Official Quant Practice--Mixed Practice p. 205, No. 19

[mattoliver.mattoliver]

19. 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-F (Monday through Saturday.)

I could use some help visualizing an easier/faster way to solve this. The explanation provided really is quite ho-hum. Can this be tied to any other broad type or category of questions that I can fit into my review? Like a least common multiple-type of thing?

[n00bpron00bpron00b]

I don't think LCM concept can be applied here (please correct me if I am wrong). Listing down "rest period" scenarios for both cases could be one of the way to go about -

Let's just see the pattern for rest periods.

Machine A
Start : Monday 12:00 PM and Ends Sat : 12:00 PM
Work hours : 20
Rest hours : 4

Rest hours -
Every day from Tuesday to Saturday - 8:00 AM - 12:00 PM

Machine B
Start : Monday 12:00 PM and Ends : Sat : 12:00 PM
Work hours : 40
Rest hours : 8

Rest hours -
Wednesday 4:00 AM - 12:00 PM
Friday 4:00 AM - 12:00 PM

So the days when both machines are at rest : Wed, Friday

[tommywallach]

Hey Matt,

Noob is right. In the GMAT, we literally have a couple questions like this in a section that's basically titled "Other Weird Question Types" in the Word Problems book. Because it's just...what it is.

That said, this question DOES make it easy, because the time periods both revolve around multiples of 24. If the schedules were more complicated (i.e. 8 hours on, 2 hours off) then this would be a nightmare. Luckily, the test is nicer than that. : )

-t

[mattoliver.mattoliver]

Cool thanks.

[tommywallach]

No problem! (And thanks, Noob.)