The last day of a century cannot be either(A) Tuesday(B) Thursday(C)…

The correct answer is Option (3) → (A), (B) and (C) only

The last day of a century is fixed by the number of odd days (days left over after whole weeks) in 100, 200, 300 and 400 years, counted from the start of the calendar, where 0 odd days means Sunday.

• 100 years have 76 ordinary years and 24 leap years: \(76+2\times24=124\) odd days, which is 17 weeks + 5 odd days, so the century ends on a Friday

• 200 years: \(2\times5=10\), that is 3 odd days, so Wednesday

• 300 years: \(3\times5=15\), that is 1 odd day, so Monday

• 400 years: \(4\times5+1=21\) (the 400th year is a leap year), that is 0 odd days, so Sunday

The pattern then repeats every 400 years, so a century can end only on a Friday, Wednesday, Monday or Sunday.

(A) Tuesday Never the last day of a century (Correct). Tuesday is not among Friday, Wednesday, Monday and Sunday.

(B) Thursday Never the last day of a century (Correct). Thursday is not among the four possible days either.

(C) Saturday Never the last day of a century (Correct). Saturday is not among the four possible days.

(D) Sunday Can be the last day of a century (Incorrect). Every 400th year ends on a Sunday, for example 31 December 2000.