ITPEC FE Morning April 2020 Question 7

Leap Year Counting — count leap years in a range using divisibility rules.

Rules for leap year:
- Divisible by 4 → leap year
- Except divisible by 100 → not a leap year
- Except divisible by 400 → leap year

Range: 1895–2021 → first leap year 1896, last 2020

Step 1: Count years divisible by 4:
- (2020 - 1896) / 4 + 1 = 32

Step 2: Subtract centurial years (divisible by 100):
- 1900, 2000 → subtract 2

Step 3: Add back years divisible by 400:
- 2000 → add 1

Result: 32 - 2 + 1 = 31

Why not others:
- (a) 30 — forgot to add back 2000 (divisible by 400)
- (c) 32 — forgot to exclude 1900 (centurial, not divisible by 400)
- (d) 33 — miscounted the range boundaries

Key rule: Leap year = divisible by 4, except centuries, except centuries divisible by 400.

AI-generated — may contain errors