Question Analysis:
The question asks us to determine the day of the week on January 1, 1991, given that January 1, 1990, was a Monday. We need to find the pattern of days and calculate the day of the week accordingly.

Solution:
To find the day of the week on January 1, 1991, we need to observe the pattern of days in a year. There are two main factors to consider: leap years and the number of days in a week.

The Pattern of Days:
There are 7 days in a week, and this cycle repeats itself. Let's assign a number to each day of the week:
- Monday: 1
- Tuesday: 2
- Wednesday: 3
- Thursday: 4
- Friday: 5
- Saturday: 6
- Sunday: 7

Leap Years:
A leap year occurs every 4 years, except for years that are divisible by 100 but not by 400. For example, 1992 and 1996 are leap years, but 1900 is not a leap year.

Calculating the Day of the Week on January 1, 1991:
To calculate the day of the week on January 1, 1991, we need to count the number of days between January 1, 1990, and January 1, 1991.

- From January 1, 1990, to January 1, 1991, there are 365 days.

Since 365 is not divisible by 7, we need to find the remainder when 365 is divided by 7. The remainder will tell us the number of days we need to add to the starting day (Monday) to find the final day of the week.

- 365 ÷ 7 = 52 remainder 1

The remainder 1 means that we need to add one day to Monday (1). Therefore, the day of the week on January 1, 1991, will be Tuesday (2).

Conclusion:
The day of the week on January 1, 1991, will be Tuesday.