Reasoning Ability - Calendar Problems
How many odd days are there in the first 50 years (Year 1 to Year 50)?
How many odd days are there in the first 50 years (Year 1 to Year 50)?
medium Q6 of 15
Step-by-Step Solution
Step 1: Count leap years from Year 1 to Year 50
Leap years occur every 4 years: 4, 8, 12, …, 48. Total leap years = 12. Ordinary years = 50 − 12 = 38.Step 2: Convert years to odd days
Odd days = (12 × 2) + (38 × 1) = 24 + 38 = 62.Step 3: Reduce modulo 7
62 ÷ 7 → remainder = 6.Final Answer:
6 odd days → Option BQuick Check:
62 mod 7 = 6 → verified correctly ✅
Quick Trick: For N years starting from Year 1, leap years = ⌊N/4⌋; compute odd days as (leaps×2 + ordinaries×1) mod 7.
Common Mistakes:
MISTAKES- Using 13 leap years or assuming leap-year distribution without specifying start year.
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