In a company, all Mondays and all Sundays are weekly off days.\nIf a 31-day month begins on a Monday, how many off days (Mondays and Sundays together) will there be in that month?

Introduction / Context:
Work-schedule and calendar questions often require counting particular weekdays in a month. Here, employees have all Mondays and Sundays off. The month has 31 days and starts on a Monday. You must determine how many off days there are in total in that month.

Given Data / Assumptions:

The month has 31 days.
Day 1 is a Monday.
Every Monday is an off day.
Every Sunday is also an off day.
We assume a standard 7-day week repeating from Monday to Sunday.

Concept / Approach:
We first distribute the weekdays across the 31 days starting with Monday on Day 1. Then we count how many days are Mondays and how many are Sundays. The total number of off days is the sum of these counts. Since 31 days correspond to 4 full weeks (28 days) plus 3 extra days, we expect four occurrences of each weekday, with some weekdays appearing a fifth time in the extra days.

Step-by-Step Solution:
Step 1: List the weekdays for the first week. Day 1: Monday, Day 2: Tuesday, Day 3: Wednesday, Day 4: Thursday, Day 5: Friday, Day 6: Saturday, Day 7: Sunday. Step 2: Note the 4 complete weeks. Days 1–28 form 4 full weeks. In 4 full weeks, every weekday (Monday to Sunday) appears exactly 4 times. So, in Days 1–28, there are 4 Mondays and 4 Sundays. Step 3: Identify weekdays for the remaining days (29, 30, 31). Day 29: After Sunday on Day 28, the sequence wraps to Monday again, so Day 29 is Monday. Day 30: Tuesday. Day 31: Wednesday. Step 4: Count total Mondays and Sundays in the full month. Mondays: 4 (from first 28 days) + 1 (Day 29) = 5. Sundays: 4 (from first 28 days); no extra Sunday in Days 29–31. Total off days = Mondays + Sundays = 5 + 4 = 9.

Verification / Alternative check:
You can also create a compact table of dates and weekdays: Mondays on Days 1, 8, 15, 22, 29; Sundays on Days 7, 14, 21, 28. Counting these confirms the total of 5 Mondays and 4 Sundays. No other days are declared as off days, so the total number of off days must be 9.

Why Other Options Are Wrong:
7 or 8 off days would occur if there were fewer Mondays or Sundays, such as in a 30-day month or one that started on a different weekday. 5 off days would correspond to only one weekday being off, not both Monday and Sunday. None of these matches the actual distribution in a 31-day month starting on Monday.

Common Pitfalls:
Learners sometimes forget to include the additional three days after the four full weeks or mislabel their weekdays when wrapping around after Day 28. Another common error is to count only Sundays or only Mondays. Carefully tracking both off days and the extra days beyond the 28th avoids these mistakes.

Final Answer:
In that 31-day month, there are 9 off days (Mondays and Sundays combined).