The last day of a century cannot be a Tuesday. Let's break down the reasoning behind this answer.

Explanation:
The last day of a century refers to the 100th day of a century. Since each century has 100 years, the last year of a century is the 100th year. For example, the last year of the 20th century is the year 2000.

Calculating the day:
To determine the day of the week for a given date, we need to apply a mathematical formula known as the Zeller's Congruence. This formula allows us to calculate the day of the week based on the given date.

The Zeller's Congruence formula:
h = (q + [(13(m+1))/5] + K + [(K/4)] + [(J/4)] - 2J) mod 7

Where:
- h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday)
- q is the day of the month
- m is the month (3 = March, 4 = April, ..., 12 = December)
- K is the year of the century (year mod 100)
- J is the zero-based century (actually ⌊ year/100 ⌋)

Applying the formula:
Let's consider the date December 31, 2000, as an example. Using the Zeller's Congruence formula, we can calculate the day of the week for this date.

q = 31 (day of the month)
m = 12 (month)
K = 0 (2000 mod 100)
J = 19 (⌊2000/100⌋)

Substituting these values into the formula:

h = (31 + [(13(12+1))/5] + 0 + [0/4] + [19/4] - 2(19)) mod 7
h = (31 + [(13*13)/5] + 0 + 0 + 4 - 38) mod 7
h = (31 + 33 + 0 + 0 + 4 - 38) mod 7
h = 30 mod 7
h = 2

According to the formula, the calculated value of h is 2, which corresponds to Monday. Therefore, December 31, 2000, was a Monday.

Conclusion:
Based on the Zeller's Congruence formula, we can see that the last day of a century, such as December 31, 2000, can be any day of the week, including Tuesday. Thus, option A is incorrect, and the correct answer to the question is not A.