Randy can rebuild an automobile engine in a hours. Alvin can : GMAT Problem Solving (PS)
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# Randy can rebuild an automobile engine in a hours. Alvin can

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Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 08:41
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56% (02:23) correct 44% (01:37) wrong based on 318 sessions

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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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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 10:59
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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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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 11:19
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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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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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01 May 2012, 14:28
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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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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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02 May 2012, 04:32
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

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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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02 May 2012, 08:03
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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: 36582 Followers: 7086 Kudos [?]: 93253 [8] , given: 10555 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] ### Show Tags 02 May 2012, 08:18 8 This post received KUDOS Expert's post 4 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: 334 Location: India Followers: 1 Kudos [?]: 201 [0], given: 33 Re: Kaplan free test PS [#permalink] ### Show Tags 26 May 2012, 21:09 ok so Kaplan solved it by substituting numbers. But can anyone explain how algebraically we can solve this? I am thoroughly perplexed! Math Expert Joined: 02 Sep 2009 Posts: 36582 Followers: 7086 Kudos [?]: 93253 [0], given: 10555 Re: Kaplan free test PS [#permalink] ### Show Tags 27 May 2012, 02:17 vibhav wrote: ok so Kaplan solved it by substituting numbers. But can anyone explain how algebraically we can solve this? I am thoroughly perplexed! Merging similar topics. Please refer to the solutions above. _________________ Senior Manager Joined: 28 Dec 2010 Posts: 334 Location: India Followers: 1 Kudos [?]: 201 [0], given: 33 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] ### Show Tags 27 May 2012, 03:35 thanks Bunuel. its clear now! Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 25 Kudos [?]: 433 [0], given: 11 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] ### Show Tags 15 Nov 2012, 22:04 $$R-rate=\frac{1}{ahrs}$$ $$A-rate=\frac{1}{bhrs}$$ 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: 916 Concentration: General Management, General Management GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32 GPA: 3.7 WE: Information Technology (Investment Banking) Followers: 23 Kudos [?]: 692 [0], given: 322 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] ### Show Tags 28 Sep 2013, 01:25 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: 221 Concentration: Finance, Economics GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Followers: 4 Kudos [?]: 139 [0], given: 40 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] ### Show Tags 21 Nov 2013, 10:46 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: 7125 Location: Pune, India Followers: 2137 Kudos [?]: 13665 [1] , given: 222 Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] ### Show Tags 21 Nov 2013, 20:16 1 This post received KUDOS Expert's post 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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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink]

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22 Nov 2013, 16:32
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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29 Jan 2016, 20:43
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