On which dates of October, 1994 did Monday fall?Select an answerA4, 11, 18, 25B2, 9, 16, 23C1, 8, 15, 22D3, 10, 17, 24, 31
Question
On which dates of October, 1994 did Monday fall?
Select an answer
A. 4, 11, 18, 25
B. 2, 9, 16, 23
C. 1, 8, 15, 22
D. 3, 10, 17, 24, 31
Solution
To answer this question, we need to find out the day of the week on October 1, 1994.
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We can use a known formula to calculate the day of the week for any given date. The formula is:
Zeller's Congruence: h = (q + [(13(m+1))/5] + K + [K/4] + [J/4] + 5J) mod 7
where, h = day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday) q = day of the month m = month (3 = March, 4 = April, 5 = May, ..., 14 = February) K = year of the century (year % 100) J = zero-based century (actually ⌊ year/100 ⌋)
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For October 1, 1994, the variables in the formula would be: q = 1 (since it's the 1st day of the month) m = 10 (October, but since January and February are counted as months 13 and 14 of the previous year, we don't need to adjust for October) The year is 1994, so K = 94 and J = 19.
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Plugging these values into the formula, we get: h = (1 + [(1311)/5] + 94 + [94/4] + [19/4] + 519) mod 7 Calculating the values in the brackets first: h = (1 + 28 + 94 + 23 + 4 + 95) mod 7 h = 245 mod 7 h = 0
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The result, h = 0, corresponds to Saturday. Therefore, October 1, 1994, was a Saturday.
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Since we're looking for the Mondays of October 1994, we need to find the first Monday after October 1. Since October 1 was a Saturday, October 3 was a Monday.
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From there, we can simply add 7 to find all the subsequent Mondays in October 1994. So, the Mondays in October 1994 were the 3rd, 10th, 17th, 24th, and 31st.
So, the correct answer is D3, 10, 17, 24, 31.
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