Concept:To find the day for January 1, 1731, calculate the total odd days up to December 31, 1730. The remainder when divided by 7 gives the day (0 = Sunday, 1 = Monday, etc.).
Explanation:Break the years into groups: 1600 years (0 odd days), 100 years (5 odd days), and 30 years (1701 to 1730).
In 30 years, there are 7 leap years (1704, 1708, 1712, 1716, 1720, 1724, 1728) and 23 ordinary years. Leap years give 2 odd days each (7 × 2 = 14), ordinary years give 1 odd day each (23 × 1 = 23). Total odd days for 30 years = 14 + 23 = 37.
37 ÷ 7 gives remainder 2.
Add all: 0 (1600 yrs) + 5 (100 yrs) + 2 (30 yrs) = 7 odd days. 7 ÷ 7 = 0 remainder → December 31, 1730 was a Sunday.
January 1, 1731 is the next day, so it was Monday.
Answer:Option A. Monday