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Working at its constant rate, a Type A riveting machine can set 12,000

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Working at its constant rate, a Type A riveting machine can set 12,000  [#permalink]

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New post 06 Mar 2019, 08:23
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Working at its constant rate, a Type A riveting machine can set 12,000 rivets in x hours. At its constant rate, a Type B riveting machine can set 12,000 rivets in 3x hours. If an equal number of each type of machine will work together to set 12,000 rivets, what is the minimum total number of machines that will be required to set the 12,000 rivets in less than x/ 9 hours?
A. 10
B. 12
C. 14
D. 16
E. 18

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Re: Working at its constant rate, a Type A riveting machine can set 12,000  [#permalink]

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New post 06 Mar 2019, 10:04
The "12,000 rivets" is just a distraction -- we can call it "one job". To work out how quickly the machines work together, we can get the same time for the two types of machine; since we have x hours and 3x hours, using 3x hours is convenient:

A does 3 jobs in 3x hours
B does 1 job in 3x hours
A+B together do 4 jobs in 3x hours
A+B together do 1 job in 3x/4 hours

That's using 1 of each type of machine. If we instead use n machines of each type, we'll divide the total time taken by n. We want this total time to be less than x/9, so we have

3x/4n < x/9
27 < 4n
27/4 < n

n needs to be an integer, so n needs to be at least 7, and since we're using 7 of each type of machine, we'll need at least 14 machines in total.
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Re: Working at its constant rate, a Type A riveting machine can set 12,000  [#permalink]

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New post 11 Mar 2019, 10:09
gmatbusters wrote:
Working at its constant rate, a Type A riveting machine can set 12,000 rivets in x hours. At its constant rate, a Type B riveting machine can set 12,000 rivets in 3x hours. If an equal number of each type of machine will work together to set 12,000 rivets, what is the minimum total number of machines that will be required to set the 12,000 rivets in less than x/ 9 hours?
A. 10
B. 12
C. 14
D. 16
E. 18


rate for A = 1/x
rate for B = 1/3x
<9/x is the rate required to be worked on at
combined rate
1/x+1/3x <9/x
or say
4x/3x^2<9x
or say
27/4<n
so 6.75<n
n = 7
answer has to be in multiple of 7
IMO C ; 14
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Re: Working at its constant rate, a Type A riveting machine can set 12,000   [#permalink] 11 Mar 2019, 10:09
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Working at its constant rate, a Type A riveting machine can set 12,000

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