Determine the dates on which it will be a Sunday in June 2004 if 1st January 2004 was a...
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Determine the dates on which it will be a Sunday in June 2004 if 1st January 2004 was a Thursday.
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Answer: B. 6, 13, 20, and 27
By calculating the total number of days from January 1st to June 1st, 2004 (a leap year), we find that June 1st was a Tuesday. Consequently, the first Sunday of June falls on June 6th, and subsequent Sundays occur every 7 days thereafter.
Step-by-step Derivation:
Step 1: Identify if 2004 is a leap year. Since 2004 is divisible by 4, it is a leap year, meaning February has 29 days.
Step 2: Calculate the total number of days from January 1st to June 1st, 2004.
- January: 31 days
- February: 29 days
- March: 31 days
- April: 30 days
- May: 31 days
- Total days until June 1st = 31 + 29 + 31 + 30 + 31 = 152 days.
Step 3: Determine the day of the week for June 1st. - We are given January 1st is a Thursday.
- The number of days elapsed from Jan 1 to June 1 is 152 days.
- Calculate the remainder: 152 mod 7 = 21 * 7 + 5. The remainder is 5.
- Counting 5 days forward from Thursday: Friday (1), Saturday (2), Sunday (3), Monday (4), Tuesday (5).
- Therefore, June 1st, 2004, was a Tuesday.
Step 4: Find the first Sunday of June. - June 1: Tuesday
- June 2: Wednesday
- June 3: Thursday
- June 4: Friday
- June 5: Saturday
- June 6: Sunday
Step 5: List all Sundays in June by adding multiples of 7 to the first Sunday. - 6 + 7 = 13
- 13 + 7 = 20
- 20 + 7 = 27
- The Sundays are 6, 13, 20, and 27.