Question

A person was born on the fifth Monday of February in a particular year.
Which one of the following statements is correct based on the above information?

• A. The 2\textsuperscript{nd} February of that year is a Tuesday
• B. There will be five Sundays in the month of February in that year
• C. The 1\textsuperscript{st} February of that year is a Sunday
• D. All Mondays of February in that year have even dates

Hint:

To solve problems involving days of the week in a given month, first determine the day of the week for the 1\textsuperscript{st} of the month and then calculate the days of the following dates. For a leap year, February will have 29 days.

Answer 1

The Correct Option is A

Let’s break down the information step-by-step:
The problem states that a person was born on the fifth Monday of February in a particular year. To get to the correct answer, we need to analyze the distribution of the days in February in that year. Step 1: Determine the conditions for five Mondays in February.
- February typically has 28 or 29 days, depending on whether the year is a leap year.
- If a person is born on the fifth Monday of February, then February must have at least five Mondays.
- In order for a month to have five Mondays, the month must have 29 days (February in a leap year) because if February has only 28 days, it can have at most four Mondays.
- So, the year must be a leap year for the person to be born on the fifth Monday.
Step 2: Understand the distribution of the dates.
In a leap year, February has 29 days. To have five Mondays, the first Monday must fall on February 1\textsuperscript{st}, and the remaining Mondays will fall on: - 1\textsuperscript{st}, 8\textsuperscript{th}, 15\textsuperscript{th}, 22\textsuperscript{nd}, and 29\textsuperscript{th}. Step 3: Determine the day of the week for February 2\textsuperscript{nd.}
- Since February 1\textsuperscript{st} is a Monday, the next day, February 2\textsuperscript{nd}, must be a Tuesday.
This is the key to answering the question because the statement in option (A) says "The 2\textsuperscript{nd} February of that year is a Tuesday", which is true based on the above calculations. Step 4: Analyze the other options.
- Option (B) suggests that there will be five Sundays in the month of February. Since February has only 29 days and we already know the distribution of Mondays, February can only have four Sundays, not five. Thus, option (B) is incorrect. - Option (C) claims that the 1\textsuperscript{st} of February is a Sunday. However, as we have already determined, February 1\textsuperscript{st} is a Monday, so option (C) is incorrect. - Option (D) states that all Mondays of February have even dates. The Mondays of February are 1\textsuperscript{st}, 8\textsuperscript{th}, 15\textsuperscript{th}, 22\textsuperscript{nd}, and 29\textsuperscript{th}. As we can see, February 1\textsuperscript{st} is an odd date, so option (D) is also incorrect. Step 5: Conclusion.
Thus, the only correct statement is (A), "The 2\textsuperscript{nd} February of that year is a Tuesday."