Work

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Mon Nov 02, 2009 6:55 pm

Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete 1/2 of the same production lot in z hours. What is the value of y in terms of x and z?

OA [spoiler]2XZ / (5X - 10Z)[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Nov 02, 2009 6:55 pm

Resurgent: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Aug 23, 2009 8:09 am; Thanked: 1 times

Re: Work

by Resurgent » Tue Nov 03, 2009 1:17 am

A takes xhrs to complete the job
B takes 5yhrs to complete the same job (given, 1/5 of the work in y hrs)

Together, A & B can complete the job in 5xy/(x+5y) hrs, i.e. half of the job can be completed in 5xy/(2*(x+5y)) hrs. This is equal to z.

So, z=5xy/(2*(x+5y))

Bring y to one side of the equation & you will get 2xy/(5*(x-2z))

Hope this helps.

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life is a test: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon Mar 02, 2009 12:02 pm; Thanked: 15 times

Re: Work

by life is a test » Tue Nov 03, 2009 2:11 am

Resurgent wrote:A takes xhrs to complete the job
B takes 5yhrs to complete the same job (given, 1/5 of the work in y hrs)

Together, A & B can complete the job in 5xy/(x+5y) hrs, i.e. half of the job can be completed in 5xy/(2*(x+5y)) hrs. This is equal to z.

So, z=5xy/(2*(x+5y))

Bring y to one side of the equation & you will get 2xy/(5*(x-2z))

Hope this helps.

Resurgent could u pls explain how you rearrange the eqn z=5xy/(2*(x+5y)) for y?

thks.

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Resurgent: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Aug 23, 2009 8:09 am; Thanked: 1 times

Re: Work

by Resurgent » Tue Nov 03, 2009 2:33 am

life is a test wrote:
Resurgent could u pls explain how you rearrange the eqn z=5xy/(2*(x+5y)) for y?

thks.

Bring all the y's to one end, take the common & equate.

z=5xy/(2*(x+5y))
==> 2xz+10zy = 5xy
==> 2xz = y(5x-10z)
==> y = 2xz/(5x-10z)
==> y = 2xz/(5*(x-2z))

Hope this helps.

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sanjana: Master | Next Rank: 500 Posts; Posts: 182; Joined: Sun Aug 02, 2009 7:19 pm; Thanked: 18 times; GMAT Score:680

by sanjana » Tue Nov 03, 2009 3:06 am

Rate Time Work
Mach A 1/X X 1
Mach B 1/5Y Y 1/5

Combined rate : (1/x+1/5y)*z = 1/2 from the given statement.

Simplify and isolate y and you will get the OA.

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