ITPEC FE Morning April 2020 Question 7
Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the years 1600 and 2000 are. How many leap years are there between 1895 and 2021?
Explanation
31 — count the multiples of 4 in the range, then correct for the century years.
- •First multiple of 4 after 1895: 1896; last before 2021: 2020
- •Multiples of 4: (2020 − 1896) ÷ 4 + 1 = 32
- •Century years among them: 1900 and 2000
- •1900 is not divisible by 400, so it is not a leap year: 32 − 1 = 31
- •2000 is divisible by 400, so it stays a leap year
Answer (b)
Why not others:
- •(a) 30 — also drops 2000, treating every century year as a common year and ignoring the 400 rule
- •(c) 32 — counts every multiple of 4 and forgets that 1900 is not a leap year
- •(d) 33 — exceeds even the 32 multiples of 4 in the range, so it must count a year outside 1895 to 2021, such as 1892 or 2024
Key rule: Count the terms of an arithmetic sequence as (last − first) ÷ step + 1, then apply the exceptions to the few special cases one at a time.
Basic Theory · AI-written, may contain errors
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