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The last day of a century cannot be either
I. Tuesday.
II. Thursday.
III. Saturday.
IV. Sunday.
  • a)
    I and II.
  • b)
    I and IV.
  • c)
    I, II and III.
  • d)
    III and IV.
Correct answer is option 'C'. Can you explain this answer?
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The last day of a century cannot be eitherI. Tuesday.II. Thursday.III...
The last day of century cannot be either Tuesday, Thursday or Saturday.
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The last day of a century cannot be eitherI. Tuesday.II. Thursday.III...
Understanding the Last Day of a Century
The last day of a century falls on December 31 of a year that ends in "00." For example, the last day of the 20th century was December 31, 2000. To determine the day of the week for this date, we can analyze the distribution of leap years and the standard weekly cycle.
Days of the Week Calculation
- A century has 100 years, which includes 24 leap years (divisible by 4 but not by 100, except for 2000 which is a leap year).
- Regular years contribute 1 day each, while leap years contribute an extra day.
- Total days = (76 regular years * 1) + (24 leap years * 2) = 76 + 48 = 124 days.
- 124 days modulo 7 (days of the week) = 5.
Identifying the Day of the Week
- If January 1 of a century starts on a Monday, December 31 of that century will be 5 days later, which lands on a Saturday.
- Therefore, the last day of a century can only be a Saturday if it starts on a Monday.
Excluding Certain Days
- We need to check the specific days mentioned:
- Tuesday: Possible.
- Thursday: Possible.
- Saturday: Not possible (as shown).
- Sunday: Not possible (as it falls on Saturday).
Conclusion
Based on the calculations, the last day of a century cannot be a Saturday or a Sunday. Thus, the correct answer includes options III and IV, leading to the conclusion:
- Correct answer is option 'C': I, II, and III are not possible days for the last day of a century.
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