Introduction
Problems that ask for the weekday a certain number of days before or after a known weekday are frequent in aptitude tests. They train you to use simple modular arithmetic (mod 7) and to think in remainders rather than counting day-by-day.
Pattern: Day of the Week (Future/Past Days)
Pattern
Compute the weekday after moving forward or backward by N days by reducing N modulo 7 and shifting the base weekday accordingly.
Step-by-Step Example
Question
If today is Monday, what day will it be after 10 days?
Solution
Step 1: Convert the shift into remainder
Find 10 mod 7 = 3. So moving forward 10 days is equivalent to moving forward 3 days.Step 2: Shift the base weekday forward
Start at Monday → +1 = Tuesday, +2 = Wednesday, +3 = Thursday.Final Answer:
ThursdayQuick Check:
10 = 7 + 3 → after one full week weekday repeats, remaining +3 → Monday → Thursday ✅
Quick Variations
1. Backward shifts: subtract the remainder (use negative shift or go forward by 7 - r).
2. Large N: reduce N modulo 7 first to simplify.
3. Mixed spans: when combining month/year shifts, convert each span to odd days then apply modulo 7.
Trick to Always Use
- Step 1 → Reduce the number of days modulo 7 (N mod 7).
- Step 2 → For forward moves add the remainder to base weekday; for backward moves subtract it (or add 7 - remainder).
Summary
Summary
- Always reduce large day-shifts by taking N mod 7 to get the effective shift.
- Forward shift: add the remainder to the base weekday; backward shift: subtract the remainder or add (7 - remainder).
- Full weeks (multiples of 7) produce no change in weekday - ignore them.
- When combining spans (months/years), convert each to odd days and then reduce modulo 7 before applying.
Example to remember:
Start: Monday. Move forward 10 days → 10 mod 7 = 3 → Monday + 3 = Thursday.
Hint: Divide given days by 7 and use remainder to find shift.
Common Mistakes: Counting all 9 days directly without using mod 7 simplification.