For a certain month, the dates of three of the Sundays are even numbers. Then, the 15th of the that month falls on a

### Concept & Weekly Date Patterns Days of the week are spaced exactly 7 days apart. Consequently, the parity (even/odd) of the dates for a specific weekday alternates. If the 1st is even, the next is odd, the next is even, and so on. ### Step-by-Step Solution - We are told that three Sundays in a single month have even dates. - Since a month has a maximum of 31 days, a day of the week can appear at most 5 times. - Let's map the sequence of even (E) and odd (O) dates for consecutive weeks: E, O, E, O, E. - To have three even-numbered Sundays, the month MUST have exactly 5 Sundays, and they must follow the E-O-E-O-E pattern. - The lowest possible even date for the first Sunday is the 2nd. - Let's test if the 1st Sunday is on the 2nd: - 1st Sunday: 2nd (Even) - 2nd Sunday: $2 + 7 = 9$th (Odd) - 3rd Sunday: $9 + 7 = 16$th (Even) - 4th Sunday: $16 + 7 = 23$rd (Odd) - 5th Sunday: $23 + 7 = 30$th (Even) - This perfectly satisfies the condition of having three even-dated Sundays (2nd, 16th, 30th) within a valid month length (30 or 31 days). - If the 16th is a Sunday, we can find the day for the 15th by stepping backward by one day. - Sunday - 1 day = Saturday. ### Exam Strategy & Shortcut Memorize that if a month has 3 even occurrences of a weekday, those dates MUST be the 2nd, 16th, and 30th. Once you know the 16th is that specific weekday (Sunday), the 15th is always the day before (Saturday). ### Common Pitfall Trying to start the first Sunday on an odd date (like the 1st or 3rd), which only yields two even Sundays (8, 22 or 10, 24). ### Final Answer Therefore, the correct answer is **Saturday**.