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Jack's watch gains 10 seconds every hour
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Author:  shreyasharma1206 [ 31 Jul 2020, 06:36 ]
Post subject:  Jack's watch gains 10 seconds every hour

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

Author:  yashikaaggarwal [ 31 Jul 2020, 07:45 ]
Post subject:  Re: Jack's watch gains 10 seconds every hour

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

Author:  AndrewN [ 31 Jul 2020, 07:55 ]
Post subject:  Re: Jack's watch gains 10 seconds every hour

yashikaaggarwal wrote:
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

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

Author:  AnirudhaS [ 31 Jul 2020, 08:23 ]
Post subject:  Re: Jack's watch gains 10 seconds every hour

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"!

Author:  shreyasharma1206 [ 31 Jul 2020, 20:21 ]
Post subject:  Re: Jack's watch gains 10 seconds every hour

Official answer provided by Experts Global is 1080 hours

Posted from my mobile device

Author:  GMATinsight [ 31 Jul 2020, 21:18 ]
Post subject:  Jack's watch gains 10 seconds every hour

shreyasharma1206 wrote:
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


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

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Author:  effatara [ 31 Jul 2020, 23:35 ]
Post subject:  Re: Jack's watch gains 10 seconds every hour

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

Author:  yashikaaggarwal [ 31 Jul 2020, 23:42 ]
Post subject:  Re: Jack's watch gains 10 seconds every hour

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

Author:  GMATinsight [ 01 Aug 2020, 00:46 ]
Post subject:  Re: Jack's watch gains 10 seconds every hour

yashikaaggarwal wrote:
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


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

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Post subject:  Re: Jack's watch gains 10 seconds every hour

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