Question

What is the day of \(31^{st}\) December of any year? I) In that year the first of March was Monday.
II) That year was a leap year.

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question
• C. Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
• D. Both the statements I and II together are not sufficient to answer the question and additional data is required

Hint:

If a known date is after February, leap year information does not affect the day calculation for later dates in the same year.

Answer 1

The Correct Option is A

Concept:
To find the day of a future date, we need the day of some known date and then count the number of odd days between them. Here, the target date is \[ 31^{st}\text{ December} \]

Step 1: Check Statement I. Statement I says that \[ 1^{st}\text{ March was Monday} \] From \(1^{st}\) March to \(31^{st}\) December, the number of days difference is fixed for every year because February is already over. So the leap year information does not affect dates from March to December. Thus, Statement I alone is enough to determine the day of \(31^{st}\) December.

Step 2: Check Statement II. Statement II says the year was a leap year. Knowing only that a year is leap year does not tell the day of \(31^{st}\) December. For example, different leap years may have different weekdays on \(31^{st}\) December. So Statement II alone is not sufficient.

Step 3: Final answer. \[ \boxed{\text{Statement I alone is sufficient}} \]