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# Machine A and Machine B are each used to manufacture 660

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Director
Joined: 16 Aug 2005
Posts: 950
Location: France
Followers: 1

Kudos [?]: 8 [0], given: 0

Machine A and Machine B are each used to manufacture 660 [#permalink]  18 May 2006, 18:34
00:00

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Machine A and Machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machine A produce

A. 6
B. 6.6
C. 60
D. 100
E. 110

This took me a long time to calculate and figure out. Does anyone have a quick method that you can show me?

Source suggested backsolving due to time constraints.
Manager
Joined: 04 May 2006
Posts: 53
Followers: 1

Kudos [?]: 1 [0], given: 0

Using POE, answers C, D and E look too big because the difference in time it takes for A and B is [u]only[/u] 10% and it takes [u]10 hrs more [/u] for A than B to make 660.

Now going by backsolving, start with A (as it's easy one without decimals :-D ).

If A makes 6/hr --> B makes 6.6/hr.
It takes A 110 hrs for 660 sprockets (ot whatever they are) and
it takes B 100 hrs for the same.

Hence A.
Manager
Joined: 28 Mar 2006
Posts: 158
Followers: 1

Kudos [?]: 2 [0], given: 0

B = x hrs to produce 660
A = x + 10 hrs to produce 660

in one hr B produces 660/x
in one hr a produces 660/x + 10
660/x - 660/x+10 = 1/10(660/x+10)
solving we get x = 100
x + 10 = 110...
Thus Aproduces 660/110 =6 sprockets in an hour.

I couldnt think of a faster approach, but the above one dint take much time either.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5099
Location: Singapore
Followers: 15

Kudos [?]: 116 [0], given: 0

Machine B: Takes x hours to produce 660 sprockets
Machine A: Takes (x+10) hours to produce 660 sprockets

Machine B: In 1 hour, B makes 660/x sprockets
Machine A: In 1 hour, A makes 660/(x+10) sprockets

Equating:

1.1(660/(x+10)) = 660/x
726/(x+10) = 660/x
726x = 660x+6600
66x = 6600
x = 100

A makes 660/(110) = 6 sprockets per hour
Director
Joined: 24 Oct 2005
Posts: 664
Location: London
Followers: 1

Kudos [?]: 6 [0], given: 0

We get two equations here for number of sockets by B in 1hr

Let time taken by A for 660 sockets = x

1) B in 1 hr = 1.1 * (a in 1 hr)

ie. 1.1 * 660/x = 726/x

2) B taken 10 hrs less than A for 660 sockets

660 sockets in (x-10) hrs
Therefore 1hr = 660/x-10

Using these two,

726/x = 660/(x-10)

So, x = 110.
In 1 hr A makes 660/110 = 6 sockts
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