Jack's watch gains 10 seconds every hour

Question

Jack's watch gains 10 seconds every hour. Jose's watch loses 15 seconds every 30 minutes. If they set their watches correctly at 10:00 am, after how many hours will the two watches show the same time again?

A.360
B. 720
C. 1080
D. 1440
E. 2160

A.360
B. 720
C. 1080
D. 1440
E. 2160

yashikaaggarwal · Answer

1 hour have 3600 second
Jack's watch gains 10 seconds every hour. 
jack's watch will gain 1 hour or 3600 seconds in 3600/10 = 360 hours
that means jack's watch will show 1 hour more than 10:00 am 15 days later (360/24 = 15 days)
Also,
Jose's watch loses 15 seconds every 30 minutes. or 30 seconds per hour
jose's watch will lose 1 hour or 3600 seconds in 3600/30 = 120 hours
that means jose's watch will show 1 hour less than 10:00 am 5 days later (120/24 = 5 days)
or will show 3 hours less than 10:00 am 15 days later.
hence 
Today set time = 10:00 am
15 days later, (360 hours later)
Jack's watch will show 11:00 AM and Jose's watch will show 7:00 AM
= Total 360 hours
Another 15 days later, (360 hours later) 
Jack's watch will show 12:00 PM and Jose's watch will show 4:00 AM
= Total 720 hours
Another 15 days later, (360 hours later)
Jack's watch will show 13:00 PM and Jose's watch will show 1:00 AM
= Total 1080 hours
Another 15 days later, (360 hours later)
Jack's watch will show 14:00 PM and Jose's watch will show 22:00PM
= Total 1440 hours
Another 15 days later, (360 hours later)
Jack's watch will show 15:00 PM and Jose's watch will show 19:00PM
= Total 1800 hours
Another 15 days later, (360 hours later)
Jack's watch will show 16:00 PM and Jose's watch will show 16:00PM
= Total 2160 hours

So  shreyasharma1206 , your question is ambiguous here because the clock needles does meet after 1080 hours but they are showing same time after 2160 hours. kindly rectify the part, what's been asked specifically

AndrewN · Answer

I think the point is that 1.00pm and 1.00am look identical on an analog watch, but I agree that the problem could more clearly convey such vital information:  show the same time  is indeed unclear, particularly in an age in which digital watches, which is not to even mention smart watches, are increasingly common.

Thank you, in any case,  yashikaaggarwal , for providing such a detailed response, and for sharing in the first place,  shreyasharma1206 .

- Andrew

AnirudhaS · Answer

When you say the "same time" it has to be the "same". One cannot be AM and the other PM!
And for me the answer is undoubtedly 2160 hours, unless it is changed to "it looks the same"!

shreyasharma1206 · Answer

Official answer provided by Experts Global is 1080 hours

Posted from my mobile device

GMATinsight · Answer

Jack's watch  gains  10 seconds every hour

Jose's watch loses 15 seconds every 30 minutes
 i.e. Jose's watch  loses  30 seconds every hour

The relative gap change between their watches =  10 + 30  =  40 seconds every hour

Two watches will show same time when gap between them is 12 hours

40 seconds gap comes in 1 hour
ie. 12 hours gap will come in  (\frac{1}{40})*(12*60*60) = 1080  hours

Answer: Option C

https://gmatinsight.com/all-courses/

effatara · Answer

Excellent solution,  GMATinsight !
I will try to make this conceptually easier to grasp. Imagine that the clock-face is a circular race track and the hour hands of the watches are two runners who start running clock-wise from the same point at the same time. The circumference of the track is, of course, 12 hrs (12*60*60 secs) where hours and seconds are, in this context, units of distance, not time. The Faster Hour Hand (FHH) moves 40 secs more than the Slower Hour Hand (SHH) in each hour. The FHH must come up from behind and catch up with the SHH for the two clocks to display the same time. To do this, FHH must make up for the length of the circumference of the track (12*60*60 secs). FHH gains 40 secs on SHH in 1 hr. FHH gains 1 second on SHH in 1/40 hrs. FHH gains 12*60*60 secs on SHH (catching up with it) in (12*60*60)/40 hrs = 1080 hrs

yashikaaggarwal · Answer

So we are considering the time, the respective watches are showing irrespective of day/night 12 hour interval in between them?

Posted from my mobile device

GMATinsight · Answer

Two analog watches (usually used in questions of clocks unless mentioned otherwise) show the same time when they are 12 hours apart.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Jack's watch gains 10 seconds every hour

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards