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In a factory, machine A operates on a cycle of 20 hours of work follow

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Bunuel
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In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink] New post   05 Jun 2019, 01:14
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In a factory, machine A operates on a cycle of 20 hours of work followed by 4 hours of rest, and machine B operates on a cycle of 40 hours of work followed by 8 hours of rest. Last week, the two machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. On which days during that time period was there a time when both machines were at rest?

I. Wednesday
II. Thursday
III. Friday

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
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Re: In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink] New post   05 Jun 2019, 02:50
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Bunuel wrote:
In a factory, machine A operates on a cycle of 20 hours of work followed by 4 hours of rest, and machine B operates on a cycle of 40 hours of work followed by 8 hours of rest. Last week, the two machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. On which days during that time period was there a time when both machines were at rest?

I. Wednesday
II. Thursday
III. Friday

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


Since the machines have a Work+Rest combined cycle of 24 and 48 hrs respectively, On Wednesday just before noon there will be a 4 hour time where both will be on rest and again will repeat on Friday (as they will be in the same position as on Monday noon) IMO Option D
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Re: In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink] New post   05 Jun 2019, 03:04
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machine A will be on rest from 08:00 to 12:00 every day whereas Machine B will be on rest from 04:00 to 12:00 every alternate day. So, only on Wednesday and Friday they will have common time of rest.
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Re: In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink] New post   06 Jun 2019, 18:02
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Bunuel wrote:
In a factory, machine A operates on a cycle of 20 hours of work followed by 4 hours of rest, and machine B operates on a cycle of 40 hours of work followed by 8 hours of rest. Last week, the two machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. On which days during that time period was there a time when both machines were at rest?

I. Wednesday
II. Thursday
III. Friday

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


After machine A completes one work-rest cycle, which will take 20 + 4 = 24 hours, it will rest again between 24 + 20 = 44 and 44 + 4 = 48 hours after starting the first cycle.

Machine B rests between 40 and 48 hours after starting the first cycle.

Therefore, the two machines are resting at the same time at the second rest stop of machine A, which is between 44 and 48 hours after Monday 12:00p.m. Since 48 hours following Monday 12:00p.m. is Wednesday 12:00p.m., the two machines rest together for the first time between 8:00am and 12:00p.m. on Wednesday.

The above cycle will repeat once more, and thus, the two machines will rest together between 44 and 48 hours after Wednesday 12:00p.m.; which will be between 8:00a.m. and 12:00p.m. on Friday, by the same reasoning as above.

Since another 48 hours from Wednesday 12:00p.m. brings us to Sunday, the only days where the two machines are resting together in the given time period are Wednesday and Friday.

Answer: D
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In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink] New post   11 Nov 2019, 03:21
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Let's focus on 1 machine at a time and list the starting and stopping time.
We'll start with Machine A

MONDAY
12 noon: Machine A starts

TUESDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

WEDNESDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

THURSDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

FRIDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

SATURDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

------------------------------------------------------
Now let's add Machine B

MONDAY
12 noon: Machine A starts
12 noon: Machine B starts

TUESDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

WEDNESDAY
4:00 am: Machine B stops
8:00 am: Machine A stops
12:00 noon: Machine A starts
12:00 noon: Machine B starts

THURSDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

FRIDAY
4:00 am: Machine B stops
8:00 am: Machine A stops
12:00 noon: Machine A starts
12:00 noon: Machine B starts

SATURDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

As we can see, both machines are stopped at the same time on Wednesday and Friday.

#Courtesy goes to @greenlightprep
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In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink]
11 Nov 2019, 03:21
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