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A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds.They beeped together at 10 AM.The immediate next time that they will beep together is _____.
- a)10.42 AM
- b)10.00 PM
- c)10.08 AM
- d)11.00 AM
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A digital watch X beeps every 30 seconds while watch Y beeps every 32 ...
Given:
- Digital watch X beeps every 30 seconds
- Digital watch Y beeps every 32 seconds
- They beeped together at 10 AM
To find:
- The immediate next time that they will beep together
Solution:
To find the next time they beep together, we need to find the LCM (Least Common Multiple) of 30 and 32.
Prime factorization of 30: 2 x 3 x 5
Prime factorization of 32: 2 x 2 x 2 x 2 x 2
LCM: 2 x 2 x 2 x 2 x 3 x 5 = 240
Therefore, the watches will beep together every 240 seconds.
To find the next time they will beep together after 10 AM:
- We need to find out how many seconds have passed since 10 AM.
- Since there are 60 minutes in an hour and 60 seconds in a minute, 1 hour = 60 x 60 = 3600 seconds.
- At 10 AM, 3,600 seconds have passed.
- Add the seconds in the current time to get the total number of seconds passed since 10 AM.
- For example, if the current time is 10:08 AM, then 3,600 + 8 x 60 = 4,980 seconds have passed.
- Now, divide the total number of seconds passed by 240 (the LCM) and take the remainder.
- If the remainder is 0, then the watches will beep together now.
- If the remainder is not 0, then the next time they will beep together is when the number of seconds passed plus the remainder equals a multiple of 240.
Let's apply this to the answer choices:
a) 10.42 AM: 10,620 seconds have passed (3,600 + 42 x 60). Remainder = 60. Next beep together at 10,680 seconds (10.08 AM + 9 minutes)
b) 10.00 PM: 12 hours = 43,200 seconds. Remainder = 0. They will beep together at 10 PM.
c) 10.08 AM: 4,080 seconds have passed. Remainder = 0. They will beep together now.
d) 11.00 AM: 7,200 seconds have passed. Remainder = 0. They will beep together at 11 AM.
Therefore, the immediate next time they will beep together is 10.08 AM, which is option (c).
- Digital watch X beeps every 30 seconds
- Digital watch Y beeps every 32 seconds
- They beeped together at 10 AM
To find:
- The immediate next time that they will beep together
Solution:
To find the next time they beep together, we need to find the LCM (Least Common Multiple) of 30 and 32.
Prime factorization of 30: 2 x 3 x 5
Prime factorization of 32: 2 x 2 x 2 x 2 x 2
LCM: 2 x 2 x 2 x 2 x 3 x 5 = 240
Therefore, the watches will beep together every 240 seconds.
To find the next time they will beep together after 10 AM:
- We need to find out how many seconds have passed since 10 AM.
- Since there are 60 minutes in an hour and 60 seconds in a minute, 1 hour = 60 x 60 = 3600 seconds.
- At 10 AM, 3,600 seconds have passed.
- Add the seconds in the current time to get the total number of seconds passed since 10 AM.
- For example, if the current time is 10:08 AM, then 3,600 + 8 x 60 = 4,980 seconds have passed.
- Now, divide the total number of seconds passed by 240 (the LCM) and take the remainder.
- If the remainder is 0, then the watches will beep together now.
- If the remainder is not 0, then the next time they will beep together is when the number of seconds passed plus the remainder equals a multiple of 240.
Let's apply this to the answer choices:
a) 10.42 AM: 10,620 seconds have passed (3,600 + 42 x 60). Remainder = 60. Next beep together at 10,680 seconds (10.08 AM + 9 minutes)
b) 10.00 PM: 12 hours = 43,200 seconds. Remainder = 0. They will beep together at 10 PM.
c) 10.08 AM: 4,080 seconds have passed. Remainder = 0. They will beep together now.
d) 11.00 AM: 7,200 seconds have passed. Remainder = 0. They will beep together at 11 AM.
Therefore, the immediate next time they will beep together is 10.08 AM, which is option (c).
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Community Answer
A digital watch X beeps every 30 seconds while watch Y beeps every 32 ...
Concept:
The Watched will beep together at the time of their Least Common Multiple (LCM).
Calculation:
Given:
Watch X beeps at = 30 sec
Watch Y beeps at = 32 sec
They beep together at = 10.00 AM
LCM of (30 & 32) = 480 sec
And X and Y will beep together after 480 sec or 8 minutes.
So Next beep time = 10.08 AM
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A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds.They beeped together at 10 AM.The immediate next time that they will beep together is _____.a)10.42 AMb)10.00 PMc)10.08 AMd)11.00 AMCorrect answer is option 'C'. Can you explain this answer?
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