Reasoning Ability - Calendar Problems
Find the next year after 2004 that will have the same calendar as 2004 (a leap year).
Find the next year after 2004 that will have the same calendar as 2004 (a leap year).
medium Q15 of 15
Step-by-Step Solution
Step 1: Identify base year type
2004 is a leap year (divisible by 4 and not a century exception).Step 2: Use the 28-year leap-cycle heuristic
Leap-year calendars typically repeat after 28 years because the odd-day total over 28 years equals a multiple of 7.Step 3: Verify odd days (2004 → 2032)
Count the 28 years from 2004 up to 2031: leap years = 2004, 2008, 2012, 2016, 2020, 2024, 2028 → 7 leaps; ordinary = 21.
Odd days = (21 × 1) + (7 × 2) = 21 + 14 = 35 → 35 mod 7 = 0.Final Answer:
2032 → Option BQuick Check:
Odd days total 35 ≡ 0 (mod 7) and both years are leap years → calendars match ✅
Quick Trick: For leap-year repeats, check +28 years first; verify by counting 7 leap years in the 28-year block to get 35 odd days → 0 mod 7.
Common Mistakes:
MISTAKES- Choosing 24-year or 20-year gaps without verifying that the odd-day sum ≡ 0 (mod 7).
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