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cypherskull: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sat Mar 31, 2012 3:39 am; Location: Calcutta; Thanked: 8 times

Help..!

by cypherskull » Sun Aug 19, 2012 10:39 am

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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Sunit

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Source: Beat The GMAT — Problem Solving | Sun Aug 19, 2012 10:39 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 am; Location: Utrecht, The Netherlands; Thanked: 318 times; Followed by:52 members

by neelgandham » Sun Aug 19, 2012 11:03 am

If Randy can rebuild an automobile engine in a hours. What part of the automobile can he rebuild in 1 hour ? It is 1/a

Similarly, If Alvin can rebuild the same engine in b hours. What part of the automobile can he rebuild in 1 hour ? It is 1/b.

In one hour Randy and Alvin working together can rebuild (1/a + 1/b)th part of an automobile.
Total time taken by Randy and Alvin to rebuild the automobile = 1/(1/a + 1/b) = ab/(a+b) hours

Portion of work Randy completed in ab/(a+b) hours = [ab/(a+b)]*1/a = b/(a+b)
Portion of work Randy will not have to complete = 1 - [b/(a+b)] = a/(a+b)

IMO D

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

Anil Gandham
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