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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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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

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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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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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8 days needed to make 16 birdhouses by 4 machines
1………………………...........16………………........8 x 4

1………………………...........1……………….........(8 x 4)/16

1………………………..........64……………….........(64*4*8)/16

16……………………...........64……………….........(64*4*8)/(16*16)
= 8 machines(E)
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We have a straight formula for such type of questions. And memorising this formula saves a lot of time in such questions.

(M1*D1*H1)/W1 = (M2*D2*H2)/W2

M1- Number of people or men
D1- Number of days required to complete the job
H1- Hours required
W1- Work units

Same goes for the other side as well.
Applying this formula makes the problems easier.
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GMATPrepNow
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

Solution:

The rate of 4 machines is 16/8 = 2 birdhouses per day.

We need to determine the number of machines that must work at a rate of 64/16 = 4.

We can create the equation where x is the number of machines needed to make 64 birdhouses in 16 days:

4/2 = x/4

2x = 16

x = 8

Alternate Solution:

First, note that if it takes 8 days for the 4 machines to build 16 birdhouses, then in 16 days, the 4 machines can build 16 x 2 = 32 birdhouses.

In order to build 64 birdhouses (instead of 32) in 16 days, the number of machines should be doubled. Thus, 4 x 2 = 8 machines are needed.

Answer: C

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