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

4

Expert Reply

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Question Stats:

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

_________________

Indicate all such days.

A. Monday

B. Tuesday

C. Wednesday

D. Thursday

E. Friday

F. Saturday

Practice Questions

Question: 19

Page: 207

Question: 19

Page: 207

_________________

Sandy

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Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
15 Jun 2019, 09:01

5

1

both machines should stop at a 40 hours interval [ as the LCM of 20,40 is 40]

so, starting from 12.00 noon of Monday we can take a 40 hour working time followed by a rest .

thus, 12noo+40 hours lead to a rest on Wednesday

again another 40 hours, now it's on Friday.

so, starting from 12.00 noon of Monday we can take a 40 hour working time followed by a rest .

thus, 12noo+40 hours lead to a rest on Wednesday

again another 40 hours, now it's on Friday.

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
20 Sep 2016, 14:44

1

Explanation

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.

Answer: C and E

Cheers,

Brent

_________________

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.

Answer: C and E

Cheers,

Brent

_________________

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

1

is there any quicker method to do this calculation?

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.

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

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]
08 Oct 2019, 06:23

Yes we can find the LCM of total hours in order to have answer

eg: LCM of 24 hrs and 48 hrs

eg: LCM of 24 hrs and 48 hrs

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
30 Oct 2019, 20:46

1

Yes we can find the LCM of total hours in order to have answer

eg: LCM of 24 hrs and 48 hrs

eg: LCM of 24 hrs and 48 hrs

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
29 Jan 2020, 23:14

i saw this question in the ETS practice book but was a bit confused by the wording...

thought that "following saturday" meant we needed to calculate two weeks worth, which would mean it would include Monday...

was wondering if that confused anyone else?

thought that "following saturday" meant we needed to calculate two weeks worth, which would mean it would include Monday...

was wondering if that confused anyone else?

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Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
30 Jan 2020, 04:15

1

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

Indicate all such days.

A. Monday

B. Tuesday

C. Wednesday

D. Thursday

E. Friday

F. Saturday

Practice Questions

Question: 19

Page: 207

Question: 19

Page: 207

For Machine A: For 20 hours of work, it takes 4 hours rest

=> In a span of 24 hours, the last 4 hours are for rest ... (i)

For Machine B: For 40 hours of work, it takes 8 hours rest

=> In a span of 48 hours, the last 8 hours are for rest ... (ii)

Thus, for the last 4 hours (out of the 8 hours) when Machine B is at rest, Machine A is also at rest.

This scenario occurs at the end of the 2nd day from when both A and B have started to work together

Thus, in every 2 days (48 hours), both machines are at rest in the last 4 hours

The machines start on Monday 12 noon

# First time both rest are the last 4 hrs of the 2nd day i.e. 8 am to 12 noon of Wednesday

(after this, both start working together from 12 noon of Wednesday)

# Thus, the second time both rest are the last 4 hrs of the 2nd day from Wednesday i.e. 8 am to 12 noon of Friday

There would be no more opportunities of resting together since they work only till Saturday.

Answers: C and E

_________________

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Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
27 May 2020, 05:51

1

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

Indicate all such days.

A. Monday

B. Tuesday

C. Wednesday

D. Thursday

E. Friday

F. Saturday

Practice Questions

Question: 19

Page: 207

Question: 19

Page: 207

With such exercises I feel they look harder then they are.

Starting off with looking at mac a

mac a works 20hr and then rests 4 hr

Meaning that we would see their cycle looking like the following 20 work 4 rest= 24 hr, 24+20work + 4rest= 48 hr

Now B goes 40 work + 8 rest =48hr , 48+40work+8rest= 96hr

Now a thing we can spot or search for is how long does it take the lower one to catch up with the bigger one logic.

We look at A--> A will start their second round of rest at 44hr, which coincides with the rest of B.

Meaning that at the beginning of every second rest from A the two will rest simultaneously.

