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A factory has two machines. Machine X can produce 200 pins per hour an

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A factory has two machines. Machine X can produce 200 pins per hour an [#permalink] New post   24 Jun 2019, 01:17
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[GMAT math practice question]

A factory has two machines. Machine X can produce 200 pins per hour and machine Y can produce 500 pins per hour. At least one machine is in operation throughout the 8-hour work day. The factory must produce 5,000 pins every day. What is the least possible number of hours that machines X and Y must work together on each day?

A. 4
B. 5
C. 6
D. 7
E. 8
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B
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Re: A factory has two machines. Machine X can produce 200 pins per hour an [#permalink] New post   24 Jun 2019, 01:39
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Machine x- 200 pins/hr
Machine y-500 pins/hr

they will run least together when machine with high output works the most

therefore, in 8 hrs Machine y will produce 500x8=4000 pins
remaining pins= 5000- 4000=1000pins

Machine x will have to work for= 1000/200=5 hrs.

hence option B.
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Re: A factory has two machines. Machine X can produce 200 pins per hour an [#permalink] New post   24 Jun 2019, 01:39
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A+B working together = 700 pins/hr
We need minimum number of both machines working together, so we need to maximize the period of 8 hours and produce as close to as 5000 pins.
Option 1 : 7 hours work : 7*700= 4900 + MachineX/Y any to complete anonther 100
Option 2 : 6 hours work
7*600 = 4200 + Machine Y for another 800
Option 3 : 5 hours work :
7*500 = 3500 + Machine Y for another 1500 (3 hrs)
This 5 hours is the correct answer. If we go to 4 hours we can maximum 4800 and not 5000

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Re: A factory has two machines. Machine X can produce 200 pins per hour an [#permalink] New post   24 Jun 2019, 01:58
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MathRevolution wrote:
[GMAT math practice question]

A factory has two machines. Machine X can produce 200 pins per hour and machine Y can produce 500 pins per hour. At least one machine is in operation throughout the 8-hour work day. The factory must produce 5,000 pins every day. What is the least possible number of hours that machines X and Y must work together on each day?

A. 4
B. 5
C. 6
D. 7
E. 8


question needs to be understood well before solving as i found it to be a bit confusing;

given ; At least one machine is in operation throughout the 8-hour work day
since we need to find the least together working hours so so let the machine Y with highest rate be in operation for 8 hrs ; it will produce ; 8*500; 4000 pins
left with 5000-4000; 1000 pins ; since contribution of both machines is required so machine x will take ; 1000/200; 5 hrs
now see wording
what is the least possible number of hours that machines X and Y must work together on each day
the least hours worked by both machine will be 5 hrs ; but total hours would be 13 ..
IMO B
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Re: A factory has two machines. Machine X can produce 200 pins per hour an [#permalink] New post   26 Jun 2019, 01:06
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=>

In order to minimize the number of hours that the two machines work together, the more efficient machine \(Y\) should work for the entire day.

Thus, \(Y\) works for \(8\) hours and produces \(8 * 500 = 4,000\) pins.

There are \(1,000\) pins remaining for machine \(X\) to produce. This takes \(\frac{1,000}{200} = 5 hours.\)

Therefore, B is the answer.
Answer: B
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Re: A factory has two machines. Machine X can produce 200 pins per hour an [#permalink] New post   31 May 2023, 02:40
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Re: A factory has two machines. Machine X can produce 200 pins per hour an [#permalink]
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