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Working at the same constant rate, 4 machines, working together, take

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Working at the same constant rate, 4 machines, working together, take  [#permalink]

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New post 29 Dec 2016, 12:12
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Question Stats:

74% (01:28) correct 26% (01:36) wrong based on 212 sessions

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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

*Kudos for all correct solutions

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Re: Working at the same constant rate, 4 machines, working together, take  [#permalink]

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New post 29 Dec 2016, 12:48
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GMATPrepNow wrote:
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

*Kudos for all correct solutions


4 machines working at a constant rate:

\(\frac{1}{x} + \frac{1}{x} + \frac{1}{x} + \frac{1}{x} = \frac{16}{8}\)

\(\frac{4}{x} = 2\)

\(x=2\) (days per birdhouse) or just \(\frac{8}{4} = 2\) (days per birdhouse)

Had the rate been kept the same we would have got 32 houses in 16 days not 64. That means we need to double the rate to fulfill this job or to double the number of machines.

y - new # of machines

\(\frac{y}{2} = 2*2\)

\(\frac{y}{2} = 4\)

\(y=8\)

Answer C
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Re: Working at the same constant rate, 4 machines, working together, take  [#permalink]

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New post 29 Dec 2016, 18:29
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Given :4 Machines - > 8 Days -> 16 Bird Houses
Need : ___ Machines -> 16 Days -> 64 BirdHouses

From given 8 Machines - 8 Days - 32 BH
=> 16 M - 16 D - 64 BH
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Re: Working at the same constant rate, 4 machines, working together, take  [#permalink]

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New post 29 Dec 2016, 19:07
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GMATPrepNow wrote:
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

*Kudos for all correct solutions


Another 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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Re: Working at the same constant rate, 4 machines, working together, take  [#permalink]

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New post 14 Oct 2018, 05:51
4
GMATPrepNow wrote:
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

*Kudos for all correct solutions



Important Rule:

no. of machine *rate *Time = work.

Given,

Machine = 4

Time = 8

work = 16

we can find out the rate.

4*8*r = 16

r = 1/2.

This rate can be used to 2nd case.

machine * rate * time = work

m * 1/2 * 16 = 64

m = 8.

The best answer is C.
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Re: Working at the same constant rate, 4 machines, working together, take  [#permalink]

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New post 17 Oct 2018, 10:13
4 machines, working together, take 8 days to make a total of 16 birdhouses

Therefore in 4*8-----32 mach-days=6 Birdhouses
1 Bird house=2 mach-days

Similarly 64birdhouses=64*2 mach-days
Given days 16 and we need to find number of machines m

Answer:- m= (64*2)/16=8 mach

IMO C.
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Re: Working at the same constant rate, 4 machines, working together, take   [#permalink] 17 Oct 2018, 10:13
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