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Question
The sum of the digits displayed on a 24-hour clock is 18. When does this happen at the earliest?
The sum of the digits displayed on a 24-hour clock is 18. When does this happen at the earliest?
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Solution
The correct option is A 1 minute before 5 AM
To get the earliest time, we have to maximise the sum of the digits in the minutes displayed.
Hence, the minutes displayed is 59.
The sum of all digits displayed is 18.
Hence,
Sum of the digits of the hour=5+9=18
Sum of the digits of the hour=18−14=4
The lowest hour that satisfies this is 04.
Hence, the earliest when the digits displayed by a 24-hour clock add up to 18 is at 04:59, which is 1 minute before 5 AM.
To get the earliest time, we have to maximise the sum of the digits in the minutes displayed.
Hence, the minutes displayed is 59.
The sum of all digits displayed is 18.
Hence,
Sum of the digits of the hour=5+9=18
Sum of the digits of the hour=18−14=4
The lowest hour that satisfies this is 04.
Hence, the earliest when the digits displayed by a 24-hour clock add up to 18 is at 04:59, which is 1 minute before 5 AM.
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