This leading us to the conclusion that every 44 hours the two will rest together for 4 hr.

This would mean the first rest that the two will have together will be on WED-->12+24+8=44-->leaving us with 16 hr left in wed

the next rest will be on friday 16+24+4=44-->leaving us with 20+12 hr from friday and saturday which is not enough to get a rest in together

Thereby getting the answers c and e

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
24 Jun 2020, 17:05

anita123 wrote:

Yes we can find the LCM of total hours in order to have answer

eg: LCM of 24 hrs and 48 hrs

eg: LCM of 24 hrs and 48 hrs

Hi, can you explain me how you get the result by LCM?

Thx,Regards

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
13 Aug 2021, 13:08

1

Process

Since they start on Monday and work until Saturday, they have 5x24 = 120 hours of work. This never intuitively clicks in my brain so, if you're like me, here's proof:

- 24 hours between 12pm Mon and 12pm Tue -> 24 hrs. total so far

- 24 hours between 12pm Tue and 12pm Wed -> 48 hrs. total so far

- 24 hours between 12pm Wed and 12pm Thu -> 72 hrs. total so far

- 24 hours between 12pm Thu and 12pm Fri -> 96 hrs. total so far

- 24 hours between 12pm Fri and 12pm Sat -> 120 hrs. total

Let's define a "day" as being the time span between 12 noon and the next 12 noon (e.g. 12pm Mon to 12pm Tue):

Machine A rests during the last four hours of each day: 8am to 12pm.

Machine B rests during the last eight hours of each two-day cycle: 4am to 12pm.

That means that, whenever Machine B is resting, Machine A also has to be resting. Since we're interested in overlap, we only need to worry about Machine B.

Let's find multiples of 48 between 0 and 120: 48, 96.

What would those times correspond to?

- 12pm Wednesday --> C

- 12pm Friday --> E

Hence, C and E.

Since they start on Monday and work until Saturday, they have 5x24 = 120 hours of work. This never intuitively clicks in my brain so, if you're like me, here's proof:

- 24 hours between 12pm Mon and 12pm Tue -> 24 hrs. total so far

- 24 hours between 12pm Tue and 12pm Wed -> 48 hrs. total so far

- 24 hours between 12pm Wed and 12pm Thu -> 72 hrs. total so far

- 24 hours between 12pm Thu and 12pm Fri -> 96 hrs. total so far

- 24 hours between 12pm Fri and 12pm Sat -> 120 hrs. total

Let's define a "day" as being the time span between 12 noon and the next 12 noon (e.g. 12pm Mon to 12pm Tue):

Machine A rests during the last four hours of each day: 8am to 12pm.

Machine B rests during the last eight hours of each two-day cycle: 4am to 12pm.

That means that, whenever Machine B is resting, Machine A also has to be resting. Since we're interested in overlap, we only need to worry about Machine B.

Let's find multiples of 48 between 0 and 120: 48, 96.

What would those times correspond to?

- 12pm Wednesday --> C

- 12pm Friday --> E

Hence, C and E.

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
24 May 2022, 08:49

GreenlightTestPrep wrote:

Explanation

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.

Answer: C and E

Cheers,

Brent

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.

Answer: C and E

Cheers,

Brent

Hey appreciate that! but isn't it a tedious and time consuming method? Is there like a way to make it more pithy!

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
24 May 2022, 09:19

1

akash0698 wrote:

Hey appreciate that! but isn't it a tedious and time consuming method? Is there like a way to make it more pithy!

On test day, I'd probably create a table, which would speed things up a bit,

_________________

Re: QOTD#9 In a factory, machine A operates on a cycle of 20
[#permalink]
24 May 2022, 21:46

GreenlightTestPrep wrote:

akash0698 wrote:

Hey appreciate that! but isn't it a tedious and time consuming method? Is there like a way to make it more pithy!

On test day, I'd probably create a table, which would speed things up a bit,

Alright! fair enough...Thank you!

gmatclubot

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