Last visit was: 25 Jul 2024, 08:15 It is currently 25 Jul 2024, 08:15
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94614
Own Kudos [?]: 643801 [8]
Given Kudos: 86753
Senior Manager
Joined: 22 Nov 2018
Posts: 430
Own Kudos [?]: 496 [1]
Given Kudos: 292
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 740 Q49 V41
Intern
Joined: 08 Apr 2019
Posts: 24
Own Kudos [?]: 9 [1]
Given Kudos: 43
Location: India
GMAT 1: 700 Q50 V34
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19199
Own Kudos [?]: 22719 [1]
Given Kudos: 286
Location: United States (CA)
Re: In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink]
1
Kudos
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.

Manager
Joined: 16 Dec 2018
Posts: 59
Own Kudos [?]: 103 [3]
Given Kudos: 48
In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink]
3
Kudos
Let's focus on 1 machine at a time and list the starting and stopping time.

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
In a factory, machine A operates on a cycle of 20 hours of work follow [#permalink]
Moderator:
Math Expert
94614 posts