Understanding the Wedding Anniversary Question

The question asks for the specific date (day and month) of Yuvi's wedding anniversary. To answer this question, we need information that uniquely identifies both the day and the month of the anniversary.

We are given two statements, and we need to determine if either statement alone or both statements together provide enough information to find the exact date of the wedding anniversary.

Analyzing Statement 1: Anniversary Day

Statement 1 says: "On the 7 th day of a month."

• This statement tells us the day of the month for the wedding anniversary is the 7th.
• However, it does not specify which month the anniversary falls in.

Since the month is unknown, Statement 1 alone is not sufficient to determine the exact date of Yuvi's wedding anniversary.

Analyzing Statement 2: Anniversary Month Clue

Statement 2 says: "The month has 29 days only in a leap year."

• We need to identify which month has 29 days exclusively in a leap year.
• Let's consider the number of days in each month:
  • January: 31 days
  • February: 28 days (common year), 29 days (leap year)
  • March: 31 days
  • April: 30 days
  • May: 31 days
  • June: 30 days
  • July: 31 days
  • August: 31 days
  • September: 30 days
  • October: 31 days
  • November: 30 days
  • December: 31 days
• The only month that has 29 days specifically and only in a leap year is February. In a common year, February has 28 days.
• All other months have either 30 or 31 days, which does not change between common and leap years.

Therefore, Statement 2 identifies the month of the wedding anniversary as February. However, it does not tell us the day of the month.

Since the day is unknown, Statement 2 alone is not sufficient to determine the exact date of Yuvi's wedding anniversary.

Analyzing Statements 1 and 2 Together: Finding the Date

Let's combine the information from both statements:

• From Statement 1, the day of the anniversary is the 7th.
• From Statement 2, the month of the anniversary is February.

By combining both pieces of information, we can determine the exact date of the wedding anniversary: February 7th.

Since both statements together provide enough information to answer the question, they are sufficient together.

Evaluating the Options

Based on our analysis:

• Only statement 1 is sufficient? No.
• Both statement 1 and statement 2 are sufficient independently? No.
• Only statement 2 is sufficient? No.
• Both statement 1 and statement 2 are sufficient together? Yes.

The option that matches our conclusion is "Both statement 1 and statement 2 are sufficient together."

Conclusion

Statement 1 gives the day (7th), but not the month. Statement 2 gives the month (February), but not the day. Neither statement alone is sufficient. However, when combined, Statement 1 provides the day and Statement 2 provides the month, allowing us to pinpoint the exact date of Yuvi's wedding anniversary as February 7th. Therefore, both statements together are sufficient.

Revision Table: Wedding Anniversary Date Sufficiency

Additional Information: Months and Leap Years

Understanding the number of days in each month and the concept of a leap year is crucial for solving problems like this. A leap year occurs approximately every four years, adding an extra day to February (making it 29 days instead of 28). This fact is key to Statement 2 uniquely identifying February.

• Most months have 30 or 31 days, irrespective of whether it's a leap year or not.
• February is the only exception where the number of days changes significantly between a common year (28 days) and a leap year (29 days).
• The rule for leap years is: A year is a leap year if it is divisible by 4, unless it is divisible by 100 but not by 400. (e.g., 2000 and 2020 were leap years; 1900 was not; 2100 will not be).

In data sufficiency questions, precisely identifying unique characteristics, such as February being the only month with 29 days only in a leap year, is often the key to determining sufficiency.