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QOTD#9 In a factory, machine A operates on a cycle of 20

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QOTD#9 In a factory, machine A operates on a cycle of 20 [#permalink] New post 12 Sep 2016, 11:31
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Question Stats:

38% (01:57) correct 61% (02:26) wrong based on 18 sessions
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?

Indicate all such days.

A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
F. Saturday

[Reveal] Spoiler: OA
C and E

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Question: 19
Page: 207
[Reveal] Spoiler: OA

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Joined: 07 Jun 2014
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Re: QOTD#9 In a factory, machine A operates on a cycle of 20 [#permalink] New post 12 Sep 2016, 11:35
Expert's post
Explanation

Both machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. Note that 1 day has 24 hours and 2 days have 48 hours.

Machine A operates on a cycle of 20 hours of work followed by 4 hours of rest, so it was at rest from 8 o’clock in the morning until 12 noon every day from Tuesday to Saturday.

Machine B operates on a cycle of 40 hours of work followed by 8 hours of rest, so it was at rest from 4 o’clock in the morning until 12 noon on Wednesday and Friday.

Thus both machines were at rest from 8 o’clock in the morning until 12 noon on Wednesday and Friday. The correct answer consists of Choices C and E.
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Re: QOTD#9 In a factory, machine A operates on a cycle of 20 [#permalink] New post 20 Sep 2016, 14:44
Expert's post
sandy 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?

Indicate all such days.

A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
F. Saturday


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.
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Re: QOTD#9 In a factory, machine A operates on a cycle of 20 [#permalink] New post 29 May 2017, 19:57
is there any quicker method to do this calculation?

GreenlightTestPrep wrote:
sandy 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?

Indicate all such days.

A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
F. Saturday


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.
Re: QOTD#9 In a factory, machine A operates on a cycle of 20   [#permalink] 29 May 2017, 19:57
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QOTD#9 In a factory, machine A operates on a cycle of 20

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