greatest part of work (man hours)

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kishokbabu: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed May 04, 2011 9:50 pmFollowed by: 2 members; Thanked: 2 times

by kishokbabu » Tue Dec 27, 2011 9:16 am

3 machines individually can do a certain job in 4,5 & 6 hrs respectively.What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

A) 11/30
B) 9/20
C) 3/5
D) 11/15
E) 5/6

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Tue Dec 27, 2011 9:35 am

(4+5)/4*5=9/20

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Vanshika21: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Fri Dec 16, 2011 11:02 am; Thanked: 1 times

by Vanshika21 » Fri Mar 09, 2012 10:23 am

LalaB wrote:(4+5)/4*5=9/20[/quote

Hi,

Can you pls explain why you took 4 and 5 and not 5 and 6?

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Fri Mar 09, 2012 10:29 am

Vanshika21 wrote:
LalaB wrote:(4+5)/4*5=9/20
Hi,

Can you pls explain why you took 4 and 5 and not 5 and 6?

I surely can

U are asked about "the greatest part"

so lets take 5 and 6 hours

then u will have
(5+6)/5*6=11/30

please note, that 11/30 <9/20
since u r asked about the greatest part, u better get the least hours

,i.e. 4 and 5

hope it is clear

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Mar 09, 2012 8:43 pm

kishokbabu wrote:3 machines individually can do a certain job in 4,5 & 6 hrs respectively.What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

A) 11/30
B) 9/20
C) 3/5
D) 11/15
E) 5/6

Since we must MAXIMIZE the amount of work produced, the SLOWEST machine cannot be used.
The fastest machine takes 4 hours to complete the job; the next fastest machine takes 5 hours.
Let the job = 20 units.
Rate for the fastest machine = w/t = 20/4 = 5 units per hour.
Rate for the next fastest machine = w/t = 20/5 = 4 units per hour.
(Work produced by the 2 machines in 1 hour)/(Total job) = (5+4)/20 = 9/20.

The correct answer is B.

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mjmehta81: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Mon Feb 06, 2012 5:07 am; Thanked: 1 times

by mjmehta81 » Sun Mar 11, 2012 4:31 am

Here we have to compare work fastest machine with other two.
Work completed A in 1 hr is 1/4,
Work completed B in 1 hr is 1/5
Work completed C in 1 hr is 1/6

A+B = 9/20 ~ 1/2.22
A+C = 10/24 = 5/12 ~ 1/2.4

So A+B takes 2.22 hrs to complete 1 work, so can complete more work.
So answer B

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