Reasoning Ability - Calendar Problems
Which year after 2009 will have the same calendar as 2009?
Which year after 2009 will have the same calendar as 2009?
medium Q7 of 15
Step-by-Step Solution
Step 1: Identify base year type
2009 is an ordinary (non-leap) year. The repeating year must also be ordinary.Step 2: Check 6-year and 17-year gaps
For 6-year gap (2009 → 2015): leap years = 2012; ordinary = 5.
Odd days = (5×1) + (1×2) = 7 → 7 mod 7 = 0 → 2015 is a correct repeat (ordinary year).
For 17-year gap (2009 → 2026): leap years = 2012, 2016, 2020, 2024; ordinary = 13.
Odd days = (13×1) + (4×2) = 21 → 21 mod 7 = 0 → 2026 also matches.Step 3: Choose the earliest valid repeat among options
Since 2015 is not listed, the next valid repeat is 2026.Final Answer:
2026 → Option DQuick Check:
2009 (ordinary) and 2026 (ordinary) with total odd days = 21 ≡ 0 mod 7 → same calendar ✅
Quick Trick: Both years must have identical leap status and total odd days ≡ 0 (mod 7).
Common Mistakes:
MISTAKES- Assuming only 0 mod 7 suffices without checking that both years are of the same type (ordinary vs leap).
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