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?

1. 360
2. 720
3. 1080
4. 1440
5. 2160

Answer:
Solution with Explanation
Approach Solution (1):

1 hour have 3600 seconds
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 (120/4 = 5 days)
Or will show 3 hours less than 10:00 am 15 days later
Hence
Total 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)
Jack’s watch will show 13:00 pm and Jose’s watch will show 1:00 am
= Total 1080 hours

Correct Option: C

Approach Solution (2):

Jack’s watch gains 10 seconds every hour
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
i.e., 12 hours gap will come in \(\frac{1}{40}*12*60*60 = 1080\) hours

Correct Option: C

Approach Solution (3):

Given: Jack’s watch gains 10 seconds every hour
Jose’s watch loses 15 seconds every 30 minutes
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
12 hours gap will come in\(\frac{1}{40}*12*60*60 = 1080\) hours

Correct Option: C

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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