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Working at the same constant rate, 4 machines,

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Working at the same constant rate, 4 machines,

by Brent@GMATPrepNow » Thu Dec 29, 2016 12:22 pm
Here's a 600-level work question I just made up.
Working at the same constant rate, 4 machines, working together, take 8 days to make a total of 16 birdhouses.
How many such machines are required to make 64 birdhouses in 16 days?
A) 2
B) 4
C) 8
D) 16
E) 32

Answer: C
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by Brent@GMATPrepNow » Fri Dec 30, 2016 8:53 am
Working at the same constant rate, 4 machines, working together, take 8 days to make a total of 16 birdhouses.
How many such machines are required to make 64 birdhouses in 16 days?
A) 2
B) 4
C) 8
D) 16
E) 32

Answer: C
One approach is to see what the original 4 machines can do in 16 days.

4 machines take 8 days to make 16 birdhouses.
So, in 16 days, those same 4 machines can make 32 birdhouses
So, if we add an additional 4 machines (that can also make 32 birdhouses in 16 days), the 8 combined machines will make 64 birdhouses in 16 days.

Answer: C
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by rsarashi » Fri Dec 30, 2016 9:17 am
Hi ,

In 1 day, 1 Machine can make = 16/8*4 = 1/2 right?

so what will be next ?

Please explain.

Thanks
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by Brent@GMATPrepNow » Fri Dec 30, 2016 9:27 am
rsarashi wrote:Hi ,

In 1 day, 1 Machine can make = 16/8*4 = 1/2 right?

so what will be next ?

Please explain.

Thanks
That's correct; in 1 day, 1 machine can make 1/2 birdhouses
So, in 2 days, 1 machine can make 1 birdhouse
In 16 days, 1 machine can make 8 birdhouses
So, in 16 days, 2 machines can make 16 birdhouses
In 16 days, 4 machines can make 32 birdhouses
In 16 days, 8 machines can make 64 birdhouses

I could have skipped a few steps, but I think this might be clearer.

Does that help?

Cheers,
Brent
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by rsarashi » Sun Jan 01, 2017 5:42 am
That's correct; in 1 day, 1 machine can make 1/2 birdhouses
So, in 2 days, 1 machine can make 1 birdhouse
In 16 days, 1 machine can make 8 birdhouses
So, in 16 days, 2 machines can make 16 birdhouses
In 16 days, 4 machines can make 32 birdhouses
In 16 days, 8 machines can make 64 birdhouses

I could have skipped a few steps, but I think this might be clearer.

Does that help?

Hi Brent ,

Thanks for the explanation. All clear.

Thanks,

Rashi
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