Answer :
Final answer:
The clock will show 1:02 PM on the sixth day after gaining 12 minutes every 12 hours starting from 11 AM on the first day. The provided options do not contain this answer, signaling the need for a review of the choices.
Explanation:
The clock is set correctly at 11 AM and it gains 12 minutes every 12 hours. Therefore, it gains 1 minute every hour.
From 11 AM on the first day to 1 PM on the sixth day is a total of 5 days and 2 hours, which equates to 122 hours (5 days * 24 hours + 2 hours).
Since the clock gains 1 minute every hour, over 122 hours it will have gained 122 minutes. We need to express this excess time in hours and minutes to add to the initial time.
122 minutes is equivalent to 2 hours and 2 minutes (since there are 60 minutes in an hour, 122 minutes / 60 minutes = 2 hours with 2 minutes left over).
Adding 2 hours and 2 minutes to 11 AM yields: 11 AM + 2 hours = 1 PM; then adding 2 minutes gives us 1:02 PM on the sixth day. So, the correct answer is not listed in the options provided and requires further review.
