The calendar for the year 2019 will be the same as the calendar for which of the following year?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2030
Two years have the same calendar when both begin on the same weekday and both are ordinary years (or both leap years). The weekday moves on only by the odd days, the days left over after whole weeks: an ordinary year of 365 days is 52 weeks + 1 day, and a leap year 52 weeks + 2 days.
2019 to 2024 (odd days added year by year from 1 January 2019, with the running total):
2019: 1 (total 1)
2020, a leap year: 2 (total 3)
2021: 1 (total 4)
2022: 1 (total 5)
2023: 1 (total 6)
2024, a leap year: 2 (total 8, that is, 1 week + 1)
2025 to 2029 (counting on from 1):
2025: 1 (total 2)
2026: 1 (total 3)
2027: 1 (total 4)
2028, a leap year: 2 (total 6)
2029: 1 (total 7, a whole week)
So 1 January 2030 falls on the same weekday as 1 January 2019 (a Tuesday), and 2030, like 2019, is not a leap year. The two years have the same calendar.
The year 2024 in Option (1) is a leap year and begins on a Monday, so its calendar is different.