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Re: In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink]
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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]
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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]
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