The correct answer is (a) Monday.
If Sunday comes 6 days from today, then today is not a Sunday. The days of the week repeat in a cycle of 7 days, so if today is not a Sunday, then it must be one of the other 6 days of the week. Since today is October 15th, and there are 31 days in October, then January 1st of next year will be 3 months and 16 days after today. In 3 months and 16 days, there will be 104 days. Since there are 7 days in a week, then 104 days is equal to 14 weeks and 2 days. Since today is not a Sunday, then 14 weeks and 2 days after today will be a Monday.
Here is a brief explanation of each option:
(a) Monday: This is the correct answer. As explained above, if Sunday comes 6 days from today, then today is not a Sunday. The days of the week repeat in a cycle of 7 days, so if today is not a Sunday, then it must be one of the other 6 days of the week. Since today is October 15th, and there are 31 days in October, then January 1st of next year will be 3 months and 16 days after today. In 3 months and 16 days, there will be 104 days. Since there are 7 days in a week, then 104 days is equal to 14 weeks and 2 days. Since today is not a Sunday, then 14 weeks and 2 days after today will be a Monday.
(b) Tuesday: This is not the correct answer. As explained above, if Sunday comes 6 days from today, then today is not a Sunday. The days of the week repeat in a cycle of 7 days, so if today is not a Sunday, then it must be one of the other 6 days of the week. Since today is October 15th, and there are 31 days in October, then January 1st of next year will be 3 months and 16 days after today. In 3 months and 16 days, there will be 104 days. Since there are 7 days in a week, then 104 days is equal to 14 weeks and 2 days. Since today is not a Sunday, then 14 weeks and 2 days after today will be a Monday, not a Tuesday.
(c) Wednesday: This is not the correct answer. As explained above, if Sunday comes 6 days from today, then today is not a Sunday. The days of the week repeat in a cycle of 7 days, so if today is not a Sunday, then it must be one of the other 6 days of the week. Since today is October 15th, and there are 31 days in October, then January 1st of next year will be 3 months and 16 days after today. In 3 months and 16 days, there will be 104 days. Since there are 7 days in a week, then 104 days is equal to 14 weeks and 2 days. Since today is not a Sunday, then 14 weeks and 2 days after today will be a Monday, not a Wednesday.
(d) Friday: This is not the correct answer. As explained above, if Sunday comes 6 days from today, then today is not a Sunday. The days of the week repeat in a cycle of 7 days, so if today is not a Sunday, then it must be one of the other 6 days of the week. Since today is October 15th, and there are 31 days in October, then January 1st of next year will be 3 months and 16 days after today. In 3 months and 16 days, there will be 104 days. Since there are 7 days in a week, then 104 days is equal to 14 weeks and 2 days. Since today is not a Sunday, then 14 weeks and 2 days after today will be a Monday, not a Friday.