspective. Work done by Alvin = (Rate of Alvin)*(Time taken to complete the job together) = (1/b)*(ab/(a+b)) = a/(a+b) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Manager
Joined: 26 Sep 2013
Posts: 204
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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22 Nov 2013, 17:32
VeritasPrepKarishma wrote:
AccipiterQ wrote:
I solved by plugging smart numbers. I don't get it conceptually though, how can the amount of work someone DOESN'T have to do be their time to do the job, divided by the total time each would take to do the job. Seems like that would give you the amount of time it took Randy to do the work, not the portion he DIDN'T have to do.

When the question asks you: which of the following represents the portion of the job that Randy will not have to complete?
it is just another way of saying: which of the following represents the portion of the job that Alvin will do?

If I and you are working on something, you will not have to do the work that I am completing. So look at it from Alvin's perspective.

Work done by Alvin = (Rate of Alvin)*(Time taken to complete the job together) = (1/b)*(ab/(a+b)) = a/(a+b)

ah, when you word it that way it makes perfect sense!
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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Re: Randy can rebuild an automobile engine in a hours. Alvin can   [#permalink] 13 Mar 2018, 11:37
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