Question

Which weekday is the last day of 1996?
I) The year has 53 Mondays and 53 Tuesdays.
II) 1996 is a leap year.

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

Hint:

In leap years, 2 extra consecutive days occur 53 times. Identifying them reveals the starting day of the year.

Answer 1

The Correct Option is A

Concept: A leap year has 366 days = 52 weeks + 2 extra days. These extra two consecutive weekdays occur 53 times.
Step 1: Analyze Statement I alone.
Given: 53 Mondays and 53 Tuesdays.
This means the extra two days are Monday and Tuesday.
So, the year starts on Monday. Now, in a leap year: \[ {Last day} = {First day} + 1 \] So, \[ {Last day} = {Tuesday} \] Thus, the last day is uniquely determined.
Statement I alone is sufficient.
Step 2: Analyze Statement II alone.
Only tells that it is a leap year, but starting day is unknown.
Statement II alone is NOT sufficient.
Step 3: Combine both statements.
Not required, since Statement I alone is sufficient.
Hence, Statement I alone is sufficient.